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Numerical simulations in climate, chemistry, or astrophysics arecomputationally too expensive for uncertainty quantification orparameter-exploration at high-resolution. Reduced-order or surrogate models aremultiple orders of magnitude faster, but traditional surrogates are inflexibleor inaccurate and pure machine learning (ML)-based surrogates too data-hungry.We propose a hybrid, flexible surrogate model that exploits known physics forsimulating large-scale dynamics and limits learning to the hard-to-model term,which is called parametrization or closure and captures the effect of fine-onto large-scale dynamics. Leveraging neural operators, we are the first tolearn grid-independent, non-local, and flexible parametrizations. Our\textit{multiscale neural operator} is motivated by a rich literature inmultiscale modeling, has quasilinear runtime complexity, is more accurate orflexible than state-of-the-art parametrizations and demonstrated on the chaoticequation multiscale Lorenz96.

Multiscale Neural Operator: Learning Fast and Grid-independent PDE Solvers