Semigroup Consistency Diagnoses Learned Physics Simulators
A team of researchers has introduced the normalized semigroup error as a tool for assessing learned physics simulators, focusing on long-horizon rollouts and temporal composition in addition to one-step prediction error. In experiments involving one-dimensional heat and Burgers dynamics using time-conditioned ConvNet and FNO benchmarks, a significant correlation was found between semigroup error and rollout degradation (Spearman ρ=0.635, 95% CI [0.621,0.649]). While semigroup regularization exhibited varied outcomes, it is suggested to be more effective as an evaluation diagnostic than as a training goal.
Key facts
- Semigroup consistency compares direct evolution over s+t with evolution over s followed by t.
- Normalized semigroup error is a post hoc, model-agnostic diagnostic.
- Tested on 1D heat and Burgers dynamics with ConvNet and FNO baselines.
- Trajectory-level Spearman correlation ρ=0.635 with 95% CI [0.621,0.649].
- Semigroup regularization has mixed effects.
- Diagnostic is intended for autonomous, state-complete systems.
- Proposed as an evaluation diagnostic rather than training objective.
- Published on arXiv under Computer Science > Machine Learning.
Entities
Institutions
- arXiv