Enforcing Symmetries on Pre-trained ML Models for Physics

The paper investigates post‑hoc symmetry enforcement on pre‑trained machine‑learning models used for physics simulations. For finite, compact groups, simple group averaging (the Reynolds operator) projects predictors onto invariant or equivariant functions with non‑increasing risk guarantees, and numerical experiments confirm its effectiveness. The authors extend the framework to non‑compact groups, proposing three alternatives—Weyl unitary trick, data‑dependent orthogonal projection, and frame averaging—each evaluated theoretically and empirically on the unit‑rescaling and Lorentz groups; results show that only the orthogonal projection consistently improves performance, while the other methods help mainly in out‑of‑distribution or low‑data scenarios, and that training directly on invariant features can match or surpass post‑hoc projections.

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