Constants of motion network revisited
This work addresses the challenge of automating constant discovery in dynamical systems for researchers, offering an incremental improvement over existing deep learning methods.
The paper tackles the problem of discovering constants of motion in dynamical systems by proposing a novel neural network architecture using singular-value-decomposition and a two-phase training algorithm to improve the COMET method, resulting in a more lightweight and noise-robust approach that retains advantages like applicability to non-Hamiltonian systems.
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.