Unsupervised Adaptation of PDE Foundation Models
Pretrained partial differential equation (PDE) foundation models can generalize across different equations, but adapting them to unseen PDE systems typically requires dense solution data, which is often expensive or unavailable. To address this limitation, we propose an unsupervised PDE-based finetuning framework that eliminates the need for ground-truth solutions. We first pretrain a neighborhood attention Transformer on diverse time-dependent PDEs spanning varying spatial scales, yielding transferable representations across heterogeneous equations. In the adaptation stage, we construct a physics-based objective using the PDE residual and boundary conditions, and finetune the model on un...
| Authors | Ziye Song, Zhao Wei, Xin Yu et al. |
|---|---|
| Primary category | cs.AI |
| Published | 7 August 2026 |
| Last updated at source | 7 August 2026 |
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