Constants of motion network reexamined

Discovering constants of motion is meaningful in helping understand the dynamical systems, but it inevitably needs proficient mathematical skills and keen analytical capabilities. With the prevalence of deep learning, methods employing neural networks, such as Constant of Motion Networkk (COMET), are promising in handling this scientific problem. While the COMET method improves dynamic predictions by leveraging discovered constants of motion, there remains significant room for further refinement. In this paper, we propose a neural network architecture, built using the singular-value-decomposition 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.