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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.