Law Violation Determines How Strongly Physics Should Constrain Learning

A physical law helps learning only while it matches the observed dynamics; once violated, enforcing it introduces systematic bias. We show that measured law violation determines how strongly physics should constrain a model. Our rule maps an invariance-specific violation to hard constraints, soft penalties, or unconstrained learning using two thresholds calibrated on reference dynamics. Across 12 PDE systems, five conservation or symmetry classes, and nine noise and sample-size regimes, the rule selects a model family before target training. On held-out conservation and mechanism-aligned translation systems, it reduces rollout error by 12.1% relative to a validation-selected fixed CNN. After separate calibration for one Fourier neural operator, it reduces error by 12.8% across 18 conditions and requires one target fit instead of seven. A linear-Gaussian analysis recovers the same three regimes and an inverse-square law for the optimal penalty. Law violation converts constraint choice from a target-specific sweep into a quantitative decision grounded in the observed dynamics.