Trained physics models need no retraining: group averaging enforces symmetry on pretrained predictors, even for non-compact groups
A trained physics surrogate can be made to respect a known symmetry at test time by transforming the input over the symmetry group, transforming the prediction back, and averaging, without changing the architecture or retraining. For compact groups this averaging carries a known non-increasing-risk guarantee and lowered errors on several The Well surrogates; for non-compact groups such as unit rescalings and the Lorentz group, normalized averaging no longer exists, and the Weyl trick and frame averaging gave clear gains mainly out of distribution or in low-data regimes, while models trained directly on invariant features matched or beat them.