Deep Learning-Based Discrete-Time Simulation of Physical Phenomena and its Energetic Behavior

Abstract

Machine learning-based modeling of physics phenomena is expected to accelerate simulations and to find a new phenomenon. Physics phenomena are often associated with conservation and dissipation laws of certain quantities. A dependable simulation must guarantee the laws of physics in discrete time. In this paper, we propose a deep learning-based modeling that ensures such laws of physics, and automatic discrete differentiation algorithm, which is an algorithm that ensures the laws in discrete-time. Experimental results demonstrate that the proposed framework ensures the energy conservation and dissipation laws up to the rounding error, and it learns a given dynamics more accurately than existing methods based on ordinary numerical integrators.