2025-04-15 北海道大学,早稲田大学,神戸大学
＜関連情報＞
- https://www.hokudai.ac.jp/news/2025/04/post-1854.html
- https://www.hokudai.ac.jp/news/pdf/250415_pr3.pdf
- https://arxiv.org/abs/2410.11480
ドメインをまたいだ連成系をモデルかするためのポアソン＝ディラックニューラルネットワーク Poisson-Dirac Neural Networks for Modeling Coupled Dynamical Systems across Domains
Razmik Arman Khosrovian, Takaharu Yaguchi, Hiroaki Yoshimura, Takashi Matsubara
arXiv Submitted on 15 Oct 2024
DOI:https://doi.org/10.48550/arXiv.2410.11480
Abstract
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.
