Deep PDE Solvers for Subgrid Modelling and Out-of-Distribution Generalization

Patrick Chatain, Adam M Oberman

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Keywords: Machine Learning for Sciences, PDE modelling, Subgrid modelling, Out of Distribution Generalization

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TL;DR: A novel architecture for machine learning PDE solvers that permits accurate subgrid modelling and that succeeds in out-of-distribution generalization.

Abstract: Climate and weather modelling (CWM) is an important area where ML models are constantly being used for subgrid modelling: making predictions of processes occurring at scales too small to be resolved (Brasseur & Jacob, 2017). In addition to accuracy, these models are relied on to make accurate predictions even on out-of-distribution data and should respect physical constraints (Kashinath et al., 2021). While many specialized ML PDE solvers have been developed, these particular requirements have not been addressed so far. The challenge we address in this paper is to build subgrid PDE solvers which satisfy these additional requirements of the CWM models. We propose and develop a novel architecture, which matches or exceeds the performance of standard ML models, and which demonstrably succeeds in OOD generalization. The architecture is based on expert knowledge of the structure of PDE solution operators which are designed to obey physical constraints and to enforce numerical stability.

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Submission Number: 4622