Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs
Abstract
Existing neural operator architectures face challenges when solving multiphysics problems with coupled partial differential equations (PDEs) due to complex geometries, interactions between physical variables, and the limited amounts of high-resolution training data. To address these issues, we propose Codomain Attention Neural Operator (CoDA-NO), which tokenizes functions along the codomain or channel space, enabling self-supervised learning or pretraining of multiple PDE systems. Specifically, we extend positional encoding, self-attention, and normalization layers to function spaces. CoDA-NO can learn representations of different PDE systems with a single model. We evaluate CoDA-NO's potential as a backbone for learning multiphysics PDEs over multiple systems by considering few-shot learning settings. On complex downstream tasks with limited data, such as fluid flow simulations, fluid-structure interactions, and Rayleigh-B\'enard convection, we found CoDA-NO to outperform existing methods by over 36%.
Cite
@article{arxiv.2403.12553,
title = {Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs},
author = {Md Ashiqur Rahman and Robert Joseph George and Mogab Elleithy and Daniel Leibovici and Zongyi Li and Boris Bonev and Colin White and Julius Berner and Raymond A. Yeh and Jean Kossaifi and Kamyar Azizzadenesheli and Anima Anandkumar},
journal= {arXiv preprint arXiv:2403.12553},
year = {2024}
}