Adaptive physics-informed neural networks for dynamic thermo-mechanical coupling problems in large-size-ratio functionally graded materials

In this paper, we present the adaptive physics-informed neural networks (PINNs) for resolving three dimensional (3D) dynamic thermo-mechanical coupling problems in large-size-ratio functionally graded materials (FGMs). The physical laws described by coupled governing equations and the constraints imposed by the initial and boundary conditions are leveraged to form the loss function of PINNs by means of the automatic differentiation algorithm, and an adaptive loss balancing scheme is introduced to improve the performance of PINNs. The adaptive PINNs are meshfree and trained on batches of randomly sampled collocation points, which is the key feature and superiority of the approach, since mesh-based methods will encounter difficulties in solving problems with large size ratios. The developed methodology is tested for several 3D thermo-mechanical coupling problems in large-size-ratio FGMs, and the numerical results demonstrate that the adaptive PINNs are effective and reliable for dealing with coupled problems in coating structures with large size ratios up to 109, as well as complex large-size-ratio geometries such as the electrostatic comb, the airplane and the submarine.