DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training

TL;DR

This paper introduces DPOT, a large-scale PDE pre-training framework using an auto-regressive denoising strategy and Fourier attention, achieving state-of-the-art results on multiple PDE benchmarks and demonstrating strong generalizability.

Contribution

The paper proposes a novel auto-regressive denoising pre-training method and a scalable Fourier attention-based architecture for large-scale PDE modeling, enabling effective pre-training on diverse PDE datasets.

Findings

Achieves SOTA performance on multiple PDE benchmarks.

Successfully scales up to 0.5B parameters for large PDE datasets.

Demonstrates strong generalization to 3D PDE tasks.

Abstract

Pre-training has been investigated to improve the efficiency and performance of training neural operators in data-scarce settings. However, it is largely in its infancy due to the inherent complexity and diversity, such as long trajectories, multiple scales and varying dimensions of partial differential equations (PDEs) data. In this paper, we present a new auto-regressive denoising pre-training strategy, which allows for more stable and efficient pre-training on PDE data and generalizes to various downstream tasks. Moreover, by designing a flexible and scalable model architecture based on Fourier attention, we can easily scale up the model for large-scale pre-training. We train our PDE foundation model with up to 0.5B parameters on 10+ PDE datasets with more than 100k trajectories. Extensive experiments show that we achieve SOTA on these benchmarks and validate the strong generalizability of our model to significantly enhance performance on diverse downstream PDE tasks like 3D data. Code is available at \url{https://github.com/thu-ml/DPOT}.