Deep Learning-Based Modeling of Coupled Systems and Multiphysics Using Poisson-Dirac Structures

Abstract

Deep learning has achieved significant success in modeling dynamical systems with unknown governing equations. However, existing models tend to treat systems as monolithic and indivisible entities, making it challenging to accurately model coupled systems. Furthermore, they are often inapplicable to domains outside mechanical systems, such as electrical circuits and hydraulic systems. To address these limitations, we propose Poisson-Dirac Neural Networks (PoDiNNs), which are based on the Dirac structure that unifies the port-Hamiltonian and Poisson formulations. The proposed approach enables a unified representation of various systems spanning multiple domains, as well as the interactions and degeneracies arising from the components that constitute these systems. Experimental results demonstrate that the proposed method effectively learns the interactions between components and achieves superior long-term prediction performance compared to existing methods.