# Autoregressive Renaissance in Neural PDE Solvers

arXiv: https://arxiv.org/abs/2310.19763 · HTML: https://mlsanity.com/paper/2310.19763/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 39 references that are in the map.
- First posted on arXiv 30 Oct 2023.

## Builds on (most cited first, 1 of 1)

- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)

## Built on by (most cited first, 5 of 5)

- [Plasma Surrogate Modelling using Fourier Neural Operators](https://mlsanity.com/paper/2311.05967/) (2023)
- [Learning Physical Operators using Neural Operators](https://mlsanity.com/paper/2602.23113/) (2026)
- [Generalization vs. Memorization in Autoregressive Deep Learning: Or, Examining Temporal Decay of Gradient Coherence](https://mlsanity.com/paper/2509.00024/) (2025)
- [Operator Flow Matching for Timeseries Forecasting](https://mlsanity.com/paper/2510.15101/) (2025)
- [A Multimodal Vision Transformer-based Modeling Framework for Prediction of Fluid Flows in Energy Systems](https://mlsanity.com/paper/2604.02483/) (2026)

## Abstract (arXiv)

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.