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

• URL: http://arxiv.org/abs/2207.11417v1
• Date: Sat, 23 Jul 2022 05:01:03 GMT
• Title: Multiscale Neural Operator: Learning Fast and Grid-independent PDE Solvers
• Authors: Bj\"orn L\"utjens, Catherine H. Crawford, Campbell D Watson, Christopher Hill, Dava Newman
• Abstract summary: We propose a hybrid, flexible surrogate model that exploits known physics for simulating large-scale dynamics. We are the first to learn grid-independent, non-local, and flexible parametrizations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Numerical simulations in climate, chemistry, or astrophysics are computationally too expensive for uncertainty quantification or parameter-exploration at high-resolution. Reduced-order or surrogate models are multiple orders of magnitude faster, but traditional surrogates are inflexible or inaccurate and pure machine learning (ML)-based surrogates too data-hungry. We propose a hybrid, flexible surrogate model that exploits known physics for simulating 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 to learn grid-independent, non-local, and flexible parametrizations. Our \textit{multiscale neural operator} is motivated by a rich literature in multiscale modeling, has quasilinear runtime complexity, is more accurate or flexible than state-of-the-art parametrizations and demonstrated on the chaotic equation multiscale Lorenz96.

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