IPFLSTM: Enhancing physics-informed neural networks with LSTM and Informer for efficient long-term prediction of dynamic multiphysics fields

Abstract

Multi-physics coupling, such as in metal solidification, involves complex interactions among physical fields like heat transfer, fluid flow, and phase change. Traditional numerical simulation methods, though accurate, are computationally expensive and struggle with long-term predictions due to the fine resolution required to capture these coupled phenomena. Furthermore, emerging machine learning methods that represent these phenomena for simulation tasks are not subject to complex physical constraints, and are only confined to fitting their numerical distributions. To address these issues, we introduce an enhanced physics-informed neural network framework. First, we employ LSTM as a spatio-temporal coordinates projection layer to transform actual physical positional relationships into positional encodings within the Informer framework. Second, we incorporate a physics-informed function for network parameters adjustment, thereby leveraging the physical constrain and the Informer model’s long-term dynamic prediction capability for final predictions. Experiments on the Cu-1wt.%Ag solidification process show that IPFLSTM reduces prediction L2 errors in velocity (u, v) and temperature fields by 56.8%, 51.74%, and 51.49% relative to PINNsFormer while cutting training time by 23.71%, outperforming traditional PINNs and their variants. This model offers a promising approach for simulating complex dynamic physical fields, addressing challenging boundary conditions, and extending to multi-scale, coupled systems in engineering applications.