arXiv:2605.26324v1 Announce Type: new 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 Co
The proliferation of learned physics simulators necessitates robust validation metrics beyond short-term accuracy, and the paper proposes 'semigroup consistency' as a diagnostic to address this. This timing reflects the maturation of AI in scientific computing and the increasing need for reliable long-term predictions from these models.
This work introduces a critical diagnostic tool for evaluating learned physics simulators, which are foundational for advancing AI in scientific discovery, engineering, and autonomous systems. Ensuring long-term consistency is paramount for deploying AI in high-stakes applications.
The standard for evaluating physics simulators shifts to include not just short-term predictive accuracy but also long-term temporal consistency, potentially leading to more reliable and trustworthy AI models for dynamic systems. This will force developers to consider new types of validation tests.
- · AI researchers in scientific computing
- · Developers of physics simulators
- · Industries relying on long-term AI predictions (e.g., climate, engineering)
- · Autonomous systems developers
- · AI models that overfit to short-term data but lack temporal consistency
- · Developers neglecting rigorous long-term validation
- · Applications where current simulator reliability is overstated
Improved reliability and deeper understanding of learned physics simulators' long-term behavior become possible through 'semigroup consistency' analysis.
The adoption of such robust diagnostics fosters greater trust and accelerates the deployment of AI in complex scientific and engineering domains where long-horizon accuracy is crucial.
This could contribute to breakthroughs in areas requiring highly accurate and stable long-term predictions, from climate modeling to advanced materials science and autonomous decision-making.
This signal links to a primary source. Continuum Brief monitors and indexes it as part of the live intelligence stream — we do not republish source content.
Read at arXiv cs.LG