TITLE:
Mathematical Analysis of Two Approaches for Optimal Parameter Estimates to Modeling Time Dependent Properties of Viscoelastic Materials
AUTHORS:
Irina Viktorova, Sofya Alekseeva, Muhammed Kose
KEYWORDS:
Laplace Transform, Viscoelastic Composite, Norm Space, Inner Product Space, Least Squares Minimization, Optimal Parameter Estimation
JOURNAL NAME:
Applied Mathematics,
Vol.13 No.12,
December
29,
2022
ABSTRACT: Mathematical models for phenomena in the physical sciences are typically parameter-dependent, and the estimation of parameters that optimally model the trends suggested by experimental observation depends on how model-observation discrepancies are quantified. Commonly used parameter estimation techniques based on least-squares minimization of the model-observation discrepancies assume that the discrepancies are quantified with the L2-norm applied to a discrepancy function. While techniques based on such an assumption work well for many applications, other applications are better suited for least-squared minimization approaches that are based on other norm or inner-product induced topologies. Motivated by an application in the material sciences, the new alternative least-squares approach is defined and an insightful analytical comparison with a baseline least-squares approach is provided.