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

Results in Engineering, vol. 32, pp. 112132

Abstract

This work extends finite element–guided physics–informed operator learning to multiphysics problems with coupled partial differential equations (PDEs) and systematically evaluates its performance across several representative problem settings. The extended formulation for multiphysics problems learns solution operators with a weighted residual formulation based on the finite element method, enabling predictions on discretizations different from the training resolution without relying on labeled simulation data. It is implemented in Folax, a JAX–based operator–learning platform, and is evaluated on nonlinear thermo–mechanical and chemo–mechanical problems. Two– and three–dimensional representative volume elements with varying heterogeneous microstructures, and an application–oriented industrial casting example with a fixed irregular geometry and parametrically varying boundary conditions are investigated as the example problems. We investigate the potential of several neural operators combined with the finite element–guided approach, including Fourier neural operators (FNOs), deep operator networks (DeepONets), and an adapted 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 features can be efficiently learned in the spectral domain, and iFOL offers efficient parametric operator learning capabilities on the complex irregular casting geometry considered in this study. Furthermore, additional studies identify trade–offs among training strategies and network decomposition schemes in terms of prediction accuracy and computational efficiency. Overall, the results clarify the capabilities and limitations of finite element–guided operator learning for coupled multiphysics problems and provide practical insights into the selection of neural operator architectures and training strategies.

Authors 5

1. Yusuke Yamazaki corresponding

   Keio University

   Affiliation as printed

   Graduate School of Science and Technology, Keio University, Hiyoshi 3–1–1, Kohoku–ku, Yokohama, 223–8522, Japan

2. Reza Najian Asl

   Technical University of Munich

   Affiliation as printed

   Chair of Structural Analysis, Technical University of Munich, Arcisstra β e 21, 80333, Munich, Germany

3. Markus Apel Aachen Access e.V

   Access

   Affiliation as printed

   ACCESS e.V, Intzestr. 5, 52072, Aachen, Germany

4. Mayu Muramatsu

   Keio University

   Affiliation as printed

   Department of Mechanical Engineering, Keio University, Hiyoshi 3–14–1, Kohoku–ku, Yokohama, 223–8522, Japan

5. Shahed Rezaei corresponding Aachen Access e.V

   Access

   Affiliation as printed

   ACCESS e.V, Intzestr. 5, 52072, Aachen, Germany