PDE-Diffusion: Physic guided diffusion model for solving partial derivative equations

Chonghan Gao, Haoyi Zhou, wen xin gong, QING PO WU WU, Tianyu Chen, Qian Yu, Shanghang Zhang, Jianxin Li

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Keywords: AI for science, PDE, diffusion model, generative model

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TL;DR: In this paper we propose to solve PDE with a physical guided diffusion model whose reverse process is conditioned by initial/boundary and PDE guidance.

Abstract: Solving partial differential equations (PDEs) is crucial in various disciplines, and their resolution often necessitates the use of computationally intensive numerical methods as well as specialized domain expertise. While data-driven approaches have emerged as promising alternatives, they encounter limitations in terms of generalizability, interpretability, and long-horizon predictive performance, as well as issues related to temporal incoherence. To address these challenges, we introduce the PDE-Diffusion, a two-stage model with three distinctive features: (i) the incorporation of physics-based priors to enhance model interpretability and generalization, (ii) a two-stage diffusion model that efficiently handles physical field forecasting without requiring multi-frame inputs, and (iii) the assimilation of PDE-informed constraints to ensure temporal coherence while producing high-quality predictive results. We conduct extensive experiments to evaluate PDE-Diffusion's capabilities using the PDEBench dataset and two of our newly proposed datasets. The results indicate that PDE-Diffusion delivers state-of-the-art performance in all cases.

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Submission Number: 9255