mlsanityData to 14 Oct 2026

A simple equivariant machine learning method for dynamics based on scalars

arXiv 2110.03761 ↗First posted 7 Oct 2021cs.LGcited by 6

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Abstract (arXiv)

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.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 20 of its 31 references that are in the map. First posted on arXiv 7 Oct 2021.

Builds on

20 of 31 references.

References · 20

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8 more
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  3. 2021Coordinate Independent Convolutional Networks -- Isometry and Gauge Equivariant Convolutions on Riemannian Manifoldscited by 73
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Cited by year

Citing papers per year: 2021: 1; 2022: 4; 2023: 1.

6 papers.

  1. 2022Low Dimensional Invariant Embeddings for Universal Geometric Learningcited by 38
  2. 2022Dimensionless machine learning: Imposing exact units equivariancecited by 17
  3. 2021ZZ-Net: A Universal Rotation Equivariant Architecture for 2D Point Cloudscited by 15
  4. 2022Exact conservation laws for neural network integrators of dynamical systemscited by 15
  5. 2022Machine learning and invariant theorycited by 13
  6. 2023Towards fully covariant machine learningcited by 10