Dimensionless machine learning: Imposing exact units equivariance

• URL: http://arxiv.org/abs/2204.00887v1
• Date: Sat, 2 Apr 2022 15:46:20 GMT
• Title: Dimensionless machine learning: Imposing exact units equivariance
• Authors: Soledad Villar and Weichi Yao and David W. Hogg and Ben Blum-Smith and Bianca Dumitrascu
• Abstract summary: We provide a two stage learning procedure for units-equivariant machine learning. We first construct a dimensionless version of its inputs using classic results from dimensional analysis. We then perform inference in the dimensionless space.
• Score: 7.9926585627926166
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Units equivariance 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 employ dimensional analysis and ideas from equivariant machine learning to provide a two stage learning procedure for units-equivariant machine learning. For a 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.

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