When Can World Models Recover Physical Laws?
Read the original on arXiv AI →The Flow has not summarised this story yet — read it at arXiv AI.
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The paper introduces a world model that learns to predict the evolution of physical systems while respecting key physical principles. By hard‑coding a general structure—generating dynamics from the gradient of a learned energy via a fixed reversible operator and imposing constraints on energy, dissipation, and interventions—the model achieves second‑law compatible dissipation, accurate responses to parameter changes, long‑term stability, and robustness to disturbances. Experiments on an electromagnetic cavity, a particle‑in‑cell grid, and shallow‑water fluid demonstrate that the model can recover accurate constitutive functions, distinguish conserving from dissipating regimes, and transfer learned physics to unseen conditions, outperforming unconstrained models.
arXiv:2609.23381v1 Announce Type: new Abstract: Before a machine can discover a physical law, it must discover what its measurements are: which observations live on cells, which are intensive or exte...
The paper presents a nonlinear dissipative dynamical model of human learning, featuring a concept‑transfer matrix, per‑concept forgetting rates, and a saturating practice‑response gain. It proves a structural identifiability theorem that guarantees exact parameter recovery under explicit excitation conditions, provides closed‑form recovery for the two‑concept case, and introduces a fast, L‑stable numerical scheme enabling estimation on large learner cohorts. Empirical results show exact recovery on synthetic data with designed excitation, but failure to recover on large observational benchmarks, illustrating a sharp boundary between identifiable and unidentifiable regimes and offering a validation protocol for interpretability claims.
LLM-IDEA is an identifiability‑driven experimental agent that guides large language model scientists in autonomous discovery of mechanistic world models. It evaluates whether a plateau in learning is due to the agent’s capability limits, the model’s resolvability within the design class, or a certified exhaustion of the experiment space. The system demonstrates its effectiveness across benchmarks such as ODEBench, DiscoverPhysics, and a custom Alien Universe testbed, consistently identifying when additional experiments are futile and when new experimental designs are required.
The paper introduces LLM-IDEA, an identifiability‑driven experimental agent that guides large language model scientists in closed‑loop discovery of mechanistic world models. It incorporates an identifiability engine that classifies experimental plateaus as capability limits, resolvable within the design class, or certified exhausted, and demonstrates its effectiveness on benchmarks such as ODEBench, DiscoverPhysics, and a custom Alien Universe testbed. The agent’s ability to distinguish when further experimentation is futile versus when new designs are needed improves the efficiency and reliability of autonomous scientific discovery.
The paper investigates when the integrated information measure ζ (phi) can be reliably identified from finite, noisy experiments in small stochastic networks. It shows that even identical input‑output behavior can hide large differences in phi, that partial recordings impose hard precision limits, and that phi is highly sensitive to infinitesimal mechanism changes, often misreported by surrogate models. The authors prove that a lower bound on phi can be certified with controlled experiments and quantify the sample size needed for statistical confidence.