标题： 运动常数网络再访 显示英文标题

标题： Constants of motion network revisited

摘要： 发现运动常数对于理解动力学系统具有重要意义，但不可避免地需要熟练的数学技能和敏锐的分析能力。 随着深度学习的普及，采用神经网络的方法，例如运动常数网络（COMET），在解决这一科学问题方面前景广阔。 尽管COMET方法可以通过利用发现的运动常数来获得更好的动力学预测，但仍有许多改进的空间。 本文提出了一种基于奇异值分解（SVD）技术的新神经网络架构以及两阶段训练算法，以提升COMET的性能。 广泛的实验表明，我们的方法不仅保留了COMET的优点，例如适用于非哈密顿系统并指示运动常数的数量，而且相较于COMET更加轻量且抗噪。 显示英文摘要

摘要： Discovering constants of motion is meaningful in helping understand the dynamical systems, but inevitably needs proficient mathematical skills and keen analytical capabilities. With the prevalence of deep learning, methods employing neural networks, such as Constant Of Motion nETwork (COMET), are promising in handling this scientific problem. Although the COMET method can produce better predictions on dynamics by exploiting the discovered constants of motion, there is still plenty of room to sharpen it. In this paper, we propose a novel neural network architecture, built using the singular-value-decomposition (SVD) technique, and a two-phase training algorithm to improve the performance of COMET. Extensive experiments show that our approach not only retains the advantages of COMET, such as applying to non-Hamiltonian systems and indicating the number of constants of motion, but also can be more lightweight and noise-robust than COMET.