A new modified deep learning technique based on physics-informed neural networks (PINNs) for the shock-induced coupled thermoelasticity analysis in a porous material

In this article, a new modified deep learning (DL) method based on physics-informed neural networks (PINNs) is proposed for analyzing generalized coupled thermoelasticity in a porous material under shock loadings using Lord–Shulman (LS) theory. The PINN-based method demonstrates remarkable capabilities in solving differential equations and identifying unknown parameters. It is employed to solve a system of coupled partial differential equations (PDEs) governing a porous half-space material, considering thermal and strain relaxation coefficients in the LS theory. The optimal structure of the PINN is investigated through sensitivity analyses. Two adaptive sampling techniques, residual-based adaptive refinement (RAR) and residual-based adaptive distribution (RAD), are employed to enhance solution quality within the optimized architecture. The proposed forward PINN utilizes known values of field variables at initial and boundary conditions. The efficiency and effectiveness of the proposed PINN approach are demonstrated through three distinct scenarios. Non-parametric statistical tests and L2 relative error analysis validate the extraordinary potential of the proposed PINN-based method in accurately capturing the system behavior. The extrapolation results, represented as time history plots, showcase exceptional accuracy in this study, overcoming the limitations of conventional numerical methods in larger temporal domains.