Neural surrogates systematically under-resolve high-frequency content in multiscale PDEs due to spectral bias and irreversible coarse-graining losses, with success confined to low-dimensional manifolds and weather prediction as a non-generalizable case.
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Predictivity and Utility of Neural Surrogates of Multiscale PDEs
Neural surrogates systematically under-resolve high-frequency content in multiscale PDEs due to spectral bias and irreversible coarse-graining losses, with success confined to low-dimensional manifolds and weather prediction as a non-generalizable case.