Tackling multiphysics problems via finite element-guided physics-informed operator learning

2026-03-01

AI Summary

This work proposes implicit Finite Operator Learning (iFOL), a physics-informed operator learning framework for multiphysics problems governed by coupled partial differential equations on arbitrary domains, which operates without requiring ground-truth labeled data. Built upon the finite element weighted residual formulation, iFOL establishes a resolution-independent mapping from input parameters to the solution space and provides a unified treatment of complex geometries and multiphysics coupling. Implemented within the Folax system on the JAX platform, the approach integrates FNO, DeepONet, and iFOL, leveraging finite element residuals to construct physics-constrained loss functions. Experiments demonstrate that iFOL achieves high efficiency on complex geometries in two- and three-dimensional nonlinear thermo-mechanical coupling and industrial casting scenarios, while FNO excels in accuracy on regular domains; furthermore, a single-network end-to-end training strategy significantly outperforms baseline methods.

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Abstract

This work presents a finite element-guided physics-informed operator learning framework for multiphysics problems with coupled partial differential equations (PDEs) on arbitrary domains. Implemented with Folax, a JAX-based operator-learning platform, the proposed framework learns a mapping from the input parameter space to the solution space with a weighted residual formulation based on the finite element method, enabling discretization-independent prediction beyond the training resolution without relying on labaled simulation data. The present framework for multiphysics problems is verified on nonlinear thermo-mechanical problems. Two- and three-dimensional representative volume elements with varying heterogeneous microstructures, and a close-to-reality industrial casting example under varying boundary conditions are investigated as the example problems. We investigate the potential of several neural operator backbones, including Fourier neural operators (FNOs), deep operator networks (DeepONets), and a newly proposed implicit finite operator learning (iFOL) approach based on conditional neural fields. The results demonstrate that FNOs yield highly accurate solution operators on regular domains, where the global topology can be efficiently learned in the spectral domain, and iFOL offers efficient parametric operator learning capabilities for complex and irregular geometries. Furthermore, studies on training strategies, network decomposition, and training sample quality reveal that a monolithic training strategy using a single network is sufficient for accurate predictions, while training sample quality strongly influences performance. Overall, the present approach highlights the potential of physics-informed operator learning with a finite element-based loss as a unified and scalable approach for coupled multiphysics simulations.

Problem

• multiphysics problems
• coupled PDEs
• operator learning
• finite element method
• physics-informed

Innovation

• physics-informed operator learning
• finite element method
• multiphysics problems
• implicit finite operator learning (iFOL)
• discretization-independent prediction