Physics-Informed Self-Guided Diffusion Model for High-Fidelity Simulations

Ruoyan Li, Zijie Huang, Yizhou Sun, Wei Wang

Keywords: Physics-informed Neural Networks, Computational Fluid Dynamics

Abstract: Machine learning (ML) models are increasingly explored in fluid dynamics as a promising way to generate high-fidelity computational fluid dynamics data more efficiently. A common strategy is to use low-fidelity data as computational-efficient inputs, and employ ML techniques to reconstruct high-fidelity flow fields. However, existing work typically assumes that low-fidelity data is artificially downsampled from high-fidelity sources, which limits model performance. In real-world applications, low-fidelity data is generated directly by numerical solvers with a lower initial state resolution, resulting in large deviations from high-fidelity data. To address this gap, we propose PG-Diff, a novel diffusion model for reconstructing high-fidelity flow fields, where both low- and high-fidelity data are generated from numerical solvers. Our experiments reveal that state-of-the-art models struggle to recover fine-grained high-fidelity details when using solver-generated low-fidelity inputs, due to distribution shift. To overcome this challenge, we introduce an \textit{Importance Weight} strategy during training as self-guidance and a training-free \textit{Residual Correction} method during inference as physical inductive bias, guiding the diffusion model toward higher-quality reconstructions. Experiments on four 2D turbulent flow datasets demonstrate the effectiveness of our proposed method.

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

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Submission Number: 4262