Multiscale Neural Operator: Learning Fast and Grid-independent PDE Solvers
This work addresses the problem of expensive simulations in fields like climate and chemistry by providing a faster, more flexible surrogate model, though it is incremental as it builds on existing multiscale modeling and neural operator techniques.
The paper tackles the computational expense of high-resolution numerical simulations for uncertainty quantification by proposing a hybrid surrogate model that combines known physics with machine learning to learn grid-independent parametrizations, achieving quasilinear runtime complexity and demonstrating improved accuracy or flexibility on the multiscale Lorenz96 chaotic equation.
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.