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.

翻译：本文主要研究耦合热弹性效应并包含第二声效应的Timoshenko系统数值解的行为特性。为实现这一目标，我们采用物理信息神经网络（PINNs）框架推导该系统的近似解。本研究深入探讨了该近似解在何种程度上能够精确捕捉离散能量的渐近行为，该行为取决于稳定性参数$\chi$。值得注意的是，PINNs克服了使用传统数值方法时遇到的主要困难。