Self-Guided Diffusion Model for Accelerating Computational Fluid Dynamics

Abstract: Machine learning methods, such as diffusion models, are widely explored as a promising way to accelerate high-fidelity fluid dynamics computation via a super-resolution process from faster-to-compute low-fidelity input. However, existing approaches usually make impractical assumptions that the low-fidelity data is down-sampled from high-fidelity data. In reality, low-fidelity data is produced by numerical solvers that use a coarser resolution. Solver-generated low-fidelity data usually sacrifices fine-grained details, such as small-scale vortices compared to high-fidelity ones. Our findings show that SOTA diffusion models struggle to reconstruct fine-scale details when faced with solver-generated low-fidelity inputs. To bridge this gap, we propose SG-Diff, a novel diffusion model for reconstruction, where both low-fidelity inputs and high-fidelity targets are generated from numerical solvers. We propose an \textit{Importance Weight} strategy during training that serves as a form of self-guidance, focusing on intricate fluid details, and a \textit{Predictor-Corrector-Advancer} SDE solver that embeds physical guidance into the diffusion sampling process. Together, these techniques steer the diffusion model toward more accurate reconstructions. Experimental results on four 2D turbulent flow datasets demonstrate the efficacy of \model~against state-of-the-art baselines.