arXiv:2602.03627 · v2

Ultra Fast PDE Solving via Physics Guided Few-step Diffusion

首次提交 2026-02-03 23:16

版本更新 2026-11-11 03:14

雷达观测 2026-11-13 11:12

摘要

Diffusion-based models have demonstrated impressive accuracy and generalization in solving partial differential equations (PDEs). However, their practical utility still suffers from high sampling costs and insufficient physical consistency, mainly due to many-step iterative sampling and insufficient physics guidance. To address these issues, we propose \emph{Phys-Instruct}, a physics-guided distillation framework that compresses a pre-trained diffusion PDE solver into a few-step generator while explicitly enforcing PDE consistency through distillation guidance. We reformulate the training objective as a constrained problem with PDE residual, and derive a score-function identity that leads to a practical physics-guided generator update. Across five PDE benchmarks, Phys-Instruct achieves orders-of-magnitude faster inference while reducing the PDE Error by factors of $2.4$ to $15.5$, compared with the corresponding 200-step EDM teachers. Moreover, the resulting unconditional student model functions as a compact prior, enabling efficient and physically consistent inference for various downstream conditional tasks. Our results indicate that Phys-Instruct is an effective and efficient framework for ultra-fast PDE solving powered by generative models.