mlsanityData to 13 Oct 2026

Semigroup Consistency as a Diagnostic for Learned Physics Simulators

arXiv 2605.26324 ↗First posted 25 May 2026cs.LG cs.AI cs.NAcited by 3

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Abstract (arXiv)

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 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.

Key facts. Cited by 3 papers in the map (data through 13 Oct 2026). Builds on 27 of its 40 references that are in the map. First posted on arXiv 25 May 2026.

Builds on

27 of 40 references.

References · 27

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15 more
  1. 2023Convolutional Neural Operators for robust and accurate learning of PDEscited by 209
  2. 2022FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operatorscited by 188
  3. 2024The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learningcited by 140
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  10. 2025SIMSHIFT: A Benchmark for Adapting Neural Surrogates to Distribution Shiftscited by 6
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  12. 2026One Operator to Rule Them All? On Boundary-Indexed Operator Families in Neural PDE Solverscited by 5
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  15. 2026Out-of-distribution generalization of deep-learning surrogates for 2D PDE-generated dynamics in the small-data regimecited by 2

Built on by

Cited by year (2026 to 13 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Forecasting Without Full Identification: Reliability and Computational Cost in Clot-Growth Simulationcited by 0
  2. 2026Does Text Steer Neural PDE Surrogates? A Controlled Diagnostic with OperatorCLIPcited by 0
  3. 2026Physics is the Best Teacher: Consistency Learning for Time-Invariant Operators of Chaotic Dynamicscited by 0