学习哈密顿神经Koopman算子并同时维持与发现守恒定律
Learning Hamiltonian neural Koopman operator and simultaneously sustaining and discovering conservation law
AI总结：
针对含噪声观测数据的动力学预测难题，提出哈密顿神经Koopman算子（HNKO），通过融合数学物理先验知识，实现自动维持与发现守恒定律，并在高自由度物理系统中展现出优越性能。
摘要：
基于含噪声扰动的观测数据准确寻找和预测动力学至关重要，但目前仍是重大挑战。在此，针对哈密顿力学，我们提出了哈密顿神经Koopman算子（HNKO），将数学物理知识融入Koopman算子的学习中，使其自动维持甚至发现守恒定律。我们利用多个具有代表性的物理系统（甚至包含成百上千个自由度）证明了HNKO及其扩展的优越性。结果表明，将底层系统的先验知识和数学理论适当地引入学习框架，能够增强机器学习解决物理问题的能力。
英文摘要：
Accurately finding and predicting dynamics based on the observational data with noise perturbations is of paramount significance but still a major challenge presently. Here, for the Hamiltonian mechanics, we propose the Hamiltonian Neural Koopman Operator (HNKO), integrating the knowledge of mathematical physics in learning the Koopman operator, and making it automatically sustain and even discover the conservation laws. We demonstrate the outperformance of the HNKO and its extension using a number of representative physical systems even with hundreds or thousands of freedoms. Our results suggest that feeding the prior knowledge of the underlying system and the mathematical theory appropriately to the learning framework can reinforce the capability of machine learning in solving physical problems.
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。
