mlsanityData to 7 Oct 2026

Dimensionless machine learning: Imposing exact units equivariance

arXiv 2204.00887 ↗First posted 2 Apr 2022stat.ML cs.LG physics.data-ancited by 16

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Abstract (arXiv)

Units equivariance (or units covariance) is the exact symmetry that follows from the requirement that relationships among measured quantities of physics relevance must obey self-consistent dimensional scalings. Here, we express this symmetry in terms of a (non-compact) group action, and we employ dimensional analysis and ideas from equivariant machine learning to provide a methodology for exactly units-equivariant machine learning: For any given learning task, we first construct a dimensionless version of its inputs using classic results from dimensional analysis, and then perform inference in the dimensionless space. Our approach can be used to impose units equivariance across a broad range of machine learning methods which are equivariant to rotations and other groups. We discuss the in-sample and out-of-sample prediction accuracy gains one can obtain in contexts like symbolic regression and emulation, where symmetry is important. We illustrate our approach with simple numerical examples involving dynamical systems in physics and ecology.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 52 of its 95 references that are in the map. First posted on arXiv 2 Apr 2022.

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52 of 95 references.

References · 52

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Citing papers per year: 2022: 1; 2023: 8; 2024: 3; 2025: 1; 2026: 3.

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  1. 2024Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groupscited by 23
  2. 2023Automated Scientific Discovery: From Equation Discovery to Autonomous Discovery Systemscited by 18
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  4. 2026Warm-starting PDE solvers with any-dimensional machine learningcited by 0