Constants of motion network
This addresses the challenge of manually finding conserved quantities in physics, which is crucial for understanding system dynamics but often requires expert analytical skills, offering a more automated and generalizable approach.
The paper tackles the problem of automatically discovering constants of motion in physical systems from data, presenting a neural network that learns both system dynamics and these constants, resulting in improved prediction accuracy and broader applicability compared to Hamiltonian-based neural networks.
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.