让神经网络学物理：用能量守恒保证稳定，小数据也能准预测。
Stable Port-Hamiltonian Neural Networks
- 在神经网络中嵌入能量守恒与耗散的物理规律
- 在稀疏数据下仍能保持动态稳定且预测更准
- 适合需要安全可靠建模的工程仿真场景
近年来，利用人工神经网络进行非线性动态系统识别受到广泛关注，因其在科学与工程中的广泛应用潜力。然而，纯数据驱动方法常面临外推能力差和产生物理上不合理的预测问题，且学习到的动力学可能不稳定，难以安全可靠地应用。本文提出稳定的端口-哈密顿神经网络，通过引入能量守恒与耗散的物理先验，确保学习到的动力学具有全局李雅普诺夫稳定性。通过示范性及真实世界案例，我们证明这些强归纳偏置有助于从稀疏数据中稳健学习稳定动力学，避免不稳定现象，并在准确性和物理可解释的泛化能力上超越纯数据驱动方法。此外，该模型在多物理场仿真数据上展示了其在数据驱动代理建模中的适用性与潜力。
原文摘要 · Abstract (English)
In recent years, nonlinear dynamic system identification using artificial neural networks has garnered attention due to its broad potential applications across science and engineering. However, purely data-driven approaches often struggle with extrapolation and may yield physically implausible forecasts. Furthermore, the learned dynamics can exhibit instabilities, making it difficult to apply such models safely and robustly. This article introduces stable port-Hamiltonian neural networks, a machine learning architecture that incorporates physical biases of energy conservation and dissipation while ensuring global Lyapunov stability of the learned dynamics. Through illustrative and real-world examples, we demonstrate that these strong inductive biases facilitate robust learning of stable dynamics from sparse data, while avoiding instability and surpassing purely data-driven approaches in accuracy and physically meaningful generalization. Furthermore, the model's applicability and potential for data-driven surrogate modeling are showcased on multi-physics simulation data.
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