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Workshop: The Symbiosis of Deep Learning and Differential Equations -- III

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

Patrick Chatain · Adam Oberman

Keywords: [ Subgrid modelling ] [ PDE modelling ] [ Machine Learning for Sciences ] [ out of distribution generalization ]


Climate and weather modelling (CWM) is an important area where ML models are used for subgrid modelling: making predictions of processes occurring at scales too small to be resolved by standard solution methods (Brasseur & Jacob, 2017). These models are expected to make accurate predictions, even on out-of-distribution (OOD) data, and are additionally expected to respect important physical constraints of the ground truth model (Kashinath et al., 2021). While many specialized ML PDE solvers have been developed, the particular requirements of CWM models have not been addressed so far. The goal of this work is to address them. 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 permits the model to also obey important physical constraints.

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