Raymond A. Yeh

Excited to present our work on CoDA-NO at #NeurIPS2024 We develop a novel neural operator architecture designed to solve coupled partial differential equations (PDEs) in multiphysics systems. Unlike existing approaches that are limited to fixed sets of variables, CoDA-NO can handle varying combinations of physical variables by tokenizing functions along their codomain space. It extends transformer architecture concepts like positional encoding, self-attention, and normalization to function spaces, allowing it to learn representations of different PDE systems with a single model. We demonstrate CoDA-NO's effectiveness through experiments on complex multiphysics problems like fluid-structure interactions and Rayleigh-Bénard convection. Using a two-stage approach of self-supervised pretraining followed by few-shot supervised finetuning, CoDA-NO outperforms existing methods by over 36% on these challenging tasks. The architecture shows strong generalization capabilities, being able to adapt to new physical variables and geometries not seen during training, while maintaining discretization convergence properties that make it resolution-agnostic. Come view our poster on Wednesday the 11th from 11 am to 2 pm PST. Links: Paper: arxiv.org/abs/2403.125532 Poster: neurips.cc/virtual/2024/post… Codebase: github.com/neuraloperator/Co… Authors: @Ashiq_Rahman_s @Robertljg, Mogab Elleithy, @DanielLeibovici, @ZongyiLiCaltech, Boris Bonev, @crwhite_ml, @julberner, @RaymondYeh, @JeanKossaifi, @Azizzadenesheli