  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.
