The novel PINN/gPINN-based deep learning schemes for non-Fickian coupled diffusion-elastic wave propagation analysis

Abstract

This paper presents a cutting-edge approach inspired by the physics-informed neural network (PINN) to solve the coupled non-Fickian diffusion-elasticity system. This is the first time that the PINN framework has been applied to non-Fick diffusion-elasticity in order to investigate the transient behavior of the concentration and displacement fields. This problem pertains to a strip subjected to a time-dependent shock loading. In light of recent developments in gradient-enhanced PINN (gPINN), there is now considerable concern regarding its applicability to systems of coupled partial differential equations (PDEs). As of yet, this methodology has only been applied to a single ordinary differential equation (ODE) or a single PDE. gPINN's performance is also examined for coupled PDEs in the current problem. Moreover, some analyses are performed to analyze the impact of parameter selection on the outputs. Successful implementations of the PINN approach without the need for mesh generation or the limitations of earlier numerical approaches confirm its capabilities in solving complex systems of coupled PDEs.