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  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher-id">Oalib</journal-id>
      <journal-title-group>
        <journal-title>Open Access Library Journal</journal-title>
      </journal-title-group>
      <issn pub-type="epub">2333-9721</issn>
      <issn pub-type="ppub">2333-9705</issn>
      <publisher>
        <publisher-name>Scientific Research Publishing</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.4236/oalib.1113752</article-id>
      <article-id pub-id-type="publisher-id">Oalib-149361</article-id>
      <article-categories>
        <subj-group>
          <subject>Article</subject>
        </subj-group>
        <subj-group>
          <subject>Biomedical</subject>
          <subject>Life Sciences</subject>
          <subject>Business</subject>
          <subject>Economics</subject>
          <subject>Chemistry</subject>
          <subject>Materials Science</subject>
          <subject>Computer Science</subject>
          <subject>Communications</subject>
          <subject>Earth</subject>
          <subject>Environmental Sciences</subject>
          <subject>Engineering</subject>
          <subject>Medicine</subject>
          <subject>Healthcare</subject>
          <subject>Physics</subject>
          <subject>Mathematics</subject>
          <subject>Social Sciences</subject>
          <subject>Humanities</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title>AI-Driven Carbon Release Reduction: A Hoochens Inc Framework for Assessing AI’s Impact on Fossil Fuel Intake Optimization</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name name-style="western">
            <surname>Egbuonu</surname>
            <given-names>Chinedu</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
      </contrib-group>
      <aff id="aff1"><label>1</label> Software Engineering, Fairfield University, Fairfield, USA </aff>
      <author-notes>
        <fn fn-type="conflict" id="fn-conflict">
          <p>The author declares no conflicts of interest.</p>
        </fn>
      </author-notes>
      <pub-date pub-type="epub">
        <day>02</day>
        <month>02</month>
        <year>2026</year>
      </pub-date>
      <pub-date pub-type="collection">
        <month>02</month>
        <year>2026</year>
      </pub-date>
      <volume>13</volume>
      <issue>02</issue>
      <fpage>1</fpage>
      <lpage>22</lpage>
      <history>
        <date date-type="received">
          <day>09</day>
          <month>06</month>
          <year>2025</year>
        </date>
        <date date-type="accepted">
          <day>31</day>
          <month>01</month>
          <year>2026</year>
        </date>
        <date date-type="published">
          <day>03</day>
          <month>02</month>
          <year>2026</year>
        </date>
      </history>
      <permissions>
        <copyright-statement>© 2026 by the authors and Scientific Research Publishing Inc.</copyright-statement>
        <copyright-year>2026</copyright-year>
        <license license-type="open-access">
          <license-p> This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link> ). </license-p>
        </license>
      </permissions>
      <self-uri content-type="doi" xlink:href="https://doi.org/10.4236/oalib.1113752">https://doi.org/10.4236/oalib.1113752</self-uri>
      <abstract>
        <p>This paper presents a novel framework for optimizing Carbon Release (CR) through an AI-driven approach to Fossil Fuel Intake (FFI) management. We propose a new training methodology for AI models to enhance their effectiveness in reducing FFI by learning from historical energy consumption trends and emissions data. By attributing specific quantities to key optimization components such as combustion efficiency, renewable integration, and AI impact, we derive a detailed matrix that quantifies their contributions to carbon reduction. Furthermore, we introduce a method for retroactively calculating the impact of each optimization item on overall CR, offering a data-driven approach to assess the effectiveness of AI interventions. This analysis is crucial for informing energy policy decisions, providing a clear understanding of how AI-based optimization strategies can significantly reduce emissions. Our findings demonstrate the potential of leveraging AI in achieving sustainable energy management, emphasizing the importance of precise quantification in guiding future efforts toward carbon neutrality.</p>
      </abstract>
      <kwd-group kwd-group-type="author-generated" xml:lang="en">
        <kwd>AI Attribution</kwd>
        <kwd>Net-Zero</kwd>
        <kwd>Reduction</kwd>
        <kwd>Fossil Fuel</kwd>
        <kwd>Optimization</kwd>
        <kwd>Intake</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec1">
      <title>1. Introduction</title>
      <p>In the face of escalating climate challenges, reducing carbon emissions has become a global priority. With the energy sector being a major contributor to Carbon Release (CR), there is an increasing need for innovative approaches that optimize Fossil Fuel Intake (FFI) and improve energy efficiency. While many traditional methods focus on optimizing specific aspects of energy consumption, they often fall short in providing a holistic reduction in carbon emissions [<xref ref-type="bibr" rid="B1">1</xref>][<xref ref-type="bibr" rid="B2">2</xref>]. This paper proposes a novel AI-driven framework that seeks to achieve a more effective reduction in CR by training models specifically designed for FFI optimization. The framework integrates advanced machine learning models that analyze historical energy consumption trends to learn and adapt strategies for reducing carbon emissions in real-time.</p>
      <p>The novelty of this approach lies in its ability to attribute specific quantities to six key components of FFI optimization, providing a detailed matrix that quantifies their contribution to reducing carbon release. This is a significant advancement over existing methods, which often lack the precision required to understand how different factors interact to affect overall emissions [<xref ref-type="bibr" rid="B3">3</xref>][<xref ref-type="bibr" rid="B4">4</xref>]. By leveraging a structured methodology, the proposed framework provides a more granular understanding of how various factors contribute to carbon release reduction, offering a new perspective on achieving sustainable energy management.</p>
      <p>The six key components of FFI optimization include: A) Fossil Fuel Intake (FFI), which focuses on reducing the amount of fossil fuels consumed; B) Combustion Efficiency, aimed at maximizing energy output per unit of fuel; C) Renewable Energy Integration, which involves increasing the share of energy derived from renewable sources; D) Operational Efficiency, which enhances how energy is used in processes; E) Carbon Capture and Storage (CCS), targeting the capture and storage of emissions; and F) AI Optimization, which utilizes machine learning algorithms to predict and adjust operational parameters dynamically [<xref ref-type="bibr" rid="B5">5</xref>]. Each component plays a critical role in minimizing carbon release, and the integration of AI allows for a more adaptive and responsive approach.</p>
      <p>Quantifying the impact of these optimization items is essential for understanding their relative contributions to carbon reduction. In this paper, the quantities assigned to each component were derived from historical energy consumption and emissions data, offering insights into how past trends can inform future strategies. For instance, analyzing data from power plants, industrial facilities, and transportation networks enables the AI model to identify patterns and predict the most effective ways to reduce fossil fuel consumption [<xref ref-type="bibr" rid="B6">6</xref>][<xref ref-type="bibr" rid="B7">7</xref>]. This quantitative approach creates a matrix that can serve as a valuable tool for policymakers, allowing them to allocate resources more effectively toward the most impactful optimization strategies.</p>
      <p>The implications of this research are far-reaching for energy policy. By providing a framework that quantifies the effect of different optimization strategies on CR, policymakers can make more informed decisions regarding investment in AI technologies and emissions reduction initiatives [<xref ref-type="bibr" rid="B8">8</xref>]. Furthermore, the ability to predict future carbon reductions based on optimized FFI provides a data-driven basis for setting realistic emission targets and developing long-term energy strategies. This paper not only offers a pathway to improved energy management but also contributes to the broader goal of achieving carbon neutrality.</p>
      <p>A brief discussion of the AI model used in this framework highlights its capability to adapt and learn from variations in energy use, making it uniquely suited for FFI optimization. The model incorporates neural networks that process complex, non-linear relationships between energy consumption, emissions, and operational factors. Its training is based on a combination of historical records, real-time data, and environmental conditions, ensuring accurate predictions and adjustments in real-world applications [<xref ref-type="bibr" rid="B9">9</xref>]. Datasets used for training include historical fossil fuel usage records, emissions data, and metrics on energy production efficiency, all of which are crucial for the model’s ability to predict and adjust for optimal results [<xref ref-type="bibr" rid="B7">7</xref>].</p>
      <p>In summary, this paper offers a comprehensive framework for optimizing carbon release through AI, presenting a novel approach that integrates advanced machine learning with data-driven insights. By quantifying the contributions of each optimization component and demonstrating how these insights can inform energy policy, this research provides a valuable tool for tackling the challenge of carbon emissions in a systematic and impactful manner.</p>
      <p>To dynamically calculate the amount of carbon released given the fossil fuel intake optimizations.</p>
    </sec>
    <sec id="sec2">
      <title>2. Literature Review</title>
      <p>Despite numerous advancements in AI for carbon reduction, existing models for optimizing Fossil Fuel Intake (FFI) have notable limitations. Many traditional approaches rely on single-model structures that, while effective for narrow applications, lack the capacity to address the multi-dimensional complexities inherent in fossil fuel optimization. For instance, several studies have focused on neural networks or regression-based approaches for emissions reduction, yet these models often fail to capture the dynamic interactions between variables like fuel efficiency, consumption rates, and real-time operational conditions. As a result, their optimization capabilities are constrained when applied to complex, fluctuating environments such as energy consumption in transportation or industrial processes [<xref ref-type="bibr" rid="B10">10</xref>]-[<xref ref-type="bibr" rid="B12">12</xref>].</p>
      <p>An ensemble method offers a promising solution by combining various models, each contributing unique strengths that can address different aspects of FFI optimization. Ensemble models, which integrate approaches like random forests, support vector machines, and deep learning algorithms, provide a holistic framework that can adapt to the diverse patterns within FFI data. For instance, Wang <italic>et al</italic>. (2019) demonstrate that ensemble models can improve prediction accuracy in fluctuating energy systems by leveraging the strengths of multiple algorithms [<xref ref-type="bibr" rid="B12">12</xref>]. Unlike single-model frameworks, ensemble methods allow for a more comprehensive view of data, enabling a nuanced approach to both short-term and long-term optimization [<xref ref-type="bibr" rid="B13">13</xref>]. In addition, Li and Huang (2018) highlight that single AI models are often too narrowly focused, missing critical variability in fossil fuel usage patterns, an issue that ensemble methods help mitigate by learning from multiple predictive outputs simultaneously [<xref ref-type="bibr" rid="B11">11</xref>].</p>
      <p>Given these factors, our proposed approach utilizes an ensemble method to optimize FFI in a way that current single-model strategies cannot match. By integrating multiple predictive models, each addressing specific facets of fossil fuel intake and emissions, our methodology enables a more adaptive and accurate framework for reducing Carbon Release (CR). This approach not only enhances predictive performance but also provides a robust foundation for real-time decision-making in energy management.</p>
      <p>While AI models for carbon reduction and fossil fuel intake optimization are advancing, a critical shortfall lies in the datasets commonly used to train these models. Many existing models lack comprehensive, high-quality data that capture the full scope of factors affecting fossil fuel intake and emissions, limiting their predictive accuracy and optimization capabilities. Key datasets, such as historical fuel consumption records, emissions data across varying levels of fuel intake, and long-term environmental impact data, are often absent or underutilized in current approaches. As a result, these models cannot fully account for the dynamic relationship between fuel usage and carbon release, leading to oversimplified predictions and suboptimal outcomes [<xref ref-type="bibr" rid="B14">14</xref>]-[<xref ref-type="bibr" rid="B16">16</xref>].</p>
      <p>For example, Smith and colleagues (2019) note that many AI models in the energy sector focus on operational efficiency but lack access to granular fuel consumption data, which is crucial for accurately modeling carbon emissions [<xref ref-type="bibr" rid="B14">14</xref>]. Similarly, Jones <italic>et al</italic>. (2018) highlight the importance of emissions data that reflects real-world fuel intake variations, arguing that without this information, models tend to produce overly generalized results that do not align with observed emissions in specific operational contexts [<xref ref-type="bibr" rid="B15">15</xref>]. The lack of datasets that integrate environmental conditions, such as temperature and humidity, further weakens the models’ ability to make precise predictions under different scenarios [<xref ref-type="bibr" rid="B17">17</xref>].</p>
      <p>Our approach addresses these gaps by integrating a wider range of critical datasets, enabling a more robust and context-sensitive AI model for FFI optimization. By training on a dataset that includes historical consumption records, emissions associated with different fuel levels, and environmental variables, our model can better capture the multifaceted nature of fossil fuel intake. This approach not only enhances predictive accuracy but also supports long-term sustainability goals by providing policymakers with more reliable data to guide decisions in carbon reduction strategies [<xref ref-type="bibr" rid="B18">18</xref>].</p>
      <p>The potential impact of AI in carbon reduction is widely acknowledged, yet a critical aspect often overlooked is the specific attribution of AI’s role in overall Carbon Release (CR) strategies. Quantifying AI’s contribution to carbon reduction, or “AI attribution”, is crucial for understanding its actual effectiveness in optimizing emissions, but few studies have examined this aspect in depth. Most existing research discusses AI as a supporting tool for carbon management without delving into its quantifiable impact on emissions or energy efficiency [<xref ref-type="bibr" rid="B19">19</xref>]-[<xref ref-type="bibr" rid="B21">21</xref>]. By omitting this information, these studies limit the ability of policymakers to measure AI’s role in carbon reduction and hinder the development of more accurate, data-driven CR strategies.</p>
      <p>For instance, Johnson <italic>et al</italic>. (2021) highlight AI’s potential for predictive analytics in energy systems but fail to address the measurable reductions directly attributable to AI’s interventions [<xref ref-type="bibr" rid="B19">19</xref>]. Similarly, Wang <italic>et al</italic>. (2022) discuss AI’s role in process optimization for industrial energy use but provide no metrics for evaluating AI’s individual impact on emissions [<xref ref-type="bibr" rid="B20">20</xref>]. Xu and Li (2021) emphasize AI’s predictive capabilities in forecasting emissions trends, yet overlook the attribution of these predictions to tangible carbon reduction outcomes, leaving a gap in accountability and planning [<xref ref-type="bibr" rid="B21">21</xref>].</p>
      <p>By focusing on AI attribution, our framework aims to quantify AI’s contribution to each component of CR strategies, enabling a clearer understanding of its value in emissions reduction. This approach not only aids in planning and forecasting but also supports strategic policy formulation by highlighting where AI investments yield the highest returns in reducing carbon emissions. By providing measurable metrics, policymakers can better evaluate AI’s effectiveness and make more informed decisions that align with sustainability goals [<xref ref-type="bibr" rid="B22">22</xref>].</p>
      <p><bold>Table 1</bold> compares the proposed framework with existing research, highlighting key differences in AI attribution, optimization scope, modeling approach, and data utilization.</p>
      <p><bold>Comparison: Proposed Model vs. Existing Research</bold></p>
      <p><bold>Table 1</bold><bold>.</bold> Comparison of strengths between the proposed model and existing research.</p>
      <table-wrap id="tbl1">
        <label>Table 1</label>
        <table>
          <tbody>
            <tr>
              <td>
                <bold>Feature</bold>
              </td>
              <td>
                <bold>Proposed Model</bold>
              </td>
              <td>
                <bold>Existing Research</bold>
              </td>
            </tr>
            <tr>
              <td>AI Attribution</td>
              <td>Quantifies AI’s direct contribution to carbon reduction, enabling precise accountability.</td>
              <td>AI’s role is often generalized and lacks measurable attribution for emissions reduction.</td>
            </tr>
            <tr>
              <td>Optimization Framework</td>
              <td>Integrates six key components (e.g., combustion efficiency, renewable energy) into a holistic matrix.</td>
              <td>Focuses on narrow optimizations without addressing multicomponent interactions.</td>
            </tr>
            <tr>
              <td>AI Modeling Approach</td>
              <td>Utilizes an ensemble AI model with submodels tailored to specific carbon release sources.</td>
              <td>Relies on single-model strategies, which struggle with multifaceted optimization tasks.</td>
            </tr>
            <tr>
              <td>Data Utilization</td>
              <td>Combines historical records, environmental variables, and realtime data for robust optimization.</td>
              <td>Often relies on limited historical data, ignoring environmental and operational factors.</td>
            </tr>
          </tbody>
        </table>
      </table-wrap>
    </sec>
    <sec id="sec3">
      <title>3. Discussion</title>
      <sec id="sec3dot1">
        <title>3.1. FFI Hazards: A Call for Action</title>
        <p>Fossil fuel intake poses significant environmental and health hazards, contributing extensively to air pollution, greenhouse gas emissions, and global climate change. The combustion of fossil fuels releases carbon dioxide (CO<sub>2</sub>), methane (CH<sub>4</sub>), and nitrogen oxides (NO<italic><sub>x</sub></italic>) which trap heat in the atmosphere, causing global warming and increasing the frequency of extreme weather events [<xref ref-type="bibr" rid="B23">23</xref>][<xref ref-type="bibr" rid="B24">24</xref>]. Furthermore, Particulate Matter (PM) from fossil fuel combustion is linked to respiratory and cardiovascular diseases, leading to increased mortality rates and healthcare burdens [<xref ref-type="bibr" rid="B25">25</xref>]. In addition to health impacts, FFI affects ecosystems by acidifying soils and water bodies, which disrupts biodiversity and harms agricultural productivity.</p>
        <p>These hazards underscore the urgent need for sustainable energy solutions that reduce reliance on fossil fuels and mitigate environmental degradation, making FFI optimization critical for achieving carbon reduction goals.</p>
      </sec>
      <sec id="sec3dot2">
        <title>3.2. A New Approach to Advocacy</title>
        <p>In recent years, the need to reduce carbon emissions has intensified, highlighting the importance of optimizing Fossil Fuel Intake (FFI) to mitigate environmental impact. <xref ref-type="fig" rid="fig1">Figure 1</xref><xref ref-type="fig" rid="fig1">Figure 1</xref> and <xref ref-type="fig" rid="fig2">Figure 2</xref><xref ref-type="fig" rid="fig2">Figure 2</xref> illustrate the broader societal and environmental consequences of unoptimized fossil fuel intake, showcasing both the human risk costs and the environmental degradation associated with continued reliance on fossil fuels. Traditional methods of managing FFI have often relied on static, one-size-fits-all strategies, which lack the adaptability to respond to the complex and fluctuating dynamics of energy demand and emissions. As global stakeholders pursue carbon reduction goals, it becomes essential to adopt a more advanced, responsive approach. This paper advocates for a paradigm shift in FFI management, arguing that the vigorous pursuit of AI-driven optimization is critical to achieving significant carbon emissions reduction. Unlike conventional models, AI offers the ability to optimize FFI in real time, analyzing vast datasets and making instantaneous adjustments that can drive down emissions more effectively [<xref ref-type="bibr" rid="B26">26</xref>][<xref ref-type="bibr" rid="B27">27</xref>].</p>
        <fig id="fig1">
          <label>Figure 1</label>
          <graphic xlink:href="https://html.scirp.org/file/1113752-rId13.jpeg?20260203023726" />
        </fig>
        <p><xref ref-type="fig" rid="fig1">Figure 1</xref><bold>.</bold> Life at risk cost.</p>
        <fig id="fig2">
          <label>Figure 2</label>
          <graphic xlink:href="https://html.scirp.org/file/1113752-rId14.jpeg?20260203023726" />
        </fig>
        <p><bold>Figure 2</bold><bold>.</bold> Environmental pollution.</p>
        <p>AI’s capability to process and learn from diverse datasets—such as historical fuel consumption, real-time energy output, emissions data, and operational metrics—positions it uniquely for transformative impact in carbon management [<xref ref-type="bibr" rid="B28">28</xref>]. By implementing AI models that dynamically adapt to changes in fuel usage patterns, organizations can significantly reduce waste and increase efficiency. For example, predictive maintenance powered by AI can detect inefficiencies in equipment before they escalate, enabling more proactive management of resources and minimizing unnecessary fuel intake [<xref ref-type="bibr" rid="B29">29</xref>]. This type of optimization can reduce not only operational costs but also the associated carbon release, creating a win-win scenario for industries and the environment. Therefore, the use of AI for carbon optimization is not merely a progressive strategy but a necessary evolution in managing FFI for sustainable impact. <xref ref-type="fig" rid="fig3">Figure 3</xref><xref ref-type="fig" rid="fig3">Figure 3</xref> presents a conceptual representation of sustainable, AI-driven solutions for carbon reduction, emphasizing the transition from fossil fuel-dependent systems toward greener, optimized energy management approaches.</p>
        <fig id="fig3">
          <label>Figure 3</label>
          <graphic xlink:href="https://html.scirp.org/file/1113752-rId15.jpeg?20260203023726" />
        </fig>
        <p><xref ref-type="fig" rid="fig3">Figure 3</xref><bold>.</bold> Green solution.</p>
        <p>Furthermore, a key aspect of effective AI-driven carbon optimization is the dynamic calculation of AI attribution—the quantification of AI’s direct contribution to carbon reduction. Historically, the impact of AI in emission reduction strategies has been generalized or aggregated, with little attention given to AI’s specific role in achieving measurable results. However, calculating AI attribution offers several critical benefits that make it indispensable for achieving net-zero goals. First, AI attribution provides accountability and transparency. As industries adopt AI for carbon management, stakeholders—including policymakers, investors, and consumers—need to understand the effectiveness of these interventions. Quantifying AI’s direct contribution to carbon reduction enables clear assessments of how valuable AI technology is in reducing emissions and whether it justifies the resources invested in its deployment [<xref ref-type="bibr" rid="B30">30</xref>]. By transparently demonstrating AI’s impact, organizations can build trust with their stakeholders, showcasing their commitment to sustainable practices and providing measurable evidence of progress [<xref ref-type="bibr" rid="B31">31</xref>].</p>
        <p>Second, AI attribution enables data-driven decision-making, an essential factor in achieving efficient and targeted carbon reduction. As AI continues to evolve, the availability of precise, quantitative metrics regarding its impact allows organizations to fine-tune their strategies based on real-world results. For instance, by understanding which aspects of AI-driven optimization yield the highest reductions in FFI, companies can allocate resources more effectively, prioritizing the most impactful interventions. This approach not only enhances operational efficiency but also accelerates progress toward achieving net-zero goals. Moreover, AI attribution helps organizations identify areas for further improvement, guiding future investments in technology and innovation. In essence, AI attribution provides a roadmap for continuous improvement, ensuring that carbon reduction strategies remain aligned with evolving technological capabilities and environmental needs.</p>
        <p>Implementing an AI attribution framework also opens opportunities for benchmarking and standardization across industries. By quantifying the impact of AI on FFI reduction, organizations can establish benchmarks for carbon management practices, promoting standardization and consistency in how AI contributions are measured and reported. This standardization can facilitate cross-industry comparisons, enabling stakeholders to identify best practices and encourage widespread adoption of successful AI-driven strategies. Additionally, as industries converge around common benchmarks for AI attribution, regulatory bodies can develop more precise guidelines for carbon management, fostering an environment where AI technologies are leveraged optimally to reduce emissions on a global scale [<xref ref-type="bibr" rid="B26">26</xref>].</p>
        <p>The benefits of AI-driven FFI optimization and attribution extend beyond immediate operational gains. By establishing AI as a core component of carbon management, organizations can foster a culture of innovation and responsibility, aligning their goals with broader environmental and societal objectives. As AI capabilities advance, organizations can harness their predictive power to anticipate future carbon reduction needs and implement preventive measures accordingly. This proactive approach creates resilience, enabling industries to adapt to regulatory changes and shifting market demands more effectively.</p>
        <p>Moreover, AI-driven carbon management aligns with the growing demand for Environmental, Social, and Governance (ESG) transparency, increasingly emphasized by investors, customers, and regulators. By adopting a model that dynamically calculates AI attribution in carbon reduction, companies can demonstrate their commitment to ESG goals and attract stakeholders who prioritize sustainability [<xref ref-type="bibr" rid="B28">28</xref>]. Investors are particularly attentive to organizations with robust ESG frameworks, recognizing that companies actively managing their environmental impact are better positioned for long-term resilience and market competitiveness. Therefore, AI attribution not only advances carbon reduction but also serves as a strategic asset, enhancing organizational value and ensuring alignment with the expectations of sustainability-focused stakeholders.</p>
        <p>The shift toward AI-driven FFI optimization represents a critical step in modernizing carbon reduction strategies. The dynamic calculation of AI attribution enables organizations to quantify their progress, make informed decisions, and foster transparency—all essential components for achieving net-zero goals. By embracing this approach, industries can drive meaningful, measurable progress in carbon reduction, contributing to global sustainability and setting a new standard for responsible energy management. The advocacy for this paradigm shift underscores the urgent need to rethink traditional carbon management practices and adopt innovative solutions that align with the complexities of today’s environmental challenges.</p>
      </sec>
      <sec id="sec3dot3">
        <title>3.3. The Hoochens Matrix</title>
        <p>The Carbon Release (CR) formula offers a comprehensive model for evaluating the effectiveness of Fossil Fuel Intake (FFI) optimization efforts in reducing carbon emissions. This model integrates multiple factors: AI Attribution (<inline-formula><mml:math><mml:mi> A </mml:mi></mml:math></inline-formula> ), Fossil Fuel Intake (FFI), Fuel Type (<inline-formula><mml:math><mml:mi> β </mml:mi></mml:math></inline-formula> ), Combustion Efficiency (<inline-formula><mml:math><mml:mi> γ </mml:mi></mml:math></inline-formula> ), and Emissions Reduction (<inline-formula><mml:math><mml:mi> δ </mml:mi></mml:math></inline-formula> ).</p>
        <p><xref ref-type="fig" rid="fig4">Figure 4</xref><xref ref-type="fig" rid="fig4">Figure 4</xref> illustrates the proposed optimization matrix, showing how weighted contributions from key factors, including AI attribution, fossil fuel intake, combustion efficiency, and emissions reduction, interact to determine overall carbon release.</p>
        <fig id="fig4">
          <label>Figure 4</label>
          <graphic xlink:href="https://html.scirp.org/file/1113752-rId24.jpeg?20260203023726" />
        </fig>
        <p><xref ref-type="fig" rid="fig4">Figure 4</xref><bold>.</bold> Matrix.</p>
        <p>Each factor carries a specific weight based on its contribution to CR, where a fully optimized FFI system is defined as one that achieves a minimum 50% reduction in CR. The formula dynamically calculates CR over time, adjusting for non-linear scaling of AI impact and incorporating stochastic elements (<inline-formula><mml:math><mml:mi> ϵ </mml:mi></mml:math></inline-formula> ) to account for uncertainties in measurement. By leveraging this model, organizations can accurately assess and verify the degree to which FFI optimization has reduced carbon emissions, with particular emphasis on AI-driven impacts.</p>
        <p><xref ref-type="fig" rid="fig5">Figure 5</xref><xref ref-type="fig" rid="fig5">Figure 5</xref> defines the variables and parameters used in the proposed optimization matrix, providing clarity on the mathematical formulation underlying the carbon release model.</p>
        <fig id="fig5">
          <label>Figure 5</label>
          <graphic xlink:href="https://html.scirp.org/file/1113752-rId27.jpeg?20260203023726" />
        </fig>
        <p><xref ref-type="fig" rid="fig5">Figure 5</xref><bold>.</bold> Matrix definition.</p>
        <p>To calculate the impact of FFI optimization on Carbon Release (CR) reduction, we model CR as a function of multiple factors, including AI attribution, fuel intake, and efficiency parameters:</p>
        <disp-formula id="FD1">
          <mml:math>
            <mml:mrow>
              <mml:mi>C</mml:mi>
              <mml:mi>R</mml:mi>
              <mml:mo>=</mml:mo>
              <mml:mi>α</mml:mi>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:mi>A</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>F</mml:mi>
                  <mml:mi>F</mml:mi>
                  <mml:mi>I</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>β</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>γ</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>δ</mml:mi>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>×</mml:mo>
              <mml:mstyle displaystyle="true">
                <mml:mrow>
                  <mml:mo>∫</mml:mo>
                  <mml:mrow>
                    <mml:mrow>
                      <mml:mo>[</mml:mo>
                      <mml:mrow>
                        <mml:mi>A</mml:mi>
                        <mml:mo>×</mml:mo>
                        <mml:mi>F</mml:mi>
                        <mml:mi>F</mml:mi>
                        <mml:mi>I</mml:mi>
                        <mml:mo>×</mml:mo>
                        <mml:mi>β</mml:mi>
                        <mml:mo>×</mml:mo>
                        <mml:mi>γ</mml:mi>
                        <mml:mo>×</mml:mo>
                        <mml:mi>δ</mml:mi>
                      </mml:mrow>
                      <mml:mo>]</mml:mo>
                    </mml:mrow>
                    <mml:mtext>d</mml:mtext>
                    <mml:mi>τ</mml:mi>
                  </mml:mrow>
                </mml:mrow>
              </mml:mstyle>
              <mml:mo>+</mml:mo>
              <mml:mi>ϵ</mml:mi>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>where:</p>
        <disp-formula id="FD2">
          <mml:math>
            <mml:mrow>
              <mml:mi>α</mml:mi>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:mi>A</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>F</mml:mi>
                  <mml:mi>F</mml:mi>
                  <mml:mi>I</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>β</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>γ</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>δ</mml:mi>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>=</mml:mo>
              <mml:mn>0.5</mml:mn>
              <mml:mo>×</mml:mo>
              <mml:mrow>
                <mml:mo>[</mml:mo>
                <mml:mrow>
                  <mml:mn>1</mml:mn>
                  <mml:mo>−</mml:mo>
                  <mml:mi>exp</mml:mi>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:mo>−</mml:mo>
                      <mml:mfrac>
                        <mml:mrow>
                          <mml:mi>A</mml:mi>
                          <mml:mo>×</mml:mo>
                          <mml:mi>F</mml:mi>
                          <mml:mi>F</mml:mi>
                          <mml:mi>I</mml:mi>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mi>β</mml:mi>
                          <mml:mo>×</mml:mo>
                          <mml:mi>γ</mml:mi>
                          <mml:mo>×</mml:mo>
                          <mml:mi>δ</mml:mi>
                        </mml:mrow>
                      </mml:mfrac>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
                <mml:mo>]</mml:mo>
              </mml:mrow>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p><bold>Variables:</bold></p>
        <p><inline-formula><mml:math display="inline"><mml:mrow><mml:mi> C </mml:mi><mml:mi> R </mml:mi></mml:mrow></mml:math></inline-formula> = Carbon Release (tons CO<sub>2</sub>-equivalent)<inline-formula><mml:math><mml:mi> A </mml:mi></mml:math></inline-formula> = AI Attribution (dimensionless, <inline-formula><mml:math><mml:mrow><mml:mn> 0 </mml:mn><mml:mo> ≤ </mml:mo><mml:mi> A </mml:mi><mml:mo> ≤ </mml:mo><mml:mn> 1 </mml:mn></mml:mrow></mml:math></inline-formula> )<inline-formula><mml:math><mml:mrow><mml:mi> F </mml:mi><mml:mi> F </mml:mi><mml:mi> I </mml:mi></mml:mrow></mml:math></inline-formula> = Fossil Fuel Intake (megajoules, MJ)<inline-formula><mml:math><mml:mi> β </mml:mi></mml:math></inline-formula> = Fuel Type Factor (dimensionless, <inline-formula><mml:math><mml:mrow><mml:mn> 0 </mml:mn><mml:mo> ≤ </mml:mo><mml:mi> β </mml:mi><mml:mo> ≤ </mml:mo><mml:mn> 1 </mml:mn></mml:mrow></mml:math></inline-formula> )<inline-formula><mml:math><mml:mi> γ </mml:mi></mml:math></inline-formula> = Combustion Efficiency Factor (dimensionless, <inline-formula><mml:math><mml:mrow><mml:mn> 0 </mml:mn><mml:mo> ≤ </mml:mo><mml:mi> γ </mml:mi><mml:mo> ≤ </mml:mo><mml:mn> 1 </mml:mn></mml:mrow></mml:math></inline-formula> )<inline-formula><mml:math><mml:mi> δ </mml:mi></mml:math></inline-formula> = Emissions Reduction Factor (dimensionless, <inline-formula><mml:math><mml:mrow><mml:mn> 0 </mml:mn><mml:mo> ≤ </mml:mo><mml:mi> δ </mml:mi><mml:mo> ≤ </mml:mo><mml:mn> 1 </mml:mn></mml:mrow></mml:math></inline-formula> )<inline-formula><mml:math><mml:mi> τ </mml:mi></mml:math></inline-formula> = Time (seconds)<inline-formula><mml:math><mml:mi> ϵ </mml:mi></mml:math></inline-formula> = Stochastic Error Term (tons CO<sub>2</sub>-equivalent)</p>
        <p><bold>Extension to Stochastic Processes:</bold></p>
        <disp-formula id="FD3">
          <mml:math display="inline">
            <mml:mrow>
              <mml:mi>C</mml:mi>
              <mml:mi>R</mml:mi>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mi>t</mml:mi>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>=</mml:mo>
              <mml:mi>α</mml:mi>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:mi>A</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>F</mml:mi>
                  <mml:mi>F</mml:mi>
                  <mml:mi>I</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>β</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>γ</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>δ</mml:mi>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>×</mml:mo>
              <mml:mstyle displaystyle="true">
                <mml:mrow>
                  <mml:mo>∫</mml:mo>
                  <mml:mrow>
                    <mml:mrow>
                      <mml:mo>[</mml:mo>
                      <mml:mrow>
                        <mml:mi>A</mml:mi>
                        <mml:mo>×</mml:mo>
                        <mml:mi>F</mml:mi>
                        <mml:mi>F</mml:mi>
                        <mml:mi>I</mml:mi>
                        <mml:mo>×</mml:mo>
                        <mml:mi>β</mml:mi>
                        <mml:mo>×</mml:mo>
                        <mml:mi>γ</mml:mi>
                        <mml:mo>×</mml:mo>
                        <mml:mi>δ</mml:mi>
                      </mml:mrow>
                      <mml:mo>]</mml:mo>
                    </mml:mrow>
                    <mml:mtext>d</mml:mtext>
                    <mml:mi>τ</mml:mi>
                  </mml:mrow>
                </mml:mrow>
              </mml:mstyle>
              <mml:mo>+</mml:mo>
              <mml:mi>ϵ</mml:mi>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mi>t</mml:mi>
                <mml:mo>)</mml:mo>
              </mml:mrow>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>where:</p>
        <disp-formula id="FD4">
          <mml:math>
            <mml:mrow>
              <mml:mi>ϵ</mml:mi>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mi>t</mml:mi>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>~</mml:mo>
              <mml:mi mathvariant="script">N</mml:mi>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:mn>0</mml:mn>
                  <mml:mo>,</mml:mo>
                  <mml:msup>
                    <mml:mi>σ</mml:mi>
                    <mml:mn>2</mml:mn>
                  </mml:msup>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>represents stochastic fluctuations with mean 0 and variance <inline-formula><mml:math><mml:mrow><mml:msup><mml:mi> σ </mml:mi><mml:mn> 2 </mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> .</p>
        <p><bold>Extended Formula with Time Decay of Efficiency, Nonlinear AI Attribution, and Noise Correction:</bold></p>
        <disp-formula id="FD5">
          <label>(1)</label>
          <mml:math>
            <mml:mtable>
              <mml:mtr>
                <mml:mtd>
                  <mml:mi>C</mml:mi>
                  <mml:mi>R</mml:mi>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mi>t</mml:mi>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                  <mml:mo>=</mml:mo>
                  <mml:mi>α</mml:mi>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:mi>A</mml:mi>
                      <mml:mo>,</mml:mo>
                      <mml:mi>F</mml:mi>
                      <mml:mi>F</mml:mi>
                      <mml:mi>I</mml:mi>
                      <mml:mo>,</mml:mo>
                      <mml:mi>β</mml:mi>
                      <mml:mo>,</mml:mo>
                      <mml:mi>γ</mml:mi>
                      <mml:mo>,</mml:mo>
                      <mml:mi>δ</mml:mi>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                  <mml:mo>×</mml:mo>
                  <mml:mstyle displaystyle="true">
                    <mml:mrow>
                      <mml:msubsup>
                        <mml:mo>∫</mml:mo>
                        <mml:mn>0</mml:mn>
                        <mml:mi>t</mml:mi>
                      </mml:msubsup>
                      <mml:mrow>
                        <mml:mrow>
                          <mml:mo>[</mml:mo>
                          <mml:mrow>
                            <mml:msup>
                              <mml:mi>A</mml:mi>
                              <mml:mi>η</mml:mi>
                            </mml:msup>
                            <mml:mo>×</mml:mo>
                            <mml:mi>F</mml:mi>
                            <mml:mi>F</mml:mi>
                            <mml:mi>I</mml:mi>
                            <mml:mo>×</mml:mo>
                            <mml:mi>β</mml:mi>
                            <mml:mo>×</mml:mo>
                            <mml:mi>γ</mml:mi>
                            <mml:msup>
                              <mml:mtext>e</mml:mtext>
                              <mml:mrow>
                                <mml:mo>−</mml:mo>
                                <mml:mi>λ</mml:mi>
                                <mml:mi>τ</mml:mi>
                              </mml:mrow>
                            </mml:msup>
                            <mml:mo>×</mml:mo>
                            <mml:mi>δ</mml:mi>
                          </mml:mrow>
                          <mml:mo>]</mml:mo>
                        </mml:mrow>
                        <mml:mtext>d</mml:mtext>
                        <mml:mi>τ</mml:mi>
                      </mml:mrow>
                    </mml:mrow>
                  </mml:mstyle>
                </mml:mtd>
              </mml:mtr>
              <mml:mtr>
                <mml:mtd>
                  <mml:mtext>
                     
                  </mml:mtext>
                  <mml:mtext>
                     
                  </mml:mtext>
                  <mml:mtext>
                     
                  </mml:mtext>
                  <mml:mo>+</mml:mo>
                  <mml:mi>ϵ</mml:mi>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mi>t</mml:mi>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                  <mml:mo>+</mml:mo>
                  <mml:mi>ϕ</mml:mi>
                  <mml:mi>ϵ</mml:mi>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:mi>t</mml:mi>
                      <mml:mo>−</mml:mo>
                      <mml:mtext>Δ</mml:mtext>
                      <mml:mi>t</mml:mi>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mtd>
              </mml:mtr>
            </mml:mtable>
          </mml:math>
        </disp-formula>
        <p>where:</p>
        <disp-formula id="FD6">
          <mml:math>
            <mml:mrow>
              <mml:mi>α</mml:mi>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:mi>A</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>F</mml:mi>
                  <mml:mi>F</mml:mi>
                  <mml:mi>I</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>β</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>γ</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>δ</mml:mi>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>=</mml:mo>
              <mml:mn>0.5</mml:mn>
              <mml:mo>×</mml:mo>
              <mml:mrow>
                <mml:mo>[</mml:mo>
                <mml:mrow>
                  <mml:mn>1</mml:mn>
                  <mml:mo>−</mml:mo>
                  <mml:mi>exp</mml:mi>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:mo>−</mml:mo>
                      <mml:mfrac>
                        <mml:mrow>
                          <mml:mi>A</mml:mi>
                          <mml:mo>×</mml:mo>
                          <mml:mi>F</mml:mi>
                          <mml:mi>F</mml:mi>
                          <mml:mi>I</mml:mi>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mi>β</mml:mi>
                          <mml:mo>×</mml:mo>
                          <mml:mi>γ</mml:mi>
                          <mml:mo>×</mml:mo>
                          <mml:mi>δ</mml:mi>
                        </mml:mrow>
                      </mml:mfrac>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
                <mml:mo>]</mml:mo>
              </mml:mrow>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p><bold>Explanation of Extensions:</bold></p>
        <p><bold>Extension 1: Time Decay of Efficiency</bold></p>
        <p>Introduce a decay factor that accounts for decreasing efficiency over time, modeled by an exponential decay term <inline-formula><mml:math><mml:mrow><mml:msup><mml:mtext> e </mml:mtext><mml:mrow><mml:mo> − </mml:mo><mml:mi> λ </mml:mi><mml:mi> t </mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> , where <inline-formula><mml:math><mml:mi> λ </mml:mi></mml:math></inline-formula> is the decay rate.</p>
        <p><bold>Extension 2: Nonlinear AI Attribution</bold></p>
        <p>Rather than assuming AI attribution scales linearly with fossil fuel intake, introduce a power-law relationship, <inline-formula><mml:math><mml:mrow><mml:msup><mml:mi> A </mml:mi><mml:mi> η </mml:mi></mml:msup></mml:mrow></mml:math></inline-formula> , where <inline-formula><mml:math><mml:mi> η </mml:mi></mml:math></inline-formula> is a parameter that controls the degree of nonlinearity.</p>
        <p><bold>Extension 3: Noise Correction</bold></p>
        <p>Add a correction term for the stochastic noise based on past values, incorporating an auto-regressive term <inline-formula><mml:math><mml:mrow><mml:mi> ϕ </mml:mi><mml:mi> ϵ </mml:mi><mml:mrow><mml:mo> ( </mml:mo><mml:mrow><mml:mi> t </mml:mi><mml:mo> − </mml:mo><mml:mtext> Δ </mml:mtext><mml:mi> t </mml:mi></mml:mrow><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> to model autocorrelation in the error term.</p>
        <p><bold>New Variables:</bold></p>
        <p><inline-formula><mml:math><mml:mi> η </mml:mi></mml:math></inline-formula> = Nonlinearity parameter for AI attribution (dimensionless)<inline-formula><mml:math><mml:mi> λ </mml:mi></mml:math></inline-formula> = Efficiency decay rate (per second)<inline-formula><mml:math><mml:mrow><mml:mtext> Δ </mml:mtext><mml:mi> t </mml:mi></mml:mrow></mml:math></inline-formula> = Time lag for noise correction (seconds)<inline-formula><mml:math><mml:mi> ϕ </mml:mi></mml:math></inline-formula> = Auto-regressive noise correction factor (dimensionless)</p>
        <p><bold>Other Variables:</bold></p>
        <p><inline-formula><mml:math><mml:mrow><mml:mi> C </mml:mi><mml:mi> R </mml:mi><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> = Carbon Release as a function of time (tons CO<sub>2</sub>-equivalent)<inline-formula><mml:math><mml:mi> A </mml:mi></mml:math></inline-formula> = AI Attribution (dimensionless, <inline-formula><mml:math><mml:mrow><mml:mn> 0 </mml:mn><mml:mo> ≤ </mml:mo><mml:mi> A </mml:mi><mml:mo> ≤ </mml:mo><mml:mn> 1 </mml:mn></mml:mrow></mml:math></inline-formula> )<inline-formula><mml:math><mml:mrow><mml:mi> F </mml:mi><mml:mi> F </mml:mi><mml:mi> I </mml:mi></mml:mrow></mml:math></inline-formula> = Fossil Fuel Intake (megajoules, MJ)<inline-formula><mml:math><mml:mi> β </mml:mi></mml:math></inline-formula> = Fuel Type Factor (dimensionless, <inline-formula><mml:math><mml:mrow><mml:mn> 0 </mml:mn><mml:mo> ≤ </mml:mo><mml:mi> β </mml:mi><mml:mo> ≤ </mml:mo><mml:mn> 1 </mml:mn></mml:mrow></mml:math></inline-formula> )<inline-formula><mml:math><mml:mi> γ </mml:mi></mml:math></inline-formula> = Combustion Efficiency Factor (dimensionless, <inline-formula><mml:math><mml:mrow><mml:mn> 0 </mml:mn><mml:mo> ≤ </mml:mo><mml:mi> γ </mml:mi><mml:mo> ≤ </mml:mo><mml:mn> 1 </mml:mn></mml:mrow></mml:math></inline-formula> )<inline-formula><mml:math><mml:mi> δ </mml:mi></mml:math></inline-formula> = Emissions Reduction Factor (dimensionless, <inline-formula><mml:math><mml:mrow><mml:mn> 0 </mml:mn><mml:mo> ≤ </mml:mo><mml:mi> δ </mml:mi><mml:mo> ≤ </mml:mo><mml:mn> 1 </mml:mn></mml:mrow></mml:math></inline-formula> )<inline-formula><mml:math><mml:mi> τ </mml:mi></mml:math></inline-formula> = Time (seconds)<inline-formula><mml:math><mml:mrow><mml:mi> ϵ </mml:mi><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> = Stochastic Error Term as a function of time, modeled as <inline-formula><mml:math><mml:mrow><mml:mi mathvariant="script"> N </mml:mi><mml:mrow><mml:mo> ( </mml:mo><mml:mrow><mml:mn> 0 </mml:mn><mml:mo> , </mml:mo><mml:msup><mml:mi> σ </mml:mi><mml:mn> 2 </mml:mn></mml:msup></mml:mrow><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula></p>
        <disp-formula id="FD7">
          <label>(2)</label>
          <mml:math>
            <mml:mtable>
              <mml:mtr>
                <mml:mtd>
                  <mml:mi>C</mml:mi>
                  <mml:mi>R</mml:mi>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mi>t</mml:mi>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                  <mml:mo>=</mml:mo>
                  <mml:mi>α</mml:mi>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:mi>A</mml:mi>
                      <mml:mo>,</mml:mo>
                      <mml:mi>F</mml:mi>
                      <mml:mi>F</mml:mi>
                      <mml:mi>I</mml:mi>
                      <mml:mo>,</mml:mo>
                      <mml:mi>β</mml:mi>
                      <mml:mo>,</mml:mo>
                      <mml:mi>γ</mml:mi>
                      <mml:mo>,</mml:mo>
                      <mml:mi>δ</mml:mi>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                  <mml:mo>×</mml:mo>
                  <mml:mstyle displaystyle="true">
                    <mml:mrow>
                      <mml:msubsup>
                        <mml:mo>∫</mml:mo>
                        <mml:mn>0</mml:mn>
                        <mml:mi>t</mml:mi>
                      </mml:msubsup>
                      <mml:mrow>
                        <mml:mrow>
                          <mml:mo>(</mml:mo>
                          <mml:mrow>
                            <mml:msup>
                              <mml:mi>A</mml:mi>
                              <mml:mi>η</mml:mi>
                            </mml:msup>
                            <mml:mi>F</mml:mi>
                            <mml:mi>F</mml:mi>
                            <mml:mi>I</mml:mi>
                            <mml:mi>β</mml:mi>
                            <mml:mi>γ</mml:mi>
                            <mml:msup>
                              <mml:mtext>e</mml:mtext>
                              <mml:mrow>
                                <mml:mo>−</mml:mo>
                                <mml:mi>λ</mml:mi>
                                <mml:mi>τ</mml:mi>
                              </mml:mrow>
                            </mml:msup>
                            <mml:mi>δ</mml:mi>
                          </mml:mrow>
                          <mml:mo>)</mml:mo>
                        </mml:mrow>
                        <mml:mtext>d</mml:mtext>
                        <mml:mi>τ</mml:mi>
                      </mml:mrow>
                    </mml:mrow>
                  </mml:mstyle>
                </mml:mtd>
              </mml:mtr>
              <mml:mtr>
                <mml:mtd>
                  <mml:mtext>
                     
                  </mml:mtext>
                  <mml:mtext>
                     
                  </mml:mtext>
                  <mml:mtext>
                     
                  </mml:mtext>
                  <mml:mo>+</mml:mo>
                  <mml:mi>ϵ</mml:mi>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mi>t</mml:mi>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                  <mml:mo>+</mml:mo>
                  <mml:mi>ϕ</mml:mi>
                  <mml:mi>ϵ</mml:mi>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:mi>t</mml:mi>
                      <mml:mo>−</mml:mo>
                      <mml:mtext>Δ</mml:mtext>
                      <mml:mi>t</mml:mi>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mtd>
              </mml:mtr>
            </mml:mtable>
          </mml:math>
        </disp-formula>
        <p>where:</p>
        <disp-formula id="FD8">
          <mml:math>
            <mml:mrow>
              <mml:mi>α</mml:mi>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:mi>A</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>F</mml:mi>
                  <mml:mi>F</mml:mi>
                  <mml:mi>I</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>β</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>γ</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>δ</mml:mi>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>=</mml:mo>
              <mml:mn>0.5</mml:mn>
              <mml:mo>×</mml:mo>
              <mml:mrow>
                <mml:mo>[</mml:mo>
                <mml:mrow>
                  <mml:mn>1</mml:mn>
                  <mml:mo>−</mml:mo>
                  <mml:mtext>exp</mml:mtext>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:mo>−</mml:mo>
                      <mml:mfrac>
                        <mml:mrow>
                          <mml:mi>A</mml:mi>
                          <mml:mo>×</mml:mo>
                          <mml:mi>F</mml:mi>
                          <mml:mi>F</mml:mi>
                          <mml:mi>I</mml:mi>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mi>β</mml:mi>
                          <mml:mo>×</mml:mo>
                          <mml:mi>γ</mml:mi>
                          <mml:mo>×</mml:mo>
                          <mml:mi>δ</mml:mi>
                        </mml:mrow>
                      </mml:mfrac>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
                <mml:mo>]</mml:mo>
              </mml:mrow>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p><bold>New Variables:</bold></p>
        <p><inline-formula><mml:math><mml:mi> η </mml:mi></mml:math></inline-formula> = Nonlinearity parameter for AI attribution (dimensionless)<inline-formula><mml:math><mml:mi> λ </mml:mi></mml:math></inline-formula> = Efficiency decay rate (per second)<inline-formula><mml:math><mml:mrow><mml:mtext> Δ </mml:mtext><mml:mi> t </mml:mi></mml:mrow></mml:math></inline-formula> = Time lag for noise correction (seconds)<inline-formula><mml:math><mml:mi> ϕ </mml:mi></mml:math></inline-formula> = Auto-regressive noise correction factor (dimensionless)</p>
        <p><bold>Other Variables:</bold></p>
        <p><inline-formula><mml:math><mml:mrow><mml:mi> C </mml:mi><mml:mi> R </mml:mi><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> = Carbon Release as a function of time (tons CO<sub>2</sub>-equivalent)<inline-formula><mml:math><mml:mi> A </mml:mi></mml:math></inline-formula> = AI Attribution (dimensionless, <inline-formula><mml:math><mml:mrow><mml:mn> 0 </mml:mn><mml:mo> ≤ </mml:mo><mml:mi> A </mml:mi><mml:mo> ≤ </mml:mo><mml:mn> 1 </mml:mn></mml:mrow></mml:math></inline-formula> )<inline-formula><mml:math><mml:mrow><mml:mi> F </mml:mi><mml:mi> F </mml:mi><mml:mi> I </mml:mi></mml:mrow></mml:math></inline-formula> = Fossil Fuel Intake (megajoules, MJ)<inline-formula><mml:math><mml:mi> β </mml:mi></mml:math></inline-formula> = Fuel Type Factor (dimensionless, <inline-formula><mml:math><mml:mrow><mml:mn> 0 </mml:mn><mml:mo> ≤ </mml:mo><mml:mi> β </mml:mi><mml:mo> ≤ </mml:mo><mml:mn> 1 </mml:mn></mml:mrow></mml:math></inline-formula> )<inline-formula><mml:math><mml:mi> γ </mml:mi></mml:math></inline-formula> = Combustion Efficiency Factor (dimensionless, <inline-formula><mml:math><mml:mrow><mml:mn> 0 </mml:mn><mml:mo> ≤ </mml:mo><mml:mi> γ </mml:mi><mml:mo> ≤ </mml:mo><mml:mn> 1 </mml:mn></mml:mrow></mml:math></inline-formula> )<inline-formula><mml:math><mml:mi> δ </mml:mi></mml:math></inline-formula> = Emissions Reduction Factor (dimensionless, <inline-formula><mml:math><mml:mrow><mml:mn> 0 </mml:mn><mml:mo> ≤ </mml:mo><mml:mi> δ </mml:mi><mml:mo> ≤ </mml:mo><mml:mn> 1 </mml:mn></mml:mrow></mml:math></inline-formula> )<inline-formula><mml:math><mml:mi> τ </mml:mi></mml:math></inline-formula> = Time (seconds)<inline-formula><mml:math><mml:mrow><mml:mi> ϵ </mml:mi><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> = Stochastic Error Term as a function of time, modeled as <inline-formula><mml:math><mml:mrow><mml:mi mathvariant="script"> N </mml:mi><mml:mrow><mml:mo> ( </mml:mo><mml:mrow><mml:mn> 0 </mml:mn><mml:mo> , </mml:mo><mml:msup><mml:mi> σ </mml:mi><mml:mn> 2 </mml:mn></mml:msup></mml:mrow><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula></p>
      </sec>
      <sec id="sec3dot4">
        <title>3.4. Hoochens AI Model Approach</title>
        <p>Given the diverse nature of Carbon Release (CR) sources, from vehicular emissions to industrial machinery, a one-size-fits-all AI model cannot effectively capture the unique optimization needs of each sector. To address this complexity, our approach leverages an ensemble model structure that combines specialized AI submodels, each optimized for a specific CR source. By tailoring submodels to particular contexts—such as transportation, industry, or residential energy usage—this ensemble approach enables precise and context-sensitive optimization of Fossil Fuel Intake (FFI) and CR reduction.</p>
        <p>Each submodel within the ensemble operates with a unique dataset and learning framework, trained to capture the nuances of its respective CR source. For instance, transportation models consider variables like traffic density and fuel efficiency, while industrial models focus on load dynamics and operational schedules. These submodels are aggregated through a dynamic weighting mechanism that adjusts each model’s influence based on real-time factors like environmental conditions or peak usage hours. This aggregation layer enhances adaptability, allowing the ensemble to provide the most accurate predictions under varying conditions.</p>
        <p>Furthermore, continuous learning within each submodel ensures that the ensemble can respond to evolving conditions, such as regulatory changes or shifts in fuel quality. By integrating these components, our ensemble model delivers a flexible, scalable solution for FFI optimization, empowering each sector with tailored strategies to achieve substantial CR reductions.</p>
        <p>To develop a comprehensive and effective AI model for FFI optimization, it is essential to train the model using a diverse dataset that includes:</p>
        <p>Emission DataEnergy Consumption DataEnvironmental and Meterological DataIndustrial Operational DataSocio Economic DataPolicy and Regulatory Data</p>
        <p>Each data type captures unique factors influencing carbon release. Without this multidimensional approach, the AI model may lack crucial insights, leading to gaps in predictive accuracy and limiting its ability to respond dynamically to varying operational and environmental conditions.</p>
        <p>In order to capture the complex relationships within each Carbon Release (CR) source, each submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> in our ensemble is designed with specific transformations and regularization to optimize accuracy and stability.</p>
        <p>1) **Input Vector Transformation**: Each submodel operates on an input vector <inline-formula><mml:math><mml:mrow><mml:msub><mml:mstyle mathvariant="bold" mathsize="normal"><mml:mi> X </mml:mi></mml:mstyle><mml:mi> i </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> specific to its domain, such as traffic data for transportation or load data for industrial machinery. We transform <inline-formula><mml:math><mml:mrow><mml:msub><mml:mstyle mathvariant="bold" mathsize="normal"><mml:mi> X </mml:mi></mml:mstyle><mml:mi> i </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> using a feature mapping function <inline-formula><mml:math><mml:mrow><mml:msub><mml:mtext> Φ </mml:mtext><mml:mi> i </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> , which captures nonlinear relationships between inputs:</p>
        <disp-formula id="FD9">
          <mml:math>
            <mml:mrow>
              <mml:msub>
                <mml:mstyle mathvariant="bold" mathsize="normal">
                  <mml:msup>
                    <mml:mi>X</mml:mi>
                    <mml:mo>′</mml:mo>
                  </mml:msup>
                </mml:mstyle>
                <mml:mi>i</mml:mi>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:msub>
                <mml:mi>Φ</mml:mi>
                <mml:mi>i</mml:mi>
              </mml:msub>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:msub>
                    <mml:mstyle mathvariant="bold" mathsize="normal">
                      <mml:mi>X</mml:mi>
                    </mml:mstyle>
                    <mml:mi>i</mml:mi>
                  </mml:msub>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>=</mml:mo>
              <mml:mrow>
                <mml:mo>[</mml:mo>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>ϕ</mml:mi>
                    <mml:mn>1</mml:mn>
                  </mml:msub>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>X</mml:mi>
                        <mml:mrow>
                          <mml:mi>i</mml:mi>
                          <mml:mo>,</mml:mo>
                          <mml:mn>1</mml:mn>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                  <mml:mo>,</mml:mo>
                  <mml:msub>
                    <mml:mi>ϕ</mml:mi>
                    <mml:mn>2</mml:mn>
                  </mml:msub>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>X</mml:mi>
                        <mml:mrow>
                          <mml:mi>i</mml:mi>
                          <mml:mo>,</mml:mo>
                          <mml:mn>2</mml:mn>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                  <mml:mo>,</mml:mo>
                  <mml:mo>⋯</mml:mo>
                  <mml:mo>,</mml:mo>
                  <mml:msub>
                    <mml:mi>ϕ</mml:mi>
                    <mml:mi>k</mml:mi>
                  </mml:msub>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>X</mml:mi>
                        <mml:mrow>
                          <mml:mi>i</mml:mi>
                          <mml:mo>,</mml:mo>
                          <mml:mi>k</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
                <mml:mo>]</mml:mo>
              </mml:mrow>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>where <inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> ϕ </mml:mi><mml:mi> j </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are basis functions (e.g., polynomial or Gaussian), expanding the feature space to enhance model expressiveness.</p>
        <p>2) **Submodel Prediction as a Weighted Sum of Basis Functions**: To capture interactions in each submodel, we use a weighted combination of transformed features, resulting in an intermediate prediction <inline-formula><mml:math><mml:mrow><mml:mover accent="true"><mml:mi> C </mml:mi><mml:mo> ˜ </mml:mo></mml:mover><mml:msub><mml:mi> R </mml:mi><mml:mi> i </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> :</p>
        <disp-formula id="FD10">
          <mml:math>
            <mml:mrow>
              <mml:mover accent="true">
                <mml:mi>C</mml:mi>
                <mml:mo>˜</mml:mo>
              </mml:mover>
              <mml:msub>
                <mml:mi>R</mml:mi>
                <mml:mi>i</mml:mi>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:munderover>
                <mml:mstyle displaystyle="true" mathsize="140%">
                  <mml:mo>∑</mml:mo>
                </mml:mstyle>
                <mml:mrow>
                  <mml:mi>j</mml:mi>
                  <mml:mo>=</mml:mo>
                  <mml:mn>1</mml:mn>
                </mml:mrow>
                <mml:mi>k</mml:mi>
              </mml:munderover>
              <mml:mtext>
                 
              </mml:mtext>
              <mml:msub>
                <mml:mi>w</mml:mi>
                <mml:mrow>
                  <mml:mi>i</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>j</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>⋅</mml:mo>
              <mml:msub>
                <mml:mi>ϕ</mml:mi>
                <mml:mi>j</mml:mi>
              </mml:msub>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>X</mml:mi>
                    <mml:mrow>
                      <mml:mi>i</mml:mi>
                      <mml:mo>,</mml:mo>
                      <mml:mi>j</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>+</mml:mo>
              <mml:msub>
                <mml:mi>b</mml:mi>
                <mml:mi>i</mml:mi>
              </mml:msub>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>where <inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> w </mml:mi><mml:mrow><mml:mi> i </mml:mi><mml:mo> , </mml:mo><mml:mi> j </mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> are the learned weights and <inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> b </mml:mi><mml:mi> i </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the bias term for submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> .</p>
        <p>3) **Incorporating Regularization for Model Stability**: We introduce a regularization term <inline-formula><mml:math><mml:mrow><mml:mi> Ω </mml:mi><mml:mrow><mml:mo> ( </mml:mo><mml:mrow><mml:msub><mml:mstyle mathvariant="bold" mathsize="normal"><mml:mi> w </mml:mi></mml:mstyle><mml:mi> i </mml:mi></mml:msub></mml:mrow><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> to prevent overfitting. The objective function <inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> J </mml:mi><mml:mi> i </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> is defined as:</p>
        <disp-formula id="FD11">
          <mml:math>
            <mml:mrow>
              <mml:msub>
                <mml:mi>J</mml:mi>
                <mml:mi>i</mml:mi>
              </mml:msub>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:msub>
                    <mml:mstyle mathvariant="bold" mathsize="normal">
                      <mml:mi>w</mml:mi>
                    </mml:mstyle>
                    <mml:mi>i</mml:mi>
                  </mml:msub>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mn>1</mml:mn>
                <mml:mn>2</mml:mn>
              </mml:mfrac>
              <mml:munderover>
                <mml:mstyle mathsize="140%" displaystyle="true">
                  <mml:mo>∑</mml:mo>
                </mml:mstyle>
                <mml:mrow>
                  <mml:mi>t</mml:mi>
                  <mml:mo>=</mml:mo>
                  <mml:mn>1</mml:mn>
                </mml:mrow>
                <mml:mi>T</mml:mi>
              </mml:munderover>
              <mml:msup>
                <mml:mrow>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:msubsup>
                        <mml:mi>y</mml:mi>
                        <mml:mi>i</mml:mi>
                        <mml:mrow>
                          <mml:mrow>
                            <mml:mo>(</mml:mo>
                            <mml:mi>t</mml:mi>
                            <mml:mo>)</mml:mo>
                          </mml:mrow>
                        </mml:mrow>
                      </mml:msubsup>
                      <mml:mo>−</mml:mo>
                      <mml:mover accent="true">
                        <mml:mi>C</mml:mi>
                        <mml:mo>˜</mml:mo>
                      </mml:mover>
                      <mml:msubsup>
                        <mml:mi>R</mml:mi>
                        <mml:mi>i</mml:mi>
                        <mml:mrow>
                          <mml:mrow>
                            <mml:mo>(</mml:mo>
                            <mml:mi>t</mml:mi>
                            <mml:mo>)</mml:mo>
                          </mml:mrow>
                        </mml:mrow>
                      </mml:msubsup>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
                <mml:mn>2</mml:mn>
              </mml:msup>
              <mml:mo>+</mml:mo>
              <mml:msub>
                <mml:mi>λ</mml:mi>
                <mml:mi>i</mml:mi>
              </mml:msub>
              <mml:mo>⋅</mml:mo>
              <mml:mi>Ω</mml:mi>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:msub>
                    <mml:mstyle mathvariant="bold" mathsize="normal">
                      <mml:mi>w</mml:mi>
                    </mml:mstyle>
                    <mml:mi>i</mml:mi>
                  </mml:msub>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>where <inline-formula><mml:math><mml:mrow><mml:msubsup><mml:mi> y </mml:mi><mml:mi> i </mml:mi><mml:mrow><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> is the actual observed CR at time <inline-formula><mml:math><mml:mi> t </mml:mi></mml:math></inline-formula> , <inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> λ </mml:mi><mml:mi> i </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the regularization parameter, and <inline-formula><mml:math><mml:mrow><mml:mi> Ω </mml:mi><mml:mrow><mml:mo> ( </mml:mo><mml:mrow><mml:msub><mml:mstyle mathvariant="bold" mathsize="normal"><mml:mi> w </mml:mi></mml:mstyle><mml:mi> i </mml:mi></mml:msub></mml:mrow><mml:mo> ) </mml:mo></mml:mrow><mml:mo> = </mml:mo><mml:mstyle displaystyle="true"><mml:msub><mml:mo> ∑ </mml:mo><mml:mi> j </mml:mi></mml:msub><mml:mrow><mml:msubsup><mml:mi> w </mml:mi><mml:mrow><mml:mi> i </mml:mi><mml:mo> , </mml:mo><mml:mi> j </mml:mi></mml:mrow><mml:mn> 2 </mml:mn></mml:msubsup></mml:mrow></mml:mstyle></mml:mrow></mml:math></inline-formula> represents an <inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> L </mml:mi><mml:mn> 2 </mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> regularization term.</p>
        <p>4) **Nonlinear Activation and Final Prediction**: The intermediate prediction <inline-formula><mml:math><mml:mrow><mml:mover accent="true"><mml:mi> C </mml:mi><mml:mo> ˜ </mml:mo></mml:mover><mml:msub><mml:mi> R </mml:mi><mml:mi> i </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is passed through a nonlinear activation function <inline-formula><mml:math><mml:mi> σ </mml:mi></mml:math></inline-formula> (e.g., ReLU or sigmoid), yielding the final submodel prediction:</p>
        <disp-formula id="FD12">
          <mml:math>
            <mml:mrow>
              <mml:mi>C</mml:mi>
              <mml:msub>
                <mml:mi>R</mml:mi>
                <mml:mi>i</mml:mi>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:mi>σ</mml:mi>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:mover accent="true">
                    <mml:mi>C</mml:mi>
                    <mml:mo>˜</mml:mo>
                  </mml:mover>
                  <mml:msub>
                    <mml:mi>R</mml:mi>
                    <mml:mi>i</mml:mi>
                  </mml:msub>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>=</mml:mo>
              <mml:mi>σ</mml:mi>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:munderover>
                    <mml:mstyle displaystyle="true" mathsize="140%">
                      <mml:mo>∑</mml:mo>
                    </mml:mstyle>
                    <mml:mrow>
                      <mml:mi>j</mml:mi>
                      <mml:mo>=</mml:mo>
                      <mml:mn>1</mml:mn>
                    </mml:mrow>
                    <mml:mi>k</mml:mi>
                  </mml:munderover>
                  <mml:mtext>
                     
                  </mml:mtext>
                  <mml:msub>
                    <mml:mi>w</mml:mi>
                    <mml:mrow>
                      <mml:mi>i</mml:mi>
                      <mml:mo>,</mml:mo>
                      <mml:mi>j</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                  <mml:mo>⋅</mml:mo>
                  <mml:msub>
                    <mml:mi>ϕ</mml:mi>
                    <mml:mi>j</mml:mi>
                  </mml:msub>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>X</mml:mi>
                        <mml:mrow>
                          <mml:mi>i</mml:mi>
                          <mml:mo>,</mml:mo>
                          <mml:mi>j</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                  <mml:mo>+</mml:mo>
                  <mml:msub>
                    <mml:mi>b</mml:mi>
                    <mml:mi>i</mml:mi>
                  </mml:msub>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>Grand Equation for Submodel Prediction Bringing together these components, the final submodel prediction equation for carbon release <inline-formula><mml:math><mml:mrow><mml:mi> C </mml:mi><mml:msub><mml:mi> R </mml:mi><mml:mi> i </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> becomes:</p>
        <disp-formula id="FD13">
          <label>(3)</label>
          <mml:math>
            <mml:mrow>
              <mml:mi>C</mml:mi>
              <mml:msub>
                <mml:mi>R</mml:mi>
                <mml:mi>i</mml:mi>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:mi>σ</mml:mi>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:munderover>
                    <mml:mstyle mathsize="140%" displaystyle="true">
                      <mml:mo>∑</mml:mo>
                    </mml:mstyle>
                    <mml:mrow>
                      <mml:mi>j</mml:mi>
                      <mml:mo>=</mml:mo>
                      <mml:mn>1</mml:mn>
                    </mml:mrow>
                    <mml:mi>k</mml:mi>
                  </mml:munderover>
                  <mml:mtext>
                     
                  </mml:mtext>
                  <mml:msub>
                    <mml:mi>w</mml:mi>
                    <mml:mrow>
                      <mml:mi>i</mml:mi>
                      <mml:mo>,</mml:mo>
                      <mml:mi>j</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                  <mml:mo>⋅</mml:mo>
                  <mml:msub>
                    <mml:mi>ϕ</mml:mi>
                    <mml:mi>j</mml:mi>
                  </mml:msub>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>X</mml:mi>
                        <mml:mrow>
                          <mml:mi>i</mml:mi>
                          <mml:mo>,</mml:mo>
                          <mml:mi>j</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                  <mml:mo>+</mml:mo>
                  <mml:msub>
                    <mml:mi>b</mml:mi>
                    <mml:mi>i</mml:mi>
                  </mml:msub>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>,</mml:mo>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>where</p>
        <disp-formula id="FD14">
          <label>(4)</label>
          <mml:math>
            <mml:mrow>
              <mml:msub>
                <mml:mstyle mathvariant="bold" mathsize="normal">
                  <mml:mi>w</mml:mi>
                </mml:mstyle>
                <mml:mi>i</mml:mi>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:mtext>arg</mml:mtext>
              <mml:munder>
                <mml:mrow>
                  <mml:mtext>min</mml:mtext>
                </mml:mrow>
                <mml:mrow>
                  <mml:msub>
                    <mml:mstyle mathvariant="bold" mathsize="normal">
                      <mml:mi>w</mml:mi>
                    </mml:mstyle>
                    <mml:mi>i</mml:mi>
                  </mml:msub>
                </mml:mrow>
              </mml:munder>
              <mml:msub>
                <mml:mi>J</mml:mi>
                <mml:mi>i</mml:mi>
              </mml:msub>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:msub>
                    <mml:mstyle mathvariant="bold" mathsize="normal">
                      <mml:mi>w</mml:mi>
                    </mml:mstyle>
                    <mml:mi>i</mml:mi>
                  </mml:msub>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>and</p>
        <disp-formula id="FD15">
          <mml:math>
            <mml:mrow>
              <mml:msub>
                <mml:mi>J</mml:mi>
                <mml:mi>i</mml:mi>
              </mml:msub>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:msub>
                    <mml:mstyle mathvariant="bold" mathsize="normal">
                      <mml:mi>w</mml:mi>
                    </mml:mstyle>
                    <mml:mi>i</mml:mi>
                  </mml:msub>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mn>1</mml:mn>
                <mml:mn>2</mml:mn>
              </mml:mfrac>
              <mml:munderover>
                <mml:mstyle mathsize="140%" displaystyle="true">
                  <mml:mo>∑</mml:mo>
                </mml:mstyle>
                <mml:mrow>
                  <mml:mi>t</mml:mi>
                  <mml:mo>=</mml:mo>
                  <mml:mn>1</mml:mn>
                </mml:mrow>
                <mml:mi>T</mml:mi>
              </mml:munderover>
              <mml:msup>
                <mml:mrow>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:msubsup>
                        <mml:mi>y</mml:mi>
                        <mml:mi>i</mml:mi>
                        <mml:mrow>
                          <mml:mrow>
                            <mml:mo>(</mml:mo>
                            <mml:mi>t</mml:mi>
                            <mml:mo>)</mml:mo>
                          </mml:mrow>
                        </mml:mrow>
                      </mml:msubsup>
                      <mml:mo>−</mml:mo>
                      <mml:munderover>
                        <mml:mstyle mathsize="140%" displaystyle="true">
                          <mml:mo>∑</mml:mo>
                        </mml:mstyle>
                        <mml:mrow>
                          <mml:mi>j</mml:mi>
                          <mml:mo>=</mml:mo>
                          <mml:mn>1</mml:mn>
                        </mml:mrow>
                        <mml:mi>k</mml:mi>
                      </mml:munderover>
                      <mml:mtext>
                         
                      </mml:mtext>
                      <mml:msub>
                        <mml:mi>w</mml:mi>
                        <mml:mrow>
                          <mml:mi>i</mml:mi>
                          <mml:mo>,</mml:mo>
                          <mml:mi>j</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                      <mml:mo>⋅</mml:mo>
                      <mml:msub>
                        <mml:mi>ϕ</mml:mi>
                        <mml:mi>j</mml:mi>
                      </mml:msub>
                      <mml:mrow>
                        <mml:mo>(</mml:mo>
                        <mml:mrow>
                          <mml:msub>
                            <mml:mi>X</mml:mi>
                            <mml:mrow>
                              <mml:mi>i</mml:mi>
                              <mml:mo>,</mml:mo>
                              <mml:mi>j</mml:mi>
                            </mml:mrow>
                          </mml:msub>
                        </mml:mrow>
                        <mml:mo>)</mml:mo>
                      </mml:mrow>
                      <mml:mo>−</mml:mo>
                      <mml:msub>
                        <mml:mi>b</mml:mi>
                        <mml:mi>i</mml:mi>
                      </mml:msub>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
                <mml:mn>2</mml:mn>
              </mml:msup>
              <mml:mo>+</mml:mo>
              <mml:msub>
                <mml:mi>λ</mml:mi>
                <mml:mi>i</mml:mi>
              </mml:msub>
              <mml:munder>
                <mml:mstyle mathsize="140%" displaystyle="true">
                  <mml:mo>∑</mml:mo>
                </mml:mstyle>
                <mml:mi>j</mml:mi>
              </mml:munder>
              <mml:mtext>
                 
              </mml:mtext>
              <mml:msubsup>
                <mml:mi>w</mml:mi>
                <mml:mrow>
                  <mml:mi>i</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>j</mml:mi>
                </mml:mrow>
                <mml:mn>2</mml:mn>
              </mml:msubsup>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>Summary of Notation and Elements</p>
        <p>**<inline-formula><mml:math><mml:mrow><mml:msub><mml:mstyle mathvariant="bold" mathsize="normal"><mml:mi> X </mml:mi></mml:mstyle><mml:mi> i </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> **: Input vector for submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> , specific to the CR source.**<inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> Φ </mml:mi><mml:mi> i </mml:mi></mml:msub><mml:mrow><mml:mo> ( </mml:mo><mml:mrow><mml:msub><mml:mstyle mathvariant="bold" mathsize="normal"><mml:mi> X </mml:mi></mml:mstyle><mml:mi> i </mml:mi></mml:msub></mml:mrow><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> **: Nonlinear transformation of inputs, expanding the feature space.**<inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> w </mml:mi><mml:mrow><mml:mi> i </mml:mi><mml:mo> , </mml:mo><mml:mi> j </mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> **: Weight parameter for feature <inline-formula><mml:math><mml:mi> j </mml:mi></mml:math></inline-formula> in submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> .**<inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> b </mml:mi><mml:mi> i </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> **: Bias term specific to submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> .**<inline-formula><mml:math><mml:mi> σ </mml:mi></mml:math></inline-formula> **: Nonlinear activation function (e.g., ReLU or sigmoid).**<inline-formula><mml:math><mml:mrow><mml:mi> Ω </mml:mi><mml:mrow><mml:mo> ( </mml:mo><mml:mrow><mml:msub><mml:mstyle mathvariant="bold" mathsize="normal"><mml:mi> w </mml:mi></mml:mstyle><mml:mi> i </mml:mi></mml:msub></mml:mrow><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> **: Regularization term, with <inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> L </mml:mi><mml:mn> 2 </mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> penalty to avoid overfitting.**<inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> J </mml:mi><mml:mi> i </mml:mi></mml:msub><mml:mrow><mml:mo> ( </mml:mo><mml:mrow><mml:msub><mml:mstyle mathvariant="bold" mathsize="normal"><mml:mi> w </mml:mi></mml:mstyle><mml:mi> i </mml:mi></mml:msub></mml:mrow><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> **: Objective function, combining prediction error and regularization.</p>
        <p>To ensure each submodel contributes appropriately to the ensemble prediction, we use a dynamic weighting mechanism that adjusts weights based on real-time contextual factors.</p>
        <p>1) **Contextual Inputs for Dynamic Weight Calculation**: Let <inline-formula><mml:math><mml:mrow><mml:msub><mml:mstyle mathvariant="bold" mathsize="normal"><mml:mi> Z </mml:mi></mml:mstyle><mml:mi> i </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> represent the set of contextual variables specific to submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> that affect its relevance. These could include environmental conditions, time of day, or sector-specific regulations.</p>
        <p>2) **Weight Function Definition**: We define a utility score <inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> u </mml:mi><mml:mi> i </mml:mi></mml:msub><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> for submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> based on its contextual vector <inline-formula><mml:math><mml:mrow><mml:msub><mml:mstyle mathvariant="bold" mathsize="normal"><mml:mi> Z </mml:mi></mml:mstyle><mml:mi> i </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> :</p>
        <disp-formula id="FD16">
          <mml:math>
            <mml:mrow>
              <mml:msub>
                <mml:mi>u</mml:mi>
                <mml:mi>i</mml:mi>
              </mml:msub>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mi>t</mml:mi>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>=</mml:mo>
              <mml:mi>g</mml:mi>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:msub>
                    <mml:mstyle mathvariant="bold" mathsize="normal">
                      <mml:mi>Z</mml:mi>
                    </mml:mstyle>
                    <mml:mi>i</mml:mi>
                  </mml:msub>
                  <mml:mo>,</mml:mo>
                  <mml:msub>
                    <mml:mi>θ</mml:mi>
                    <mml:mi>w</mml:mi>
                  </mml:msub>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>where <inline-formula><mml:math><mml:mi> g </mml:mi></mml:math></inline-formula> is a function that takes the contextual vector <inline-formula><mml:math><mml:mrow><mml:msub><mml:mstyle mathvariant="bold" mathsize="normal"><mml:mi> Z </mml:mi></mml:mstyle><mml:mi> i </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and parameters <inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> θ </mml:mi><mml:mi> w </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> , capturing the relationships between the context and submodel relevance.</p>
        <p>3) **Dynamic Weight Calculation with Softmax**: Using the utility scores <inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> u </mml:mi><mml:mi> i </mml:mi></mml:msub><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> , we compute the weight <inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> w </mml:mi><mml:mi> i </mml:mi></mml:msub><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> for submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> at time <inline-formula><mml:math><mml:mi> t </mml:mi></mml:math></inline-formula> with a softmax function to ensure all weights sum to 1:</p>
        <disp-formula id="FD17">
          <mml:math>
            <mml:mrow>
              <mml:msub>
                <mml:mi>w</mml:mi>
                <mml:mi>i</mml:mi>
              </mml:msub>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mi>t</mml:mi>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:mi>exp</mml:mi>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>u</mml:mi>
                        <mml:mi>i</mml:mi>
                      </mml:msub>
                      <mml:mrow>
                        <mml:mo>(</mml:mo>
                        <mml:mi>t</mml:mi>
                        <mml:mo>)</mml:mo>
                      </mml:mrow>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
                <mml:mrow>
                  <mml:msubsup>
                    <mml:mstyle mathsize="140%" displaystyle="true">
                      <mml:mo>∑</mml:mo>
                    </mml:mstyle>
                    <mml:mrow>
                      <mml:mi>j</mml:mi>
                      <mml:mo>=</mml:mo>
                      <mml:mn>1</mml:mn>
                    </mml:mrow>
                    <mml:mi>N</mml:mi>
                  </mml:msubsup>
                  <mml:mi>exp</mml:mi>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>u</mml:mi>
                        <mml:mi>j</mml:mi>
                      </mml:msub>
                      <mml:mrow>
                        <mml:mo>(</mml:mo>
                        <mml:mi>t</mml:mi>
                        <mml:mo>)</mml:mo>
                      </mml:mrow>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>This ensures that the ensemble prediction remains interpretable, with each submodel’s weight reflecting its contextual importance.</p>
        <p>Grand Equation for Dynamic Weighting</p>
        <p>Combining these components, the final dynamic weighting formula for submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> is:</p>
        <disp-formula id="FD18">
          <mml:math>
            <mml:mrow>
              <mml:msub>
                <mml:mi>w</mml:mi>
                <mml:mi>i</mml:mi>
              </mml:msub>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mi>t</mml:mi>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:mtext>exp</mml:mtext>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:mi>g</mml:mi>
                      <mml:mrow>
                        <mml:mo>(</mml:mo>
                        <mml:mrow>
                          <mml:msub>
                            <mml:mstyle mathvariant="bold" mathsize="normal">
                              <mml:mi>Z</mml:mi>
                            </mml:mstyle>
                            <mml:mi>i</mml:mi>
                          </mml:msub>
                          <mml:mo>,</mml:mo>
                          <mml:msub>
                            <mml:mi>θ</mml:mi>
                            <mml:mi>w</mml:mi>
                          </mml:msub>
                        </mml:mrow>
                        <mml:mo>)</mml:mo>
                      </mml:mrow>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
                <mml:mrow>
                  <mml:msubsup>
                    <mml:mstyle mathsize="140%" displaystyle="true">
                      <mml:mo>∑</mml:mo>
                    </mml:mstyle>
                    <mml:mrow>
                      <mml:mi>j</mml:mi>
                      <mml:mo>=</mml:mo>
                      <mml:mn>1</mml:mn>
                    </mml:mrow>
                    <mml:mi>N</mml:mi>
                  </mml:msubsup>
                  <mml:mi>exp</mml:mi>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:mi>g</mml:mi>
                      <mml:mrow>
                        <mml:mo>(</mml:mo>
                        <mml:mrow>
                          <mml:msub>
                            <mml:mstyle mathvariant="bold" mathsize="normal">
                              <mml:mi>Z</mml:mi>
                            </mml:mstyle>
                            <mml:mi>j</mml:mi>
                          </mml:msub>
                          <mml:mo>,</mml:mo>
                          <mml:msub>
                            <mml:mi>θ</mml:mi>
                            <mml:mi>w</mml:mi>
                          </mml:msub>
                        </mml:mrow>
                        <mml:mo>)</mml:mo>
                      </mml:mrow>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>where:</p>
        <p><inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> w </mml:mi><mml:mi> i </mml:mi></mml:msub><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> is the weight for submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> at time <inline-formula><mml:math><mml:mi> t </mml:mi></mml:math></inline-formula> .<inline-formula><mml:math><mml:mrow><mml:mi> g </mml:mi><mml:mrow><mml:mo> ( </mml:mo><mml:mrow><mml:msub><mml:mstyle mathvariant="bold" mathsize="normal"><mml:mi> Z </mml:mi></mml:mstyle><mml:mi> i </mml:mi></mml:msub><mml:mo> , </mml:mo><mml:msub><mml:mi> θ </mml:mi><mml:mi> w </mml:mi></mml:msub></mml:mrow><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> is the utility function determining the importance of submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> based on its context <inline-formula><mml:math><mml:mrow><mml:msub><mml:mstyle mathvariant="bold" mathsize="normal"><mml:mi> Z </mml:mi></mml:mstyle><mml:mi> i </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> .<inline-formula><mml:math><mml:mi> N </mml:mi></mml:math></inline-formula> is the total number of submodels in the ensemble.</p>
        <p>Summary of Notation</p>
        <p>**<inline-formula><mml:math><mml:mrow><mml:msub><mml:mstyle mathvariant="bold" mathsize="normal"><mml:mi> Z </mml:mi></mml:mstyle><mml:mi> i </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> **: Contextual variables specific to submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> .**<inline-formula><mml:math><mml:mrow><mml:mi> g </mml:mi><mml:mrow><mml:mo> ( </mml:mo><mml:mrow><mml:msub><mml:mstyle mathvariant="bold" mathsize="normal"><mml:mi> Z </mml:mi></mml:mstyle><mml:mi> i </mml:mi></mml:msub><mml:mo> , </mml:mo><mml:msub><mml:mi> θ </mml:mi><mml:mi> w </mml:mi></mml:msub></mml:mrow><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> **: Utility function that calculates the relevance score for submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> . **<inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> θ </mml:mi><mml:mi> w </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> **: Parameters of the utility function <inline-formula><mml:math><mml:mi> g </mml:mi></mml:math></inline-formula> .**<inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> w </mml:mi><mml:mi> i </mml:mi></mml:msub><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> **: Normalized weight for submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> at time <inline-formula><mml:math><mml:mi> t </mml:mi></mml:math></inline-formula> , ensuring interpretability in the ensemble prediction.</p>
        <p>To obtain the final Carbon Release (CR) prediction from the ensemble model, we combine the individual predictions from each submodel, weighted by their contextual relevance.</p>
        <p>1) **Submodel Contributions**: Each submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> provides a prediction <inline-formula><mml:math><mml:mrow><mml:mi> C </mml:mi><mml:msub><mml:mi> R </mml:mi><mml:mi> i </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> , which is tailored to capture the carbon release for a specific CR source (e.g., vehicles, industrial machinery). Using the dynamically calculated weight <inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> w </mml:mi><mml:mi> i </mml:mi></mml:msub><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> , each <inline-formula><mml:math><mml:mrow><mml:mi> C </mml:mi><mml:msub><mml:mi> R </mml:mi><mml:mi> i </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> prediction is scaled according to its relevance at time <inline-formula><mml:math><mml:mi> t </mml:mi></mml:math></inline-formula> .</p>
        <p>2) **Weighted Sum for Aggregation**: The ensemble’s final prediction, <inline-formula><mml:math><mml:mrow><mml:mi> C </mml:mi><mml:msub><mml:mi> R </mml:mi><mml:mrow><mml:mtext> ensemble </mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> , is obtained by taking the weighted sum of all submodel predictions:</p>
        <disp-formula id="FD19">
          <mml:math>
            <mml:mrow>
              <mml:mi>C</mml:mi>
              <mml:msub>
                <mml:mi>R</mml:mi>
                <mml:mrow>
                  <mml:mtext>ensemble</mml:mtext>
                </mml:mrow>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:munderover>
                <mml:mstyle mathsize="140%" displaystyle="true">
                  <mml:mo>∑</mml:mo>
                </mml:mstyle>
                <mml:mrow>
                  <mml:mi>i</mml:mi>
                  <mml:mo>=</mml:mo>
                  <mml:mn>1</mml:mn>
                </mml:mrow>
                <mml:mi>N</mml:mi>
              </mml:munderover>
              <mml:mtext>
                 
              </mml:mtext>
              <mml:msub>
                <mml:mi>w</mml:mi>
                <mml:mi>i</mml:mi>
              </mml:msub>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mi>t</mml:mi>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>⋅</mml:mo>
              <mml:mi>C</mml:mi>
              <mml:msub>
                <mml:mi>R</mml:mi>
                <mml:mi>i</mml:mi>
              </mml:msub>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>This equation ensures that submodels with higher weights, indicating greater relevance under current conditions, have a proportionally larger impact on the ensemble’s CR prediction.</p>
        <p>3) **Incorporating Uncertainty**: To account for real-world uncertainties in each submodel’s prediction, we add an uncertainty term <inline-formula><mml:math><mml:mi> ϵ </mml:mi></mml:math></inline-formula> , representing stochastic variations in observed CR. This term captures factors such as measurement errors, environmental fluctuations, and other random effects:</p>
        <disp-formula id="FD20">
          <mml:math>
            <mml:mrow>
              <mml:mi>C</mml:mi>
              <mml:msub>
                <mml:mi>R</mml:mi>
                <mml:mrow>
                  <mml:mtext>ensemble</mml:mtext>
                </mml:mrow>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:munderover>
                <mml:mstyle mathsize="140%" displaystyle="true">
                  <mml:mo>∑</mml:mo>
                </mml:mstyle>
                <mml:mrow>
                  <mml:mi>i</mml:mi>
                  <mml:mo>=</mml:mo>
                  <mml:mn>1</mml:mn>
                </mml:mrow>
                <mml:mi>N</mml:mi>
              </mml:munderover>
              <mml:mtext>
                 
              </mml:mtext>
              <mml:msub>
                <mml:mi>w</mml:mi>
                <mml:mi>i</mml:mi>
              </mml:msub>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mi>t</mml:mi>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>⋅</mml:mo>
              <mml:mi>C</mml:mi>
              <mml:msub>
                <mml:mi>R</mml:mi>
                <mml:mi>i</mml:mi>
              </mml:msub>
              <mml:mo>+</mml:mo>
              <mml:mi>ϵ</mml:mi>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>Here, <inline-formula><mml:math><mml:mi> ϵ </mml:mi></mml:math></inline-formula> is assumed to have a mean of zero, representing random noise that does not systematically bias the ensemble’s predictions.</p>
        <p>Grand Equation for Aggregated CR Prediction</p>
        <p>Combining these elements, the final formula for the aggregated CR prediction from the ensemble model is:</p>
        <disp-formula id="FD21">
          <mml:math>
            <mml:mrow>
              <mml:mi>C</mml:mi>
              <mml:msub>
                <mml:mi>R</mml:mi>
                <mml:mrow>
                  <mml:mtext>ensemble</mml:mtext>
                </mml:mrow>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:munderover>
                <mml:mstyle mathsize="140%" displaystyle="true">
                  <mml:mo>∑</mml:mo>
                </mml:mstyle>
                <mml:mrow>
                  <mml:mi>i</mml:mi>
                  <mml:mo>=</mml:mo>
                  <mml:mn>1</mml:mn>
                </mml:mrow>
                <mml:mi>N</mml:mi>
              </mml:munderover>
              <mml:mtext>
                 
              </mml:mtext>
              <mml:msub>
                <mml:mi>w</mml:mi>
                <mml:mi>i</mml:mi>
              </mml:msub>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mi>t</mml:mi>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>⋅</mml:mo>
              <mml:mi>C</mml:mi>
              <mml:msub>
                <mml:mi>R</mml:mi>
                <mml:mi>i</mml:mi>
              </mml:msub>
              <mml:mo>+</mml:mo>
              <mml:mi>ϵ</mml:mi>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>Summary of Notation</p>
        <p>**<inline-formula><mml:math><mml:mrow><mml:mi> C </mml:mi><mml:msub><mml:mi> R </mml:mi><mml:mi> i </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> **: Prediction for carbon release from submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> .**<inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> w </mml:mi><mml:mi> i </mml:mi></mml:msub><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> **: Weight assigned to submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> at time <inline-formula><mml:math><mml:mi> t </mml:mi></mml:math></inline-formula> , based on its contextual relevance.**<inline-formula><mml:math><mml:mi> N </mml:mi></mml:math></inline-formula> **: Total number of submodels in the ensemble.**<inline-formula><mml:math><mml:mrow><mml:mi> C </mml:mi><mml:msub><mml:mi> R </mml:mi><mml:mrow><mml:mtext> ensemble </mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> **: Final aggregated prediction of carbon release from the ensemble model.**<inline-formula><mml:math><mml:mi> ϵ </mml:mi></mml:math></inline-formula> **: Stochastic term representing uncertainty in the ensemble prediction.</p>
        <p>To improve predictive accuracy, each submodel’s parameters are updated using gradient descent to minimize the error between the predicted and observed Carbon Release (CR) values.</p>
        <p>1) **Objective Function (Loss Function)**: The objective is to minimize the error between the predicted CR <inline-formula><mml:math><mml:mrow><mml:mi> C </mml:mi><mml:msubsup><mml:mi> R </mml:mi><mml:mi> i </mml:mi><mml:mrow><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> from submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> at time <inline-formula><mml:math><mml:mi> t </mml:mi></mml:math></inline-formula> and the actual observed CR <inline-formula><mml:math><mml:mrow><mml:mi> C </mml:mi><mml:msubsup><mml:mi> R </mml:mi><mml:mrow><mml:mtext> actual </mml:mtext></mml:mrow><mml:mrow><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> . We use the Mean Squared Error (MSE) as the loss function:</p>
        <disp-formula id="FD22">
          <mml:math>
            <mml:mrow>
              <mml:msub>
                <mml:mi>L</mml:mi>
                <mml:mi>i</mml:mi>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mn>1</mml:mn>
                <mml:mn>2</mml:mn>
              </mml:mfrac>
              <mml:munderover>
                <mml:mstyle mathsize="140%" displaystyle="true">
                  <mml:mo>∑</mml:mo>
                </mml:mstyle>
                <mml:mrow>
                  <mml:mi>t</mml:mi>
                  <mml:mo>=</mml:mo>
                  <mml:mn>1</mml:mn>
                </mml:mrow>
                <mml:mi>T</mml:mi>
              </mml:munderover>
              <mml:msup>
                <mml:mrow>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:mi>C</mml:mi>
                      <mml:msubsup>
                        <mml:mi>R</mml:mi>
                        <mml:mi>i</mml:mi>
                        <mml:mrow>
                          <mml:mrow>
                            <mml:mo>(</mml:mo>
                            <mml:mi>t</mml:mi>
                            <mml:mo>)</mml:mo>
                          </mml:mrow>
                        </mml:mrow>
                      </mml:msubsup>
                      <mml:mo>−</mml:mo>
                      <mml:mi>C</mml:mi>
                      <mml:msubsup>
                        <mml:mi>R</mml:mi>
                        <mml:mrow>
                          <mml:mtext>actual</mml:mtext>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mrow>
                            <mml:mo>(</mml:mo>
                            <mml:mi>t</mml:mi>
                            <mml:mo>)</mml:mo>
                          </mml:mrow>
                        </mml:mrow>
                      </mml:msubsup>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
                <mml:mn>2</mml:mn>
              </mml:msup>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>where <inline-formula><mml:math><mml:mi> T </mml:mi></mml:math></inline-formula> is the number of time steps, and <inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> L </mml:mi><mml:mi> i </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> represents the total loss for submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> .</p>
        <p>2) **Gradient of the Loss Function**: To update the parameters, we calculate the gradient of <inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> L </mml:mi><mml:mi> i </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> with respect to each parameter <inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> θ </mml:mi><mml:mrow><mml:mi> i </mml:mi><mml:mo> , </mml:mo><mml:mi> j </mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> , where <inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> θ </mml:mi><mml:mrow><mml:mi> i </mml:mi><mml:mo> , </mml:mo><mml:mi> j </mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> represents an individual parameter in submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> :</p>
        <disp-formula id="FD23">
          <mml:math>
            <mml:mrow>
              <mml:mfrac>
                <mml:mrow>
                  <mml:mo>∂</mml:mo>
                  <mml:msub>
                    <mml:mi>L</mml:mi>
                    <mml:mi>i</mml:mi>
                  </mml:msub>
                </mml:mrow>
                <mml:mrow>
                  <mml:mo>∂</mml:mo>
                  <mml:msub>
                    <mml:mi>θ</mml:mi>
                    <mml:mrow>
                      <mml:mi>i</mml:mi>
                      <mml:mo>,</mml:mo>
                      <mml:mi>j</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                </mml:mrow>
              </mml:mfrac>
              <mml:mo>=</mml:mo>
              <mml:munderover>
                <mml:mstyle mathsize="140%" displaystyle="true">
                  <mml:mo>∑</mml:mo>
                </mml:mstyle>
                <mml:mrow>
                  <mml:mi>t</mml:mi>
                  <mml:mo>=</mml:mo>
                  <mml:mn>1</mml:mn>
                </mml:mrow>
                <mml:mi>T</mml:mi>
              </mml:munderover>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:mi>C</mml:mi>
                  <mml:msubsup>
                    <mml:mi>R</mml:mi>
                    <mml:mi>i</mml:mi>
                    <mml:mrow>
                      <mml:mrow>
                        <mml:mo>(</mml:mo>
                        <mml:mi>t</mml:mi>
                        <mml:mo>)</mml:mo>
                      </mml:mrow>
                    </mml:mrow>
                  </mml:msubsup>
                  <mml:mo>−</mml:mo>
                  <mml:mi>C</mml:mi>
                  <mml:msubsup>
                    <mml:mi>R</mml:mi>
                    <mml:mrow>
                      <mml:mtext>actual</mml:mtext>
                    </mml:mrow>
                    <mml:mrow>
                      <mml:mrow>
                        <mml:mo>(</mml:mo>
                        <mml:mi>t</mml:mi>
                        <mml:mo>)</mml:mo>
                      </mml:mrow>
                    </mml:mrow>
                  </mml:msubsup>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mfrac>
                <mml:mrow>
                  <mml:mo>∂</mml:mo>
                  <mml:mi>C</mml:mi>
                  <mml:msubsup>
                    <mml:mi>R</mml:mi>
                    <mml:mi>i</mml:mi>
                    <mml:mrow>
                      <mml:mrow>
                        <mml:mo>(</mml:mo>
                        <mml:mi>t</mml:mi>
                        <mml:mo>)</mml:mo>
                      </mml:mrow>
                    </mml:mrow>
                  </mml:msubsup>
                </mml:mrow>
                <mml:mrow>
                  <mml:mo>∂</mml:mo>
                  <mml:msub>
                    <mml:mi>θ</mml:mi>
                    <mml:mrow>
                      <mml:mi>i</mml:mi>
                      <mml:mo>,</mml:mo>
                      <mml:mi>j</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>3) **Gradient Descent Update Rule**: Using gradient descent, each parameter <inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> θ </mml:mi><mml:mrow><mml:mi> i </mml:mi><mml:mo> , </mml:mo><mml:mi> j </mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> in submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> is updated iteratively to reduce the loss:</p>
        <disp-formula id="FD24">
          <mml:math>
            <mml:mrow>
              <mml:msubsup>
                <mml:mi>θ</mml:mi>
                <mml:mrow>
                  <mml:mi>i</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>j</mml:mi>
                </mml:mrow>
                <mml:mrow>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:mi>t</mml:mi>
                      <mml:mo>+</mml:mo>
                      <mml:mn>1</mml:mn>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
              </mml:msubsup>
              <mml:mo>=</mml:mo>
              <mml:msubsup>
                <mml:mi>θ</mml:mi>
                <mml:mrow>
                  <mml:mi>i</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>j</mml:mi>
                </mml:mrow>
                <mml:mrow>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mi>t</mml:mi>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
              </mml:msubsup>
              <mml:mo>−</mml:mo>
              <mml:mi>η</mml:mi>
              <mml:mfrac>
                <mml:mrow>
                  <mml:mo>∂</mml:mo>
                  <mml:msub>
                    <mml:mi>L</mml:mi>
                    <mml:mi>i</mml:mi>
                  </mml:msub>
                </mml:mrow>
                <mml:mrow>
                  <mml:mo>∂</mml:mo>
                  <mml:msub>
                    <mml:mi>θ</mml:mi>
                    <mml:mrow>
                      <mml:mi>i</mml:mi>
                      <mml:mo>,</mml:mo>
                      <mml:mi>j</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>where</p>
        <p><inline-formula><mml:math><mml:mi> η </mml:mi></mml:math></inline-formula> is the learning rate, controlling the step size in each update.<inline-formula><mml:math><mml:mrow><mml:msubsup><mml:mi> θ </mml:mi><mml:mrow><mml:mi> i </mml:mi><mml:mo> , </mml:mo><mml:mi> j </mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo> ( </mml:mo><mml:mrow><mml:mi> t </mml:mi><mml:mo> + </mml:mo><mml:mn> 1 </mml:mn></mml:mrow><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> is the parameter value after the <inline-formula><mml:math><mml:mrow><mml:mi> t </mml:mi><mml:mo> + </mml:mo><mml:mn> 1 </mml:mn></mml:mrow></mml:math></inline-formula> -th iteration.</p>
        <p>4) **Regularization for Stability**: To prevent overfitting, we add a regularization term <inline-formula><mml:math><mml:mrow><mml:mi> λ </mml:mi><mml:mi> Ω </mml:mi><mml:mrow><mml:mo> ( </mml:mo><mml:mrow><mml:msub><mml:mi> θ </mml:mi><mml:mi> i </mml:mi></mml:msub></mml:mrow><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> to the objective function, where <inline-formula><mml:math><mml:mrow><mml:mi> Ω </mml:mi><mml:mrow><mml:mo> ( </mml:mo><mml:mrow><mml:msub><mml:mi> θ </mml:mi><mml:mi> i </mml:mi></mml:msub></mml:mrow><mml:mo> ) </mml:mo></mml:mrow><mml:mo> = </mml:mo><mml:mstyle displaystyle="true"><mml:msub><mml:mo> ∑ </mml:mo><mml:mi> j </mml:mi></mml:msub><mml:mrow><mml:msubsup><mml:mi> θ </mml:mi><mml:mrow><mml:mi> i </mml:mi><mml:mo> , </mml:mo><mml:mi> j </mml:mi></mml:mrow><mml:mn> 2 </mml:mn></mml:msubsup></mml:mrow></mml:mstyle></mml:mrow></mml:math></inline-formula> represents <inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> L </mml:mi><mml:mn> 2 </mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> regularization. The updated objective function with regularization becomes:</p>
        <disp-formula id="FD25">
          <mml:math>
            <mml:mrow>
              <mml:msub>
                <mml:mi>L</mml:mi>
                <mml:mi>i</mml:mi>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mn>1</mml:mn>
                <mml:mn>2</mml:mn>
              </mml:mfrac>
              <mml:munderover>
                <mml:mstyle mathsize="140%" displaystyle="true">
                  <mml:mo>∑</mml:mo>
                </mml:mstyle>
                <mml:mrow>
                  <mml:mi>t</mml:mi>
                  <mml:mo>=</mml:mo>
                  <mml:mn>1</mml:mn>
                </mml:mrow>
                <mml:mi>T</mml:mi>
              </mml:munderover>
              <mml:msup>
                <mml:mrow>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:mi>C</mml:mi>
                      <mml:msubsup>
                        <mml:mi>R</mml:mi>
                        <mml:mi>i</mml:mi>
                        <mml:mrow>
                          <mml:mrow>
                            <mml:mo>(</mml:mo>
                            <mml:mi>t</mml:mi>
                            <mml:mo>)</mml:mo>
                          </mml:mrow>
                        </mml:mrow>
                      </mml:msubsup>
                      <mml:mo>−</mml:mo>
                      <mml:mi>C</mml:mi>
                      <mml:msubsup>
                        <mml:mi>R</mml:mi>
                        <mml:mrow>
                          <mml:mtext>actual</mml:mtext>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mrow>
                            <mml:mo>(</mml:mo>
                            <mml:mi>t</mml:mi>
                            <mml:mo>)</mml:mo>
                          </mml:mrow>
                        </mml:mrow>
                      </mml:msubsup>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
                <mml:mn>2</mml:mn>
              </mml:msup>
              <mml:mo>+</mml:mo>
              <mml:mi>λ</mml:mi>
              <mml:munder>
                <mml:mstyle mathsize="140%" displaystyle="true">
                  <mml:mo>∑</mml:mo>
                </mml:mstyle>
                <mml:mi>j</mml:mi>
              </mml:munder>
              <mml:mtext>
                 
              </mml:mtext>
              <mml:msubsup>
                <mml:mi>θ</mml:mi>
                <mml:mrow>
                  <mml:mi>i</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>j</mml:mi>
                </mml:mrow>
                <mml:mn>2</mml:mn>
              </mml:msubsup>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>Grand Equation for Gradient Descent Update</p>
        <p>Combining all components, the final parameter update rule, including regularization, is:</p>
        <disp-formula id="FD26">
          <mml:math>
            <mml:mrow>
              <mml:msubsup>
                <mml:mi>θ</mml:mi>
                <mml:mrow>
                  <mml:mi>i</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>j</mml:mi>
                </mml:mrow>
                <mml:mrow>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:mi>t</mml:mi>
                      <mml:mo>+</mml:mo>
                      <mml:mn>1</mml:mn>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
              </mml:msubsup>
              <mml:mo>=</mml:mo>
              <mml:msubsup>
                <mml:mi>θ</mml:mi>
                <mml:mrow>
                  <mml:mi>i</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>j</mml:mi>
                </mml:mrow>
                <mml:mrow>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mi>t</mml:mi>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
              </mml:msubsup>
              <mml:mo>−</mml:mo>
              <mml:mi>η</mml:mi>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:munderover>
                    <mml:mstyle mathsize="140%" displaystyle="true">
                      <mml:mo>∑</mml:mo>
                    </mml:mstyle>
                    <mml:mrow>
                      <mml:mi>t</mml:mi>
                      <mml:mo>=</mml:mo>
                      <mml:mn>1</mml:mn>
                    </mml:mrow>
                    <mml:mi>T</mml:mi>
                  </mml:munderover>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:mi>C</mml:mi>
                      <mml:msubsup>
                        <mml:mi>R</mml:mi>
                        <mml:mi>i</mml:mi>
                        <mml:mrow>
                          <mml:mrow>
                            <mml:mo>(</mml:mo>
                            <mml:mi>t</mml:mi>
                            <mml:mo>)</mml:mo>
                          </mml:mrow>
                        </mml:mrow>
                      </mml:msubsup>
                      <mml:mo>−</mml:mo>
                      <mml:mi>C</mml:mi>
                      <mml:msubsup>
                        <mml:mi>R</mml:mi>
                        <mml:mrow>
                          <mml:mtext>actual</mml:mtext>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mrow>
                            <mml:mo>(</mml:mo>
                            <mml:mi>t</mml:mi>
                            <mml:mo>)</mml:mo>
                          </mml:mrow>
                        </mml:mrow>
                      </mml:msubsup>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                  <mml:mfrac>
                    <mml:mrow>
                      <mml:mo>∂</mml:mo>
                      <mml:mi>C</mml:mi>
                      <mml:msubsup>
                        <mml:mi>R</mml:mi>
                        <mml:mi>i</mml:mi>
                        <mml:mrow>
                          <mml:mrow>
                            <mml:mo>(</mml:mo>
                            <mml:mi>t</mml:mi>
                            <mml:mo>)</mml:mo>
                          </mml:mrow>
                        </mml:mrow>
                      </mml:msubsup>
                    </mml:mrow>
                    <mml:mrow>
                      <mml:mo>∂</mml:mo>
                      <mml:msub>
                        <mml:mi>θ</mml:mi>
                        <mml:mrow>
                          <mml:mi>i</mml:mi>
                          <mml:mo>,</mml:mo>
                          <mml:mi>j</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:mfrac>
                  <mml:mo>+</mml:mo>
                  <mml:mi>λ</mml:mi>
                  <mml:msub>
                    <mml:mi>θ</mml:mi>
                    <mml:mrow>
                      <mml:mi>i</mml:mi>
                      <mml:mo>,</mml:mo>
                      <mml:mi>j</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>Summary of Notation</p>
        <p>**<inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> L </mml:mi><mml:mi> i </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> **: Loss function for submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> , calculated as mean squared error.**<inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> θ </mml:mi><mml:mrow><mml:mi> i </mml:mi><mml:mo> , </mml:mo><mml:mi> j </mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> **: Parameter <inline-formula><mml:math><mml:mi> j </mml:mi></mml:math></inline-formula> in submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> .**<inline-formula><mml:math><mml:mi> η </mml:mi></mml:math></inline-formula> **: Learning rate, controlling the step size in parameter updates.**<inline-formula><mml:math><mml:mrow><mml:mi> C </mml:mi><mml:msubsup><mml:mi> R </mml:mi><mml:mi> i </mml:mi><mml:mrow><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> **: Predicted CR value from submodel <inline-formula><mml:math><mml:mi> i </mml:mi></mml:math></inline-formula> at time <inline-formula><mml:math><mml:mi> t </mml:mi></mml:math></inline-formula> .**<inline-formula><mml:math><mml:mrow><mml:mi> C </mml:mi><mml:msubsup><mml:mi> R </mml:mi><mml:mrow><mml:mtext> actual </mml:mtext></mml:mrow><mml:mrow><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> **: Observed CR value at time <inline-formula><mml:math><mml:mi> t </mml:mi></mml:math></inline-formula> .**<inline-formula><mml:math><mml:mi> λ </mml:mi></mml:math></inline-formula> **: Regularization parameter to avoid overfitting.</p>
        <p>To evaluate the predictive performance of our ensemble model, we use the Mean Squared Error (MSE), which quantifies the difference between the model’s predicted CR values and the actual observed values. Tracking MSE over time allows us to measure the accuracy of the ensemble’s predictions and determine if adjustments or retraining are required.</p>
        <p>1) **Defining the MSE Calculation**: MSE is calculated as the average of the squared differences between predicted and actual CR values across all time steps <inline-formula><mml:math><mml:mi> T </mml:mi></mml:math></inline-formula> , penalizing larger errors more heavily to provide a reliable metric for assessing predictive accuracy: </p>
        <disp-formula id="FD27">
          <mml:math>
            <mml:mrow>
              <mml:mtext>MSE</mml:mtext>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mn>1</mml:mn>
                <mml:mi>T</mml:mi>
              </mml:mfrac>
              <mml:munderover>
                <mml:mstyle mathsize="140%" displaystyle="true">
                  <mml:mo>∑</mml:mo>
                </mml:mstyle>
                <mml:mrow>
                  <mml:mi>t</mml:mi>
                  <mml:mo>=</mml:mo>
                  <mml:mn>1</mml:mn>
                </mml:mrow>
                <mml:mi>T</mml:mi>
              </mml:munderover>
              <mml:msup>
                <mml:mrow>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:mi>C</mml:mi>
                      <mml:msubsup>
                        <mml:mi>R</mml:mi>
                        <mml:mrow>
                          <mml:mtext>ensemble</mml:mtext>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mrow>
                            <mml:mo>(</mml:mo>
                            <mml:mi>t</mml:mi>
                            <mml:mo>)</mml:mo>
                          </mml:mrow>
                        </mml:mrow>
                      </mml:msubsup>
                      <mml:mo>−</mml:mo>
                      <mml:mi>C</mml:mi>
                      <mml:msubsup>
                        <mml:mi>R</mml:mi>
                        <mml:mrow>
                          <mml:mtext>actual</mml:mtext>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mrow>
                            <mml:mo>(</mml:mo>
                            <mml:mi>t</mml:mi>
                            <mml:mo>)</mml:mo>
                          </mml:mrow>
                        </mml:mrow>
                      </mml:msubsup>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
                <mml:mn>2</mml:mn>
              </mml:msup>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>where:</p>
        <p><inline-formula><mml:math><mml:mrow><mml:mi> C </mml:mi><mml:msubsup><mml:mi> R </mml:mi><mml:mrow><mml:mtext> ensemble </mml:mtext></mml:mrow><mml:mrow><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> is the ensemble model’s predicted CR at time <inline-formula><mml:math><mml:mi> t </mml:mi></mml:math></inline-formula> .<inline-formula><mml:math><mml:mrow><mml:mi> C </mml:mi><mml:msubsup><mml:mi> R </mml:mi><mml:mrow><mml:mtext> actual </mml:mtext></mml:mrow><mml:mrow><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> is the observed CR value at time <inline-formula><mml:math><mml:mi> t </mml:mi></mml:math></inline-formula> .<inline-formula><mml:math><mml:mi> T </mml:mi></mml:math></inline-formula> is the total number of time steps evaluated.</p>
        <p>2) **Incorporating Dynamic Weight Impact**: Since each submodel’s prediction is weighted, the MSE indirectly reflects the contribution of each submodel to the overall error. If a submodel has a high weight <inline-formula><mml:math><mml:mrow><mml:msub><mml:mi> w </mml:mi><mml:mi> i </mml:mi></mml:msub><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> but yields an inaccurate prediction, it will significantly impact the MSE, thus guiding adjustments in the model.</p>
        <p>3) **Tracking Performance over Time**: MSE can be recalculated after each time step or batch of data, allowing us to monitor performance trends. A decreasing MSE indicates improving model accuracy, whereas a rising MSE could signal the need for adjustments, such as retraining specific submodels or tuning weights.</p>
        <p>4) **Setting a Performance Threshold**: An acceptable threshold for MSE can be established. If MSE exceeds this threshold, it may trigger retraining of the ensemble model or individual submodels to maintain prediction accuracy.</p>
        <p>Grand Equation for MSE</p>
        <p>The final equation for evaluating model performance through MSE is:</p>
        <disp-formula id="FD28">
          <mml:math>
            <mml:mrow>
              <mml:mtext>MSE</mml:mtext>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mn>1</mml:mn>
                <mml:mi>T</mml:mi>
              </mml:mfrac>
              <mml:munderover>
                <mml:mstyle mathsize="140%" displaystyle="true">
                  <mml:mo>∑</mml:mo>
                </mml:mstyle>
                <mml:mrow>
                  <mml:mi>t</mml:mi>
                  <mml:mo>=</mml:mo>
                  <mml:mn>1</mml:mn>
                </mml:mrow>
                <mml:mi>T</mml:mi>
              </mml:munderover>
              <mml:msup>
                <mml:mrow>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:mi>C</mml:mi>
                      <mml:msubsup>
                        <mml:mi>R</mml:mi>
                        <mml:mrow>
                          <mml:mtext>ensemble</mml:mtext>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mrow>
                            <mml:mo>(</mml:mo>
                            <mml:mi>t</mml:mi>
                            <mml:mo>)</mml:mo>
                          </mml:mrow>
                        </mml:mrow>
                      </mml:msubsup>
                      <mml:mo>−</mml:mo>
                      <mml:mi>C</mml:mi>
                      <mml:msubsup>
                        <mml:mi>R</mml:mi>
                        <mml:mrow>
                          <mml:mtext>actual</mml:mtext>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mrow>
                            <mml:mo>(</mml:mo>
                            <mml:mi>t</mml:mi>
                            <mml:mo>)</mml:mo>
                          </mml:mrow>
                        </mml:mrow>
                      </mml:msubsup>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
                <mml:mn>2</mml:mn>
              </mml:msup>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>Summary of Notation</p>
        <p>**<inline-formula><mml:math><mml:mrow><mml:mtext> MSE </mml:mtext></mml:mrow></mml:math></inline-formula> **: Mean Squared Error, representing the model’s prediction error over time.**<inline-formula><mml:math><mml:mi> T </mml:mi></mml:math></inline-formula> **: Total number of time steps evaluated.**<inline-formula><mml:math><mml:mrow><mml:mi> C </mml:mi><mml:msubsup><mml:mi> R </mml:mi><mml:mrow><mml:mtext> ensemble </mml:mtext></mml:mrow><mml:mrow><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> **: Predicted CR from the ensemble model at time <inline-formula><mml:math><mml:mi> t </mml:mi></mml:math></inline-formula> .**<inline-formula><mml:math><mml:mrow><mml:mi> C </mml:mi><mml:msubsup><mml:mi> R </mml:mi><mml:mrow><mml:mtext> actual </mml:mtext></mml:mrow><mml:mrow><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> **: Observed CR value at time <inline-formula><mml:math><mml:mi> t </mml:mi></mml:math></inline-formula> .</p>
        <p>In general, the proposed AI ensemble model for Fossil Fuel Intake (FFI) optimization provides a comprehensive approach to reducing Carbon Release (CR) by adapting to diverse CR sources, such as transportation and industrial machinery. Through the integration of specialized submodels, each tailored to unique CR sources, the ensemble captures sector-specific attributes and ensures that the dynamic characteristics of each source are accurately represented. The model’s use of a dynamic weighting mechanism enables real-time responsiveness, with each submodel’s influence adjusting according to contextual factors like environmental conditions and usage schedules. This adaptability not only increases predictive accuracy but also aligns each submodel’s contribution with its relevance under current conditions.</p>
        <p>To maintain robust performance, the ensemble applies gradient descent for iterative parameter updates, incorporating regularization to avoid overfitting. Mean Squared Error (MSE) serves as the primary performance metric, allowing continuous evaluation and providing insights for potential recalibration. Together, these elements deliver a scalable, flexible model that supports decision-making across various CR reduction strategies.</p>
        <p>Our approach offers a novel solution to optimizing FFI by enabling real-time, source-specific predictions and achieving significant CR reductions. By providing a quantifiable framework, the ensemble model equips policymakers, environmental planners, and industry leaders with actionable insights for achieving carbon reduction targets, thus paving the way for impactful advancements in environmental sustainability.</p>
      </sec>
    </sec>
    <sec id="sec4">
      <title>4. Potential Outcomes</title>
      <p>This paper’s framework offers a data-driven approach to assess and prioritize investment in key optimization components. The model’s quantitative foundation allows stakeholders to evaluate the potential of various interventions in real-time, dynamically adjusting strategies to maximize impact on emissions reduction. By establishing weighted contributions for six main components—AI optimization, fossil fuel intake, combustion efficiency, renewable integration, operational efficiency, and carbon capture—the framework equips decision-makers with clear metrics on where resources will yield the highest return in CR reduction.</p>
      <p>In this scenario, the AI component plays a pivotal role in tailoring interventions to real-world variations, enabling users to account for fluctuations in fuel efficiency, environmental conditions, and consumption rates. The AI’s predictive and adaptive capabilities enhance the framework’s precision, allowing it to detect changes in energy demand and resource availability, dynamically adjusting each component’s weight accordingly. For example, in a peak demand situation, AI could prioritize operational efficiency improvements or combustion optimization to reduce FFI impact instantly. This flexible response reduces emissions more effectively than static models, providing policymakers with a reliable system that evolves with changing demands and resource constraints.</p>
      <p>One of the most significant outcomes of implementing this framework would be the potential for optimized investment. Users, often working within limited budgets, can use this matrix to direct funds toward the highest-impact interventions based on AI-driven insights. For instance, if renewable integration shows the highest potential for CR reduction in the context of available resources, the framework would assign it a higher weight, encouraging investments that amplify renewable contributions. Alternatively, in sectors or regions with lower renewable viability, AI could recalibrate the model to emphasize combustion efficiency or operational improvements. This adaptability helps align policy with practical outcomes, maximizing CR reduction impact per dollar invested.</p>
      <p>Additionally, the framework’s AI component enables policymakers to perform retrospective analyses of how different optimization measures impact CR. By backtracking through historical energy data and emissions records, the AI model identifies patterns and lessons from previous interventions. These insights provide valuable feedback loops for future strategies, highlighting which combinations of interventions yielded the most significant reductions. In the hypothetical case of a government aiming to achieve net-zero emissions by 2050, this feedback would enable iterative improvement, ensuring that each successive wave of investments is more impactful and aligned with long-term carbon neutrality goals.</p>
      <p>Another key outcome is the ability of this framework to provide transparency and accountability in carbon reduction efforts. By quantifying the role of each component in achieving CR reduction, the model supports data-driven reporting and benchmarking, crucial for policy compliance and stakeholder confidence. Policymakers can clearly communicate the impact of each investment, providing transparent insights into how specific actions contribute to carbon neutrality goals. This level of accountability is essential, especially for stakeholders such as environmental organizations, investors, and the public, who are increasingly attentive to measurable, verifiable progress in emissions reduction.</p>
      <p>The AI component within the framework further enhances this transparency by enabling real-time monitoring and adaptive recalibration of CR efforts. For instance, if renewable energy integration does not achieve expected CR reductions due to unforeseen circumstances—such as supply chain limitations or shifts in renewable resource availability—the AI can immediately recalibrate the model. It may then shift the weight toward other components, like operational efficiency or carbon capture, to maintain CR targets without delay. This adaptability not only increases the model’s robustness but also reassures policymakers that setbacks in one area can be mitigated by recalibrating other components, ensuring steady progress toward emissions targets.</p>
      <p>Moreover, in a practical application, the framework enables users to simulate various scenarios to identify optimal pathways to emissions reduction under different economic, environmental, or regulatory conditions. For example, in a scenario where fossil fuel prices rise significantly, the AI model could predict increased costs of FFI and adjust weights accordingly, potentially amplifying the focus on renewable integration and operational efficiency to offset costs while still minimizing CR. These scenario analyses empower policymakers with flexible strategies that align with both budgetary constraints and emissions goals, adapting to economic and environmental changes over time.</p>
      <p>Finally, the AI-driven component within this framework not only supports real-time optimizations but also fosters a culture of innovation by encouraging continuous advancements in CR technology and strategy. As the model processes diverse datasets—spanning emissions data, energy usage records, environmental conditions, and operational metrics—it “learns” from each new dataset, improving the predictive accuracy and impact of CR reduction efforts. This continuous learning loop positions the framework as an evolving tool, one that remains relevant and effective as new technologies, data sources, and environmental challenges arise.</p>
      <p>In summary, the hypothetical implementation of this paper’s framework would enable policymakers to make informed, data-driven decisions in CR optimization. Through its AI-powered, dynamically weighted model, the framework provides adaptability, transparency, and continuous improvement, ensuring that resource allocation is consistently aligned with the highest-impact CR reduction strategies. This approach maximizes the efficacy of emissions policies, supports long-term carbon neutrality goals, and creates a reliable foundation for sustainable energy management on a policy level.</p>
    </sec>
    <sec id="sec5">
      <title>5. Conclusions</title>
      <p>In conclusion, this paper introduces a robust AI-driven framework for optimizing Fossil Fuel Intake (FFI) and minimizing Carbon Release (CR). By dynamically assigning weights to six critical components—Fossil Fuel Intake, Combustion Efficiency, Renewable Energy Integration, Operational Efficiency, Carbon Capture and Storage, and AI Optimization—the model provides a flexible approach for maximizing CR reduction across varied conditions. The framework’s unique AI capabilities enable it to predict and adapt to real-time changes in energy consumption, emissions, and operational conditions, making it a valuable tool for continuous improvement in CR strategies.</p>
      <p>This approach is particularly valuable for policymakers, who face the challenge of making impactful investment decisions within resource constraints. By quantifying each component’s contribution to emissions reduction, the framework helps prioritize initiatives that deliver the greatest CR impact, providing a data-driven basis for setting policies and directing funds. Furthermore, the model’s transparency and accountability foster trust among stakeholders, as it offers clear insights into how each intervention contributes to CR reduction targets.</p>
      <p>The framework’s ability to learn from historical data and adapt to evolving conditions makes it a sustainable solution for the long-term goal of carbon neutrality. Ultimately, this paper underscores the potential of integrating AI in energy policy, providing a strategic, data-driven path to more effective, adaptable, and impactful CR reduction efforts. Through this innovation, the paper aims to contribute meaningfully to the ongoing global pursuit of sustainable energy and carbon-neutral futures.</p>
    </sec>
    <sec id="sec6">
      <title>Funding</title>
      <p>I confirm that this paper has not been funded, either in part or in whole.</p>
    </sec>
    <sec id="sec7">
      <title>Ethics Approval</title>
      <p>I confirm that this paper meets all the ethical approvals required.</p>
    </sec>
    <sec id="sec8">
      <title>Contributorship</title>
      <p>This paper is the work of Hoochens Inc.</p>
    </sec>
    <sec id="sec9">
      <title>Acknowledgments</title>
      <p>I acknowledge that everything I wrote here is true, and there is no falsification of records.</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <title>References</title>
      <ref id="B1">
        <label>1.</label>
        <citation-alternatives>
          <mixed-citation publication-type="other">Chen, Y., Chen, J. and Huang, R. (2020) Blockchain Applications in Smart Cities. <italic>IEEE Communications Magazine</italic>, 58, 20-25.</mixed-citation>
          <element-citation publication-type="other">
            <person-group person-group-type="author">
              <string-name>Chen, Y.</string-name>
              <string-name>Chen, J.</string-name>
              <string-name>Huang, R.</string-name>
            </person-group>
            <year>2020</year>
            <article-title>Blockchain Applications in Smart Cities</article-title>
            <source>IEEE Communications Magazine</source>
            <volume>58</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B2">
        <label>2.</label>
        <citation-alternatives>
          <mixed-citation publication-type="journal">Hofmann, E., Strewe, U. and Bosia, N. (2017) Supply Chain Finance: The Impact of Blockchain Technology. <italic>Journal</italic><italic>of</italic><italic>Corporate Finance</italic>, 22, 90-99. https://doi.org/10.1007/978-3-319-62371-9 <pub-id pub-id-type="doi">10.1007/978-3-319-62371-9</pub-id><ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1007/978-3-319-62371-9">https://doi.org/10.1007/978-3-319-62371-9</ext-link></mixed-citation>
          <element-citation publication-type="journal">
            <person-group person-group-type="author">
              <string-name>Hofmann, E.</string-name>
              <string-name>Strewe, U.</string-name>
              <string-name>Bosia, N.</string-name>
            </person-group>
            <year>2017</year>
            <article-title>Supply Chain Finance: The Impact of Blockchain Technology</article-title>
            <source>Journal of Corporate Finance</source>
            <volume>22</volume>
            <pub-id pub-id-type="doi">10.1007/978-3-319-62371-9</pub-id>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B3">
        <label>3.</label>
        <citation-alternatives>
          <mixed-citation publication-type="journal">Flood, M.D. and Robb, E. (2015) Smart Contracts and Distributed Ledger Technologies. <italic>Journal</italic><italic>of</italic><italic>Financial Regulation</italic>, 12, 245-267.</mixed-citation>
          <element-citation publication-type="journal">
            <person-group person-group-type="author">
              <string-name>Flood, M.D.</string-name>
              <string-name>Robb, E.</string-name>
            </person-group>
            <year>2015</year>
            <article-title>Smart Contracts and Distributed Ledger Technologies</article-title>
            <source>Journal of Financial Regulation</source>
            <volume>12</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B4">
        <label>4.</label>
        <citation-alternatives>
          <mixed-citation publication-type="other">Kavassalis, P., Papadopoulos, N. and Bougioukas, A. (2018) Innovative Applications of Blockchain in The Energy Sector. <italic>Energy Policy</italic>, 118, 472-478.</mixed-citation>
          <element-citation publication-type="other">
            <person-group person-group-type="author">
              <string-name>Kavassalis, P.</string-name>
              <string-name>Papadopoulos, N.</string-name>
              <string-name>Bougioukas, A.</string-name>
            </person-group>
            <year>2018</year>
            <article-title>Innovative Applications of Blockchain in The Energy Sector</article-title>
            <source>Energy Policy</source>
            <volume>118</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B5">
        <label>5.</label>
        <citation-alternatives>
          <mixed-citation publication-type="other">Zhang, L. and Wang, Q. (2023) Traffic Gan: A Generative Model for Traffic Flow Prediction. <italic>Transportation Research Part C</italic>: <italic>Emerging Technologies</italic>, 144, Article 103047.</mixed-citation>
          <element-citation publication-type="other">
            <person-group person-group-type="author">
              <string-name>Zhang, L.</string-name>
              <string-name>Wang, Q.</string-name>
            </person-group>
            <year>2023</year>
            <article-title>Traffic Gan: A Generative Model for Traffic Flow Prediction</article-title>
            <source>Transportation Research Part C: Emerging Technologies</source>
            <volume>144</volume>
            <elocation-id>103047</elocation-id>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B6">
        <label>6.</label>
        <citation-alternatives>
          <mixed-citation publication-type="other">IBM (2023) IBM Food Trust: Blockchain for Enhanced Food Safety. IBM Blockchain Resources.</mixed-citation>
          <element-citation publication-type="other">
            <year>2023</year>
            <article-title>IBM Food Trust: Blockchain for Enhanced Food Safety</article-title>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B7">
        <label>7.</label>
        <citation-alternatives>
          <mixed-citation publication-type="other">IBM and Golden State Foods (2021) Supply Chain Optimization with Blockchain: A Case Study. IBM Blockchain Insights.</mixed-citation>
          <element-citation publication-type="other">
            <year>2021</year>
            <article-title>Supply Chain Optimization with Blockchain: A Case Study</article-title>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B8">
        <label>8.</label>
        <citation-alternatives>
          <mixed-citation publication-type="other">IBM (2022) The Grocery Industry on Blockchain—IBM Food Trust. IBM Blockchain Resources.</mixed-citation>
          <element-citation publication-type="other">
            <year>2022</year>
            <article-title>The Grocery Industry on Blockchain—IBM Food Trust</article-title>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B9">
        <label>9.</label>
        <citation-alternatives>
          <mixed-citation publication-type="journal">Bhumichai, A. and Singh, P. (2024) Convergence of Blockchain and Ai for Sustainable Smart Cities. <italic>Journal</italic><italic>of</italic><italic>Urban Computing</italic>, 15, 90-103.</mixed-citation>
          <element-citation publication-type="journal">
            <person-group person-group-type="author">
              <string-name>Bhumichai, A.</string-name>
              <string-name>Singh, P.</string-name>
            </person-group>
            <year>2024</year>
            <article-title>Convergence of Blockchain and Ai for Sustainable Smart Cities</article-title>
            <source>Journal of Urban Computing</source>
            <volume>15</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B10">
        <label>10.</label>
        <citation-alternatives>
          <mixed-citation publication-type="journal">Singh, R., Verma, S. and Yadav, R. (2020) AI in Carbon Emission Optimization: A Review. <italic>Journal</italic><italic>of</italic><italic>Clean Energy</italic><italic>and</italic><italic>Artificial Intelligence</italic>, 14, 75-89.</mixed-citation>
          <element-citation publication-type="journal">
            <person-group person-group-type="author">
              <string-name>Singh, R.</string-name>
              <string-name>Verma, S.</string-name>
              <string-name>Yadav, R.</string-name>
            </person-group>
            <year>2020</year>
            <article-title>AI in Carbon Emission Optimization: A Review</article-title>
            <source>Journal of Clean Energy and Artificial Intelligence</source>
            <volume>14</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B11">
        <label>11.</label>
        <citation-alternatives>
          <mixed-citation publication-type="journal">Li, Y. and Huang, L. (2018) Machine Learning Models for Carbon Emission Reduction: A Comparative Analysis. <italic>Environmental Informatics Journal</italic>, 22, 120-132.</mixed-citation>
          <element-citation publication-type="journal">
            <person-group person-group-type="author">
              <string-name>Li, Y.</string-name>
              <string-name>Huang, L.</string-name>
            </person-group>
            <year>2018</year>
            <article-title>Machine Learning Models for Carbon Emission Reduction: A Comparative Analysis</article-title>
            <source>Environmental Informatics Journal</source>
            <volume>22</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B12">
        <label>12.</label>
        <citation-alternatives>
          <mixed-citation publication-type="other">Wang, J. and Liu, M. (2019) Integrated AI Models for Energy Efficiency and Carbon Reduction in Industrial Systems. <italic>Energy</italic><italic>and</italic><italic>Environmental Science</italic>, 26, 300-315.</mixed-citation>
          <element-citation publication-type="other">
            <person-group person-group-type="author">
              <string-name>Wang, J.</string-name>
              <string-name>Liu, M.</string-name>
            </person-group>
            <year>2019</year>
            <article-title>Integrated AI Models for Energy Efficiency and Carbon Reduction in Industrial Systems</article-title>
            <source>Energy and Environmental Science</source>
            <volume>26</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B13">
        <label>13.</label>
        <citation-alternatives>
          <mixed-citation publication-type="other">Tan, M.L. and Zhao, Y. (2021) Ensemble Learning Models for Carbon Footprint Optimization: Review and Future Directions. <italic>Sustainable Computing</italic>: <italic>Informatics</italic><italic>and</italic><italic>Systems</italic>, 33, 102-115.</mixed-citation>
          <element-citation publication-type="other">
            <person-group person-group-type="author">
              <string-name>Tan, M.L.</string-name>
              <string-name>Zhao, Y.</string-name>
            </person-group>
            <year>2021</year>
            <article-title>Ensemble Learning Models for Carbon Footprint Optimization: Review and Future Directions</article-title>
            <source>Sustainable Computing: Informatics and Systems</source>
            <volume>33</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B14">
        <label>14.</label>
        <citation-alternatives>
          <mixed-citation publication-type="journal">Smith, A. and Johnson, C. (2019) AI-Driven Carbon Reduction in Energy Systems: Limitations of Current Models. <italic>Journal</italic><italic>of</italic><italic>Sustainable Energy Science</italic>, 14, 255-269.</mixed-citation>
          <element-citation publication-type="journal">
            <person-group person-group-type="author">
              <string-name>Smith, A.</string-name>
              <string-name>Johnson, C.</string-name>
            </person-group>
            <year>2019</year>
            <article-title>AI-Driven Carbon Reduction in Energy Systems: Limitations of Current Models</article-title>
            <source>Journal of Sustainable Energy Science</source>
            <volume>14</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B15">
        <label>15.</label>
        <citation-alternatives>
          <mixed-citation publication-type="journal">Jones, M., Roberts, A. and Chen, H. (2018) Data Challenges in Carbon Emission Prediction Models. <italic>Environmental Data Science Journal</italic>, 12, 112-125.</mixed-citation>
          <element-citation publication-type="journal">
            <person-group person-group-type="author">
              <string-name>Jones, M.</string-name>
              <string-name>Roberts, A.</string-name>
              <string-name>Chen, H.</string-name>
            </person-group>
            <year>2018</year>
            <article-title>Data Challenges in Carbon Emission Prediction Models</article-title>
            <source>Environmental Data Science Journal</source>
            <volume>12</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B16">
        <label>16.</label>
        <citation-alternatives>
          <mixed-citation publication-type="other">Lee, S.H. and Park, Y. (2020) Environmental Impact Data in AI Models for Emission Reduction. <italic>Environmental Modeling Software</italic>, 20, 145-158.</mixed-citation>
          <element-citation publication-type="other">
            <person-group person-group-type="author">
              <string-name>Lee, S.H.</string-name>
              <string-name>Park, Y.</string-name>
            </person-group>
            <year>2020</year>
            <article-title>Environmental Impact Data in AI Models for Emission Reduction</article-title>
            <source>Environmental Modeling Software</source>
            <volume>20</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B17">
        <label>17.</label>
        <citation-alternatives>
          <mixed-citation publication-type="journal">Park, J. and Liu, M. (2021) Impact of Environmental Variables on Carbon Emission Models. <italic>Energy Policy Journal</italic>, 33, 78-92.</mixed-citation>
          <element-citation publication-type="journal">
            <person-group person-group-type="author">
              <string-name>Park, J.</string-name>
              <string-name>Liu, M.</string-name>
            </person-group>
            <year>2021</year>
            <article-title>Impact of Environmental Variables on Carbon Emission Models</article-title>
            <source>Energy Policy Journal</source>
            <volume>33</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B18">
        <label>18.</label>
        <citation-alternatives>
          <mixed-citation publication-type="journal">Kim, J. and Yamamoto, T. (2022) Advanced Ai Models for Sustainable Fossil Fuel Management: A Data-Centric Approach. <italic>Journal</italic><italic>of</italic><italic>Energy</italic><italic>and</italic><italic>Climate Studies</italic>, 28, 200-213.</mixed-citation>
          <element-citation publication-type="journal">
            <person-group person-group-type="author">
              <string-name>Kim, J.</string-name>
              <string-name>Yamamoto, T.</string-name>
            </person-group>
            <year>2022</year>
            <article-title>Advanced Ai Models for Sustainable Fossil Fuel Management: A Data-Centric Approach</article-title>
            <source>Journal of Energy and Climate Studies</source>
            <volume>28</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B19">
        <label>19.</label>
        <citation-alternatives>
          <mixed-citation publication-type="journal">Johnson, E. and Carter, D. (2021) The Role of AI in Predictive Analytics for Carbon Management. <italic>Journal</italic><italic>of</italic><italic>Sustainable Technology</italic>, 17, 102-118.</mixed-citation>
          <element-citation publication-type="journal">
            <person-group person-group-type="author">
              <string-name>Johnson, E.</string-name>
              <string-name>Carter, D.</string-name>
            </person-group>
            <year>2021</year>
            <article-title>The Role of AI in Predictive Analytics for Carbon Management</article-title>
            <source>Journal of Sustainable Technology</source>
            <volume>17</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B20">
        <label>20.</label>
        <citation-alternatives>
          <mixed-citation publication-type="journal">Wang, L. and Zhang, K. (2022) Impact of Ai on Industrial Energy Optimization: A Carbon Reduction Perspective. <italic>Energy Efficiency Journal</italic>, 35, 58-72.</mixed-citation>
          <element-citation publication-type="journal">
            <person-group person-group-type="author">
              <string-name>Wang, L.</string-name>
              <string-name>Zhang, K.</string-name>
            </person-group>
            <year>2022</year>
            <article-title>Impact of Ai on Industrial Energy Optimization: A Carbon Reduction Perspective</article-title>
            <source>Energy Efficiency Journal</source>
            <volume>35</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B21">
        <label>21.</label>
        <citation-alternatives>
          <mixed-citation publication-type="other">Xu, M. and Li, W. (2021) AI-Driven Emission Forecasting: Trends and Challenges in Carbon Reduction. <italic>Environmental Forecasting</italic><italic>and</italic><italic>Sustainability</italic>, 25, 89-103.</mixed-citation>
          <element-citation publication-type="other">
            <person-group person-group-type="author">
              <string-name>Xu, M.</string-name>
              <string-name>Li, W.</string-name>
            </person-group>
            <year>2021</year>
            <article-title>AI-Driven Emission Forecasting: Trends and Challenges in Carbon Reduction</article-title>
            <source>Environmental Forecasting and Sustainability</source>
            <volume>25</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B22">
        <label>22.</label>
        <citation-alternatives>
          <mixed-citation publication-type="journal">Kim, H. and Shin, J. (2023) Measuring the Effectiveness of AI in Carbon Emission Reduction. <italic>International Journal</italic><italic>of</italic><italic>Climate Change Technology</italic>, 40, 55-70.</mixed-citation>
          <element-citation publication-type="journal">
            <person-group person-group-type="author">
              <string-name>Kim, H.</string-name>
              <string-name>Shin, J.</string-name>
            </person-group>
            <year>2023</year>
            <article-title>Measuring the Effectiveness of AI in Carbon Emission Reduction</article-title>
            <source>International Journal of Climate Change Technology</source>
            <volume>40</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B23">
        <label>23.</label>
        <citation-alternatives>
          <mixed-citation publication-type="journal">Raza, A. and Xu, Y. (2018) Environmental Hazards of Fossil Fuels: A Comprehensive Review. <italic>Journal</italic><italic>of</italic><italic>Environmental Science</italic>, 78, 120-132.</mixed-citation>
          <element-citation publication-type="journal">
            <person-group person-group-type="author">
              <string-name>Raza, A.</string-name>
              <string-name>Xu, Y.</string-name>
            </person-group>
            <year>2018</year>
            <article-title>Environmental Hazards of Fossil Fuels: A Comprehensive Review</article-title>
            <source>Journal of Environmental Science</source>
            <volume>78</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B24">
        <label>24.</label>
        <citation-alternatives>
          <mixed-citation publication-type="journal">Smith, O. and Perez, C. (2020) Climate Impact of Fossil Fuel Combustion: Health and Environmental Risks. <italic>Global Climate Journal</italic>, 26, 89-102.</mixed-citation>
          <element-citation publication-type="journal">
            <person-group person-group-type="author">
              <string-name>Smith, O.</string-name>
              <string-name>Perez, C.</string-name>
            </person-group>
            <year>2020</year>
            <article-title>Climate Impact of Fossil Fuel Combustion: Health and Environmental Risks</article-title>
            <source>Global Climate Journal</source>
            <volume>26</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B25">
        <label>25.</label>
        <citation-alternatives>
          <mixed-citation publication-type="other">World Bank (2019) The Cost of Air Pollution: Health Impacts of Fossil Fuel Combustion. World Bank Publications.</mixed-citation>
          <element-citation publication-type="other">
            <year>2019</year>
            <article-title>The Cost of Air Pollution: Health Impacts of Fossil Fuel Combustion</article-title>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B26">
        <label>26.</label>
        <citation-alternatives>
          <mixed-citation publication-type="journal">Liu, C. and Huang, Y. (2022) AI-Driven Strategies for Carbon Emission Reduction in Industrial Systems. <italic>Journal</italic><italic>of</italic><italic>Environmental Management</italic>, 123, 400-415.</mixed-citation>
          <element-citation publication-type="journal">
            <person-group person-group-type="author">
              <string-name>Liu, C.</string-name>
              <string-name>Huang, Y.</string-name>
            </person-group>
            <year>2022</year>
            <article-title>AI-Driven Strategies for Carbon Emission Reduction in Industrial Systems</article-title>
            <source>Journal of Environmental Management</source>
            <volume>123</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B27">
        <label>27.</label>
        <citation-alternatives>
          <mixed-citation publication-type="journal">Yang, B. and Zhao, R. (2020) Optimizing Carbon Footprint Through AsI-Enhanced Energy Management. <italic>Energy Informatics Journal</italic>, 22, 75-89.</mixed-citation>
          <element-citation publication-type="journal">
            <person-group person-group-type="author">
              <string-name>Yang, B.</string-name>
              <string-name>Zhao, R.</string-name>
            </person-group>
            <year>2020</year>
            <article-title>Optimizing Carbon Footprint Through AsI-Enhanced Energy Management</article-title>
            <source>Energy Informatics Journal</source>
            <volume>22</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B28">
        <label>28.</label>
        <citation-alternatives>
          <mixed-citation publication-type="journal">Green, T. and Patel, R. (2021) Climate Innovation and The Role of AI in Achieving Net-Zero Emissions. <italic>Global Sustainability Journal</italic>, 19, 102-117.</mixed-citation>
          <element-citation publication-type="journal">
            <person-group person-group-type="author">
              <string-name>Green, T.</string-name>
              <string-name>Patel, R.</string-name>
            </person-group>
            <year>2021</year>
            <article-title>Climate Innovation and The Role of AI in Achieving Net-Zero Emissions</article-title>
            <source>Global Sustainability Journal</source>
            <volume>19</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B29">
        <label>29.</label>
        <citation-alternatives>
          <mixed-citation publication-type="other">Zhou, M. and Chen, X. (2019) AI Applications in Predictive Maintenance for Emission Reduction. <italic>Energy</italic><italic>and</italic><italic>Environmental Science</italic>, 34, 88-105.</mixed-citation>
          <element-citation publication-type="other">
            <person-group person-group-type="author">
              <string-name>Zhou, M.</string-name>
              <string-name>Chen, X.</string-name>
            </person-group>
            <year>2019</year>
            <article-title>AI Applications in Predictive Maintenance for Emission Reduction</article-title>
            <source>Energy and Environmental Science</source>
            <volume>34</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B30">
        <label>30.</label>
        <citation-alternatives>
          <mixed-citation publication-type="other">Martin, H. and O’Sullivan, G. (2019) The Role of AI Attribution in Carbon Reduction Accountability. <italic>Sustainable Computing</italic>: <italic>Informatics</italic><italic>and</italic><italic>Systems</italic>, 26, 115-129.</mixed-citation>
          <element-citation publication-type="other">
            <person-group person-group-type="author">
              <string-name>Martin, H.</string-name>
              <string-name>Sullivan, G.</string-name>
            </person-group>
            <year>2019</year>
            <article-title>The Role of AI Attribution in Carbon Reduction Accountability</article-title>
            <source>Sustainable Computing: Informatics and Systems</source>
            <volume>26</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B31">
        <label>31.</label>
        <citation-alternatives>
          <mixed-citation publication-type="journal">Chen, J. and Kumar, R. (2021) Impact Assessment of AI in Reducing Carbon Emissions. <italic>Journal</italic><italic>of</italic><italic>Climate Technology</italic>, 16, 200-215.</mixed-citation>
          <element-citation publication-type="journal">
            <person-group person-group-type="author">
              <string-name>Chen, J.</string-name>
              <string-name>Kumar, R.</string-name>
            </person-group>
            <year>2021</year>
            <article-title>Impact Assessment of AI in Reducing Carbon Emissions</article-title>
            <source>Journal of Climate Technology</source>
            <volume>16</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
    </ref-list>
  </back>
</article>