Latent Dynamics · 2026-10-02
Stable and Counterfactually Robust Physical World Models from Imposed Structure and Learned Physics
Yufeng Wang, Parivesh Priye, Lu Wei, Haibin Ling
AI-assisted summary based on the paper. Consult the linked source for methods and limitations. Benchmark numbers appear after editor verification.
TL;DR
The authors impose general physical structure on a learned world model—dynamics from gradients of a learned energy through a fixed reversible operator, a confining energy class, and a one-way dissipation port—and learn system-specific physics from trajectories. Across three physical regimes, a single structured model recovers constitutive functions and dissipation rate, transfers counterfactual interventions on supplied parameters, stays stable up to 100× the training horizon, and refuses interventions without a supplied parameter map.
Why it matters
World models often violate conservation, drift over long rollouts, and answer counterfactual law queries using the law seen in training. The paper tests how much general physics must be hard-coded so learned models simultaneously achieve second-law-compatible dissipation, correct parameter interventions, long-horizon stability, and disturbance robustness—plus specifies when counterfactuals are answerable by construction.
Method
- Impose a physical form: antisymmetric reversible operator acting on the gradient of a learned energy; confining energy class; scalar one-way dissipation port; known drive channel; intervened parameter enters via a separable factored map; learn energy, constitutive relations, dissipation rate, and couplings from trajectories.
- Evaluate four target behaviors (second-law-compatible dissipation, correct interventions, stability to 100× training horizon, robustness to disturbances) using controls that remove one structural component at a time, plus equal-capacity unstructured and oracle interventions.
- Measure rollout accuracy (normalised MSE), energy behavior (relative drift of true energy), and learned-rate error (relative error vs true rate), with repeated random initialisations and comparison against structured/ablated baselines.
Limitation
The dissipative-port guarantee is scoped to a quadratic diagnostic energy on the port channel and the implemented discrete update; it does not apply to the learned energy, drives/thermal noise, or arbitrary damping matrices. The full-model temperature results remain empirical.
Abstract (from arXiv)
A world model learns to forecast how a physical system evolves from recorded trajectories, yet the systems it imitates obey physical laws that are neither fully supplied nor reliably respected. The model may create energy, drift or diverge over long rollouts, and answer a changed law query using the law observed during training. We ask how much general physical structure must be hard coded into a world model, and how much system-specific physics can then be learned from data, for four properties to hold simultaneously: second law compatible dissipation, correct responses to interventions on physical parameters, stability out to one hundred times the training horizon, and robustness to disturbances. The imposed structure is general: dynamics are generated from the gradient of a learned energy through a fixed reversible operator, the energy is restricted to a confining class, a one way port can remove energy but never inject it, the drive channel is known, and the intervened parameter enters through a separable map. The model learns the energy functional, constitutive relations, dissipation rate, and couplings. Across an electromagnetic cavity, a particle in cell grid, and a shallow-water fluid, models with roughly nine thousand parameters recover constitutive functions with unit slope, separate conserving from dissipating worlds by four orders of magnitude using a single set of weights, and transfer changes in sign, magnitude, rate, and gravity to unseen values, where equal-capacity models without the same structure perform at chance or worse. A nonlinear constitutive law is recovered with its curvature preserved and predicts a held-out intervention $2$-$17\times$ better than a converged linear model.
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Publication record
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First public release: 2026-09-24 · Indexed by Pub-AI: 2026-10-02 UTC
Stable and Counterfactually Robust Physical World Models from Imposed Structure and Learned Physics
Preprint posted: 2026-09-24 · Original record ↗
- arxiv
- 2610.00280
Explicit source versions (1)
- v1 · 2026-09-24
- Preprint available
Source date: 2026-09-24 · First detected: 2026-10-25 UTC · Historical baseline
Source evidence (1)
- Official evidence ↗ · atom:published (official metadata)
Abstract · arxiv
A world model learns to forecast how a physical system evolves from recorded trajectories, yet the systems it imitates obey physical laws that are neither fully supplied nor reliably respected. The model may create energy, drift or diverge over long rollouts, and answer a changed law query using the law observed during training. We ask how much general physical structure must be hard coded into a world model, and how much system-specific physics can then be learned from data, for four properties to hold simultaneously: second law compatible dissipation, correct responses to interventions on physical parameters, stability out to one hundred times the training horizon, and robustness to disturbances. The imposed structure is general: dynamics are generated from the gradient of a learned energy through a fixed reversible operator, the energy is restricted to a confining class, a one way port can remove energy but never inject it, the drive channel is known, and the intervened parameter enters through a separable map. The model learns the energy functional, constitutive relations, dissipation rate, and couplings. Across an electromagnetic cavity, a particle in cell grid, and a shallow-water fluid, models with roughly nine thousand parameters recover constitutive functions with unit slope, separate conserving from dissipating worlds by four orders of magnitude using a single set of weights, and transfer changes in sign, magnitude, rate, and gravity to unseen values, where equal-capacity models without the same structure perform at chance or worse. A nonlinear constitutive law is recovered with its curvature preserved and predicts a held-out intervention $2$-$17\times$ better than a converged linear model.