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.

翻译：近年来，神经偏微分方程求解器领域的研究重点集中在神经算子（neural operators）上。然而，Brandstetter等人在ICLR 2022上发表的论文《消息传递神经PDE求解器》重新审视了自回归模型，并设计了一种基于消息传递的图神经网络，其泛化能力和性能可与最先进的傅里叶神经算子及传统经典PDE求解器相媲美甚至更优。本篇博文深入探讨了该工作的关键贡献，分析了解决自回归模型常见不稳定性问题的策略，以及消息传递图神经网络架构的设计选择。