  Physical systems obey strict symmetry principles. We expect that machine
learning methods that intrinsically respect these symmetries should have higher
prediction accuracy and better generalization in prediction of physical
dynamics. 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.
