Autoregressive Renaissance in Neural PDE Solvers

Yolanne Yi Ran Lee

Keywords: neural PDE solvers, message passing, autoregressive models, graph neural network

Abstract: Recent developments in the field of neural partial differential equation (PDE) solvers have placed a strong emphasis on neural operators. However, the paper "Message Passing Neural PDE Solver" by Brandstetter et al. published in ICLR 2022 revisits autoregressive models and designs a message passing graph neural network that is comparable with or outperforms both the state-of-the-art Fourier Neural Operator and traditional classical PDE solvers in its generalization capabilities and performance. This blog post delves into the key contributions of this work, exploring the strategies used to address the common problem of instability in autoregressive models and the design choices of the message passing graph neural network architecture.

Blogpost Url: https://iclr-blogposts.github.io/2023/blog/2023/autoregressive-neural-pde-solver/

ICLR Papers: https://openreview.net/forum?id=vSix3HPYKSU

ID Of The Authors Of The ICLR Paper: ~Johannes_Brandstetter1, ~Daniel_E._Worrall1, ~Max_Welling1

Conflict Of Interest: No

Community Implementations: [ 3 code implementations](https://www.catalyzex.com/paper/arxiv:2310.19763/code)