The beauty of physics is that there is usually a conserved quantity in an
always-changing system, known as the constant of motion. Finding the constant
of motion is important in understanding the dynamics of the system, but
typically requires mathematical proficiency and manual analytical work. In this
paper, we present a neural network that can simultaneously learn the dynamics
of the system and the constants of motion from data. By exploiting the
discovered constants of motion, it can produce better predictions on dynamics
and can work on a wider range of systems than Hamiltonian-based neural
networks. In addition, the training progresses of our method can be used as an
indication of the number of constants of motion in a system which could be
useful in studying a novel physical system.Comment: Accepted to NeurIPS 202