用统一框架建模跨领域耦合系统，提升精度与可解释性
Poisson-Dirac Neural Networks for Modeling Coupled Dynamical Systems across Domains
- 基于狄拉克结构构建统一神经网络框架
- 在未知耦合系统上实现更高预测精度与可解释性
- 适合电气、液压等非机械系统的建模研究者
深度学习在建模动力系统方面取得显著进展，可提供无需已知控制方程的数据驱动模拟器。然而现有模型存在两大局限：主要聚焦于机械系统，且常将系统视为整体。这限制了其在电气、液压等其他领域以及耦合系统中的应用。为此，本文提出泊松-狄拉克神经网络（PoDiNN），基于狄拉克结构，统一了几何力学中的端口-哈密顿与泊松形式。该框架能统一表示多领域动力系统及其耦合带来的相互作用与退化现象。实验表明，PoDiNN在从数据中建模未知耦合系统时，具有更高的精度和可解释性。
原文摘要 · Abstract (English)
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.
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