稳定端口哈密顿神经网络
Stable Port-Hamiltonian Neural Networks
AI总结：
本文提出稳定端口哈密顿神经网络，通过引入能量守恒与耗散物理偏置保证全局稳定性，在稀疏数据下实现鲁棒且物理一致的动力学学习，优于纯数据驱动方法。
摘要：
近年来，利用人工神经网络进行非线性动态系统辨识因其在科学与工程中的广泛潜在应用而受到关注。然而，纯数据驱动的方法通常在外推方面存在困难，并可能产生物理上不可信的预测。此外，学习到的动力学可能表现出不稳定性，使得此类模型难以被安全且鲁棒地应用。本文介绍了稳定端口哈密顿神经网络，这是一种机器学习架构，其融入了能量守恒与耗散的物理偏置，同时保证所学动力学的全局李雅普诺夫稳定性。通过说明性示例和真实世界示例，我们证明了这些强归纳偏置有助于从稀疏数据中鲁棒地学习稳定动力学，同时避免不稳定性，并在准确性和具有物理意义的泛化方面超越纯数据驱动方法。此外，该模型的适用性以及用于数据驱动代理建模的潜力在多物理场仿真数据上得到了展示。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
