TITLE:
A Spatio-Temporal Prediction Model for Wall Turbulence Based on Hybrid Neural Networks
AUTHORS:
Yushan Yao, Yuhang Guan
KEYWORDS:
Wall-Bounded Turbulence, Spatio-Temporal Prediction, CAE, VAE, LSTM, Deep Learning
JOURNAL NAME:
Applied Mathematics,
Vol.17 No.3,
March
18,
2026
ABSTRACT: The spatio-temporal evolution of wall-bounded turbulence is characterized by high nonlinearity, multi-scale dynamics, and chaotic nature, making its accurate prediction a significant challenge for flow control and drag reduction. This paper proposes a hybrid deep learning model, CAE-VAE-LSTM, for the spatio-temporal prediction of wall turbulence. The model first employs a Convolutional Autoencoder (CAE) to extract high-dimensional spatial features and perform dimensionality reduction of the flow fields. Subsequently, a Variational Autoencoder (VAE) is integrated to map these features into a probabilistic latent space, enhancing the model’s robustness and its ability to capture the inherent stochasticity of turbulence through the reparameterization trick. Finally, a Long Short-Term Memory (LSTM) network is utilized to model the temporal evolution within the latent space, enabling recursive prediction of future flow states. Experimental results based on Direct Numerical Simulation (DNS) data demonstrate that the CAE-VAE-LSTM model can accurately reconstruct and predict the evolution of coherent structures, such as low-speed streaks, while maintaining high physical fidelity and long-term stability. Compared to traditional deterministic models, this hybrid architecture exhibits superior performance in capturing statistical properties and nonlinear dynamics, providing an efficient data-driven framework for real-time turbulence simulation and active flow control.