Semigroup Consistency as a Diagnostic for Learned Physics Simulators
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Computer Science > Machine Learning
Title:Semigroup Consistency as a Diagnostic for Learned Physics Simulators
Abstract: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 $\rho = 0.635$ and $95%$ CI $[0.621, 0.649]$. Semigroup regularization has mixed effects, supporting semigroup consistency primarily as an evaluation diagnostic rather than a universally beneficial training objective.
| Comments: | 10 pages, 3 figures, 3 tables. Accepted to the AI4Physics Workshop at the 43rd International Conference on Machine Learning |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Numerical Analysis (math.NA) |
| ACM classes: | I.2.6; I.6.5; G.1.8 |
| Cite as: | arXiv:2605.26324 [cs.LG] |
| (or arXiv:2605.26324v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.26324
arXiv-issued DOI via DataCite (pending registration)
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