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This paper identifies two distinct failures in learned physical simulators—instability in long rollouts and inability to adapt to changed laws—and proposes separate structural solutions: symplectic integration for stability and explicit factorization for counterfactual generalization.
HypNO introduces a graph-based neural operator that uses physics-informed message passing on a space-time finite-volume cell graph to solve scalar hyperbolic conservation laws, accurately capturing shocks and discontinuities. The method is benchmarked on LWR and ARZ traffic-flow models.
This paper develops conservation laws for diffusion models using generalized extrinsic information transfer (GEXIT) functions, showing that the cross-entropy can be characterized as an integral of local information-theoretic derivatives along the noise path, unifying likelihood characterization for discrete and continuous diffusion.
A blog post explaining Hamiltonian Neural Networks through differential geometry, using a simple mass-spring system to demonstrate how imposing conservation laws via network architecture can lead to more efficient learning. The author builds up mathematical tools like symplectic manifolds and Poisson brackets from basic calculus.
This paper studies when conservation laws can be certified in learned latent world models, proposing bounded horizons that guarantee how long rollouts stay on physical invariant level sets using measurable model defects.
This paper studies restless bandits with binary latent states and imperfect binary feedback, developing a partial conservation laws (PCL)-based framework for establishing indexability and computing the Whittle index, with applications to opportunistic spectrum access.
This paper proposes a new architecture that augments Flux Neural Operators with recurrent Vision Transformers to solve conservation laws as a foundation model. It demonstrates robust generalization and long-time prediction capabilities across diverse conservative systems without explicit access to governing equations.