Physics-informed Temporal Alignment for Auto-regressive PDE Foundation Models
Congcong Zhu, Xiaoyan Xu, Jiayue Han, Jingrun Chen
Abstract
Auto-regressive partial differential equation (PDE) foundation models have shown great potential in handling time-dependent data. However, these models suffer from error accumulation caused by the shortcut problem deeply rooted in auto-regressive prediction. The challenge becomes particularly evident for out-of-distribution data, as the pretraining performance may approach random model initialization for downstream tasks with long-term dynamics. To deal with this problem, we propose physics-informed temporal alignment (PITA), a self-supervised learning framework inspired by inverse problem solving. Specifically, PITA aligns the physical dynamics discovered at different time steps on each given PDE trajectory by integrating physics-informed constraints into the self-supervision signal. The alignment is derived from observation data without relying on known physics priors, indicating strong generalization ability to out-of-distribution data. Extensive experiments show that PITA significantly enhances the accuracy and robustness of existing foundation models on diverse time-dependent PDE data. The code is available at \url{https://github.com/SCAILab-USTC/PITA}.
BibTeX
@inproceedings{
zhu2025physicsinformed,
title={Physics-informed Temporal Alignment for Auto-regressive {PDE} Foundation Models},
author={Congcong Zhu and Xiaoyan Xu and Jiayue Han and Jingrun Chen},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=OKDN1Hg3im}
}