Autoregressive Renaissance in Neural PDE Solvers
This work addresses instability issues in autoregressive PDE solvers, offering a competitive alternative for researchers in computational physics and machine learning, though it appears incremental by revisiting autoregressive approaches.
The paper tackles the problem of instability in autoregressive models for neural PDE solvers by designing a message passing graph neural network, achieving comparable or superior generalization and performance to state-of-the-art Fourier Neural Operator and traditional solvers.
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.