标题： 学习哈密顿神经科伊普曼算子并同时维持和发现守恒定律 显示英文标题

标题： Learning Hamiltonian neural Koopman operator and simultaneously sustaining and discovering conservation law

摘要： 准确地基于带有噪声扰动的观测数据寻找和预测动力学具有重要意义，但目前仍然是一个主要挑战。 在这里，针对哈密顿力学，我们提出了哈密顿神经库普曼算子（HNKO），将数学物理的知识整合到学习库普曼算子的过程中，并使其能够自动维持甚至发现守恒定律。 我们通过多个具有代表性的物理系统展示了 HNKO 及其扩展的优势，即使在具有数百或数千自由度的系统中也是如此。 我们的结果表明，将底层系统的先验知识和数学理论适当输入到学习框架中，可以增强机器学习在解决物理问题方面的能力。 显示英文摘要

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.