Normalized semigroup error is introduced as a diagnostic for learned simulators on 1D heat and Burgers equations; it correlates with rollout degradation (Spearman ρ=0.635) while regularization shows mixed results.
arXiv preprint arXiv:2006.09535 , year =
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Symplectic Neural Operators preserve symplectic structure for learning infinite-dimensional Hamiltonian PDEs and deliver improved long-term energy stability in theory and experiments.
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Semigroup Consistency as a Diagnostic for Learned Physics Simulators
Normalized semigroup error is introduced as a diagnostic for learned simulators on 1D heat and Burgers equations; it correlates with rollout degradation (Spearman ρ=0.635) while regularization shows mixed results.
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Symplectic Neural Operators for Learning Infinite Dimensional Hamiltonian Systems
Symplectic Neural Operators preserve symplectic structure for learning infinite-dimensional Hamiltonian PDEs and deliver improved long-term energy stability in theory and experiments.