2025/05/16 by Zhu, Congcong, Xu, Xiaoyan, Han, Jiayue +1 · 1 citation
#35Q68 #FOS: Computer and information sciences #G.1.8 #Machine Learning (cs.LG)
paper · doi:10.48550/arxiv.2505.10930
Auto-regressive partial differential equation (PDE) foundation models have shown great potential in handling time-dependent data. However, these models suffer from the shortcut problem deeply rooted in auto-regressive prediction, causing error accumulation. 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 the 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 https://github.com/SCAILab-USTC/PITA.