Shell-horizon certificates bound rollout steps on decoded physical invariants from measurable model defects in latent world models, showing some geometric priors survive representation learning while others do not.
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A product-kernel interpolation method is proposed that augments state with parameters to produce symplectic large-step predictors for Hamiltonian dynamics by construction, with error bounds that extend from the non-parameterized case.
Comparative experiments on three chaotic systems find that architectures using integrator-like updates exhibit lower bias, reduced perturbation amplification, and more stable long-horizon rollouts than other common designs when model capacity is matched.
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Symplecticity-preserving prediction of parameter-dependent Hamiltonian dynamics by Generalized Kernel Interpolation
A product-kernel interpolation method is proposed that augments state with parameters to produce symplectic large-step predictors for Hamiltonian dynamics by construction, with error bounds that extend from the non-parameterized case.