A gradient-enhanced physics-informed neural network (gPINN) scheme for the coupled non-fickian/non-fourierian diffusion-thermoelasticity analysis: A novel gPINN structure

Abstract

This paper proposes a modified artificial intelligence (AI) approach based on the gradient-enhanced physics-informed neural network (gPINN) with a novel structure for the generalized coupled non-Fickian/non-Fourierian diffusion-thermoelasticity analysis. Previous successful application of gPINN in function approximation and single partial differential equation (PDE) problems gave us enough motivation to develop its application with a novel structure for solving a system of coupled PDEs. The governing equations are formulated for a copper-made strip based upon the Lord-Shulman theory of the generalized coupled thermoelasticity. In order to shed light on the capacity of the gPINN-based approach, three examples with different boundary conditions for a one-dimensional half-space are presented, as well as an example for a two-dimensional half-space. The primary goal is to investigate the transient behavior of field variables (i.e., non-dimensional molar concentration, non-dimensional displacement, and non-dimensional temperature). Variations of dimensionless stress are also examined in depth. Performance comparisons between the gPINN-based method and commonly used approaches support the efficacy of the gPINN with a novel structure. Detailed sensitivity analyses are provided to sufficiently explore the impact of neural network hyperparameters. Moreover, the effect of relaxation time on the behavior of mass concentration is addressed in a single scenario. Overall, the proposed gPINN-based method with a novel structure yields consistently encouraging and satisfactory results, and this approach entails the capability to be applied to more complicated problems. Numerical results underline the importance of the weights assigned to the derivatives of the loss terms to achieve more accurate predictions. Nonparametric statistical tests offer further evidence for exceptional agreement between gPINN solutions with certain weights and outcomes derived by commonly used analytical techniques.