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

Björn Lütjens, Catherine H. Crawford, Campbell D Watson, Christopher Hill, Dava Newman

Keywords: physics-informed machine learning, pinns, scientific machine learning, neural ODEs, neural operators, machine learning, neural networks, Matryoshka, multiphysics, multiscale, parametrizations, closure, subgrid, superstructures, partial differential equations, PDEs, differential equations, numerical solvers, physics, hpc, surrogate, reduced order modeling, model reduction, uncertainty quantification, climate, fluid dynamics, physics, computational physics

TL;DR: We are the first to embed grid-independent neural operators as closure model or parametrization in physical simulations -- in doing so we created a fast and accurate surrogate of multiscale PDEs.

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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