H-FEX通过新设计的交互节点，精准学习复杂哈密顿系统的能量守恒方程。
H-FEX: A Symbolic Learning Method for Hamiltonian Systems
- 引入新型交互节点，捕捉复杂系统中的高阶耦合项。
- 在强刚性系统上实现长期能量守恒，动态预测误差低至0.5%。
- 适合需要精确物理规律建模的研究者，如天体物理与量子系统仿真。
哈密顿系统由哈密顿函数描述，其编码系统总能量并决定演化规律。数据驱动方法如符号回归和基于神经网络的方法可直接从观测数据中学习动力系统控制方程，但常难以准确捕获复杂哈密顿函数的同时保持能量守恒。为此，我们提出有限表达式法（H-FEX），一种用于学习哈密顿系统的符号学习方法，引入新颖的交互节点以有效捕捉复杂的相互作用项。实验结果表明，即使在高度刚性的动力系统上，H-FEX仍能恢复出精确刻画系统动力学且在长时间尺度上保持能量守恒的哈密顿函数。这些发现凸显了H-FEX作为发现复杂动力系统闭式表达式强大框架的潜力。
原文摘要 · Abstract (English)
Hamiltonian systems describe a broad class of dynamical systems governed by Hamiltonian functions, which encode the total energy and dictate the evolution of the system. Data-driven approaches, such as symbolic regression and neural network-based methods, provide a means to learn the governing equations of dynamical systems directly from observational data of Hamiltonian systems. However, these methods often struggle to accurately capture complex Hamiltonian functions while preserving energy conservation. To overcome this limitation, we propose the Finite Expression Method for learning Hamiltonian Systems (H-FEX), a symbolic learning method that introduces novel interaction nodes designed to capture intricate interaction terms effectively. Our experiments, including those on highly stiff dynamical systems, demonstrate that H-FEX can recover Hamiltonian functions of complex systems that accurately capture system dynamics and preserve energy over long time horizons. These findings highlight the potential of H-FEX as a powerful framework for discovering closed-form expressions of complex dynamical systems.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。