@inproceedings{
rahman2024pretraining,
title={Pretraining Codomain Attention Neural Operators for Solving Multiphysics {PDE}s},
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},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=wSpIdUXZYX}
}
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-Bénard convection, we found CoDA-NO to outperform existing methods by over 36%.
Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs
Md Ashiqur Rahman Robert Joseph George Mogab Elleithy Daniel Leibovici Zongyi Li Boris Bonev Colin White Julius Berner Raymond A. Yeh Jean Kossaifi Kamyar Azizzadenesheli Anima Anandkumar