Physics-informed neural networks for Timoshenko system with Thermoelasticity

TL;DR

This paper applies Physics-Informed Neural Networks to solve the Timoshenko system with Thermoelasticity and second sound effects, demonstrating improved accuracy and stability over traditional numerical methods.

Contribution

It introduces a PINNs-based approach for the Timoshenko thermoelastic system, effectively capturing asymptotic behavior and overcoming limitations of standard numerical techniques.

Findings

PINNs accurately approximate the system's behavior.

The method effectively captures the asymptotic energy decay.

PINNs outperform traditional numerical methods in stability and accuracy.

Abstract

The main focus of this paper is to analyze the behavior of a numerical solution of the Timoshenko system coupled with Thermoelasticity and incorporating second sound effects. In order to address this target, we employ the Physics-Informed Neural Networks (PINNs) framework to derive an approximate solution for the system. Our investigation delves into the extent to which this approximate solution can accurately capture the asymptotic behavior of the discrete energy, contingent upon the stability number $\chi$. Interestingly, the PINNs overcome the major difficulties encountered while using the standard numerical methods.