High-order multi-scale neural network method for quasi-static thermo-mechanical problems of composite materials

The high-accuracy simulation of multi-physics and multi-scale problems of composite materials with a neural network approach remains a challenging task due to costly computation and Frequency Principle. In this study, a novel high-order multi-scale neural network approach with high-accuracy and efficiency performance is developed to compute the quasi-static thermo-mechanical problems of composite materials, which combines the computational advantages of the high-order multi-scale method and the neural network-based method. In the computational framework of high-order multi-scale neural network, the high-order multi-scale method decomposes the original complex multi-scale problem into two parts, namely, the macroscopic homogenized problem and the microscopic unit cell problems. Then the neural network method mesh-free computes these two parts. In particular, revised physics-informed neural networks are developed to calculate macroscopic homogenized thermo-mechanical problems with significant order of magnitude differences between different physical fields. Finally, the accuracy and efficiency of the proposed high-order multi-scale neural network method are demonstrated by representative numerical examples of two- and three-dimensional simulations of composite materials.