Semigroup Consistency as a Diagnostic for Learned Physics Simulators
Learned physics simulators are often evaluated by one-step or short-horizon prediction error, but these metrics can miss failures in temporal composition and long-horizon rollout. For autonomous, state-complete systems, exact solution maps satisfy a semigroup law: direct evolution over $s+t$ should agree with evolution over $s$ followed by $t$. We propose normalized semigroup error as a post hoc, model-agnostic diagnostic comparing these direct and composed learned predictions. On one-dimensional heat and Burgers dynamics with time-conditioned ConvNet and FNO baselines, semigroup error is positively associated with rollout degradation, with trajectory-level Spearman correlation $ρ= 0.635$...
| Authors | Lennon J. Shikhman |
|---|---|
| Primary category | cs.LG |
| Published | 25 May 2026 |
| Last updated at source | 25 May 2026 |
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