Higher-order multi-scale physics-informed randomized neural network method for efficient and high-accuracy simulation of dynamic thermo-mechanical coupling problems

Deep learning methods encounter significantly low-efficiency and low-accuracy challenges in effectively computing multi-scale multi-physics problems. In this study, an innovative higher-order multi-scale physics-informed randomized neural network (HOMS-PIRNN) framework is presented to efficiently and accurately simulate the dynamic thermo-mechanical coupling problems of composite materials, which integrates the benefits of HOMS-PIRNN. In the new framework, the higher-order multi-scale method decomposes the multi-scale multi-physics physical constraints for deep learning simulation into lower-order, higher-order microscopic physical constraints (microscopic cell equations) and macroscopic physical constraints (macroscopic homogenized equations), in which higher-order microscopic cell functions are capable of precisely depicting the phenomenon of intense oscillations at the microscale. Next, PIRNN are devised to mesh-free, efficiently and accurately solve microscopic cell functions and macroscopic homogenized solutions. Furthermore, the automatic differentiation technique of neural network is employed to construct high-accuracy multi-scale asymptotic solutions. Moreover, under appropriate assumptions, the error estimation of the HOMS-PIRNN method is obtained. Finally, various numerical experiments including two-dimensional and three-dimensional composite materials, as well as porous materials are carried out to verify the proposed method, not only showing it can outperform FEM and multi-scale method in terms of efficiency, but also illustrating its validity, especially for simulating large-scale material and long-time problems in terms of computational costs.