arXiv:2602.18060cs.LG2026-02

对比三种物理信息神经网络在力学系统中的表现,发现其对混沌和耗散系统稳定性不足。

Deepmechanics

  • 将哈密顿、拉格朗日与辛递归网络架构用于动力学建模
  • 在六类经典力学系统上测试,轨迹误差在混沌系统中显著上升
  • 适合关注物理引导模型局限性的研究人员参考

物理信息深度学习模型已成为学习动力系统的重要工具,通过将物理原理直接嵌入网络结构实现建模。然而,针对多种物理现象的系统性基准测试仍不充分,尤其在保守与耗散系统方面。现有基准也未全面评估轨迹长期稳定性。本文利用DeepChem开源科学机器学习框架,对三种主流物理信息架构——哈密顿神经网络(HNN)、拉格朗日神经网络(LNN)和辛递归神经网络(SRNN)进行评测。评估涵盖六类动力系统:经典保守系统(质量-弹簧系统、单摆、双摆、三体问题、弹簧摆)及含接触的非保守系统(弹跳球)。通过量化与定性分析预测轨迹误差,结果表明所有模型在混沌或非保守系统中均难以保持长期稳定性,提示需进一步研究以提升物理信息模型在经典力学系统中的鲁棒性。

原文摘要 · Abstract (English)

Physics-informed deep learning models have emerged as powerful tools for learning dynamical systems. These models directly encode physical principles into network architectures. However, systematic benchmarking of these approaches across diverse physical phenomena remains limited, particularly in conservative and dissipative systems. In addition, benchmarking that has been done thus far does not integrate out full trajectories to check stability. In this work, we benchmark three prominent physics-informed architectures such as Hamiltonian Neural Networks (HNN), Lagrangian Neural Networks (LNN), and Symplectic Recurrent Neural Networks (SRNN) using the DeepChem framework, an open-source scientific machine learning library. We evaluate these models on six dynamical systems spanning classical conservative mechanics (mass-spring system, simple pendulum, double pendulum, and three-body problem, spring-pendulum) and non-conservative systems with contact (bouncing ball). We evaluate models by computing error on predicted trajectories and evaluate error both quantitatively and qualitatively. We find that all benchmarked models struggle to maintain stability for chaotic or nonconservative systems. Our results suggest that more research is needed for physics-informed deep learning models to learn robust models of classical mechanical systems.

物理信息网络动力系统深度学习

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