Poisson-Dirac Neural Networks for Modeling Coupled Dynamical Systems across Domains
This work addresses the limitations of existing models for dynamical systems, which are narrow in scope and treat systems monolithically, by enabling unified representation across domains like electrical and hydraulic systems, though it appears incremental as it builds on geometric mechanics.
The authors tackled the problem of modeling coupled dynamical systems across domains, proposing Poisson-Dirac Neural Networks (PoDiNNs) to unify port-Hamiltonian and Poisson formulations, resulting in improved accuracy and interpretability in experiments.
Deep learning has achieved great success in modeling dynamical systems, providing data-driven simulators to predict complex phenomena, even without known governing equations. However, existing models have two major limitations: their narrow focus on mechanical systems and their tendency to treat systems as monolithic. These limitations reduce their applicability to dynamical systems in other domains, such as electrical and hydraulic systems, and to coupled systems. To address these limitations, we propose Poisson-Dirac Neural Networks (PoDiNNs), a novel framework based on the Dirac structure that unifies the port-Hamiltonian and Poisson formulations from geometric mechanics. This framework enables a unified representation of various dynamical systems across multiple domains as well as their interactions and degeneracies arising from couplings. Our experiments demonstrate that PoDiNNs offer improved accuracy and interpretability in modeling unknown coupled dynamical systems from data.