Neural Network Model of Discrete-Time Lagrangian Mechanics

Abstract

Satisfying underlying physical laws such as the conservation law of energy is important for physical simulations. Recent studies proposed neural networks that enable a physics simulation with the conservation law of energy. They used numerical integrators such as symplectic integrators or discrete gradient methods for conserving energy. Their approaches depend on the canonical momentum or the velocity. However, obtaining the accurate velocity is difficult because of measurement errors, and their predicted states are greatly different from the real-world physical system. In this paper, we propose a neural network based on discrete-time Lagrangian mechanics, which learns the dynamics only from the position data and conserves the energy. For conserving energy strictly in discrete time, we use discrete gradient methods. For evaluating our approach, we employ physical systems such as a mass-spring system, a pendulum system, and a 2-body system. We show our approach conserves the total energy strictly.