| title | PDE-JEPA: Predictive Representation Learning of Latent Dynamics Modeling for Parametric PDEs |
|---|---|
| authors | Zhentao Tan, Jianrong Zhang, Ruijie Quan, Yi Yang |
| date | 2026-09-28 |
| venue | arXiv (preprint, not peer reviewed) |
| id | arXiv:2609.34715 |
| affiliation | Zhejiang University |
| upvotes | 36 (Hugging Face Daily Papers, 2026-11-01) |
| links | abs pdf hf code |
| abstract | Physical trajectories contain more than snapshots of a system: they also reveal how its states evolve under governing conditions. However, representation learning for parametric partial differential equations (PDEs) has largely relied on reconstruction-based objectives that emphasize recovering observed physical fields. In this paper, we investigate predictive representation pretraining as an alternative to reconstruction-based learning. We find that predictive representations preserve rich physical information, yet this advantage alone does not ensure accurate field evolution. Based on these observations, we introduce PDE-JEPA for parametric PDE dynamics. Specifically, we first train an encoder using a masked-latent prediction to capture the underlying regularities of PDE dynamics. To explicitly adapt the pretrained representation toward a more dynamics-aligned state space, we then introduce a geometry projector that aligns latent trajectory geometry with the evolution geometry of physical fields. Finally, building on this geometry-aligned latent space, we further develop a physics-structured latent predictor that decomposes the dynamics into parameter-independent evolution and parameter-dependent response components. Extensive experiments on nine widely used PDE benchmarks demonstrate that our framework outperforms existing state-of-the-art methods by an average of 33.4\% in-distribution, while achieving an average improvement of 51.4\% when extrapolating to unseen governing parameters. The project page is available https://tanpig-x.github.io/PDE-JEPA/{here}. |
cite
@misc{tan2026pde,
title={PDE-JEPA: Predictive Representation Learning of Latent Dynamics Modeling for Parametric PDEs},
author={Zhentao Tan and Jianrong Zhang and Ruijie Quan and Yi Yang},
year={2026},
eprint={2609.34715},
archivePrefix={arXiv},
url={https://arxiv.org/abs/2609.34715}
}