Drift-Correcting Multiphysics Informed Neural Network Coupled PDE Solver

Abstract

Solving the coupled partial differential equations (PDEs) that govern the dynamics of multiphysics systems is both important and challenging. Existing numerical methods such as the finite element method (FEM) are known to be computationally intensive, while machine learning techniques, like the physics-informed neural network (PINN), often falter when modeling complex systems or processes over long timescales. To overcome these limitations, we propose a new framework “Drift-Correcting Multiphysics Informed Neural Network” (DC-MPINN), specifically designed to solve coupled multiphysics problems efficiently over extended timescales–without sacrificing accuracy. This new method introduces an architecture for temporal domain decomposition that corrects drift of conserved quantities, as well as a composite loss function that allows solving coupled multiphysics problems. We demonstrate the superior performance of DC-MPINN over traditional FEM approaches in several benchmark problems. This approach represents a step forward in multiphysics computational techniques, enhancing our ability to understand and predict the behavior of physical processes across various disciplines.