# Codes and Expansions (CodEx) Seminar

## Soledad Villar (Johns Hopkins University)

Equivariant machine learning and dimensional analysis

We combine ideas from dimensional analysis and from equivariant machine learning to provide an approach for units-equivariant machine learning. Units equivariance is the exact symmetry that follows from the requirement that relationships among measured quantities must obey self-consistent dimensional scalings. Our approach is to construct a dimensionless version of the learning task, using classic results from dimensional analysis, and then perform the learning task in the dimensionless space. This approach can be used to impose units equivariance on almost any contemporary machine-learning methods, including those that are equivariant to rotations and other groups. Units equivariance is expected to be particularly valuable in the contexts of symbolic regression and emulation. We discuss the in-sample and out-of-sample prediction accuracy gains one can obtain if exact units equivariance is imposed; the symmetry is extremely powerful in some contexts. We illustrate these methods with simple numerical examples involving dynamical systems in physics and ecology.