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

Abstract

In this paper, we present the adaptive physics-informed neural networks for resolving three-dimensional dynamic coupled thermo-mechanical problems in large-size-ratio functionally graded materials. 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 networks by means of the automatic differentiation algorithm, and an adaptive loss balancing scheme is introduced to improve the performance of networks. The adaptive networks are meshfree and trained on batches of randomly sampled collocation and training points, which is the key feature and superiority of the approach, since mesh-based methods will encounter difficulties in solving problems with complex large-size-ratio structures. The developed methodology is tested for several coupled thermo-mechanical problems in large-size-ratio materials, and the numerical results demonstrate that the adaptive networks are effective and reliable for dealing with coupled problems defined in coating structures with large size ratios up to 10⁹, as well as complex large-size-ratio geometries such as the electrostatic comb and the flange.