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A simple equivariant machine learning method for dynamics based on scalars
Weichi Yao · Kate Storey-Fisher · David W Hogg · Soledad Villar

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 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.

Author Information

Weichi Yao (New York University)
Kate Storey-Fisher (New York University)

Kate Storey-Fisher is a PhD candidate in Physics at New York University and a NASA FINESST Fellow. Her research is on the large-scale structure of the universe, focusing on statistical and data-science methods for observational cosmology.

David W Hogg (New York University)

David W Hogg is Professor of Physics and Data Science at New York University and Group Leader of the Astronomical Data Group at the Flatiron Institute. His work is on computational data analysis in all areas of astrophysics, from extra-solar planet discovery to mapping the dark matter to measuring the expansion history of the Universe.

Soledad Villar (Johns Hopkins University)

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