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.

翻译：本文提出自适应物理信息神经网络（PINNs），用于求解大尺寸比功能梯度材料（FGMs）中的三维动态热力耦合问题。利用耦合控制方程描述的物理定律以及初始条件和边界条件施加的约束，通过自动微分算法构建PINNs的损失函数，并引入自适应损失平衡机制以提升PINNs性能。自适应PINNs无需网格划分，可在随机采样的配置点批次上进行训练，这是该方法的关键特征与优势所在——因为基于网格的方法在求解大尺寸比问题时将面临困难。通过测试大尺寸比FGMs中的多个三维热力耦合问题，数值结果表明，自适应PINNs在处理尺寸比高达10⁹的涂层结构及静电梳齿、飞机、潜艇等复杂大尺寸比几何构型的耦合问题时，具有有效性与可靠性。