A simple equivariant machine learning method for dynamics based on scalars

• URL: http://arxiv.org/abs/2110.03761v2
• Date: Mon, 11 Oct 2021 14:56:33 GMT
• Title: A simple equivariant machine learning method for dynamics based on scalars
• Authors: Weichi Yao and Kate Storey-Fisher and David W. Hogg and Soledad Villar
• Abstract summary: We show that the Scalars method outperforms state-of-the-art approaches for learning the properties of physical systems with symmetries. Because the method incorporates the fundamental symmetries, we expect it to generalize to different settings, such as changes in the force laws in the system.
• Score: 7.224406794844708
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Physical systems obey strict symmetry principles. We expect that machine learning methods that intrinsically respect these symmetries should perform better than those that do not. In this work we implement a principled model based on invariant scalars, and release open-source code. We apply this \textsl{Scalars} method to a simple chaotic dynamical system, the springy double pendulum. We show that the Scalars method outperforms state-of-the-art approaches for learning the properties of physical systems with symmetries, both in terms of accuracy and speed. Because the method incorporates the fundamental symmetries, we expect it to generalize to different settings, such as changes in the force laws in the system.

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