Guiding diffusion models to reconstruct flow fields from sparse data

2025-10-22

AI Summary

Addressing the critical challenge of high-fidelity reconstruction of unsteady flow fields from sparse measurements, this paper proposes a diffusion-based generative model that synergistically integrates physical priors with data-driven learning. Methodologically, it introduces: (1) an observation-guided conditional reverse sampling scheme that directly incorporates sparse measurements into the denoising process; (2) a conflict-free physics-constrained update strategy that explicitly enforces Navier–Stokes equation regularization during training; and (3) an iterative denoising framework coupled with scale-aware reconstruction to enhance recovery of fine-scale turbulent structures. Evaluated on 2D and 3D direct numerical simulation (DNS) turbulence datasets, the method achieves state-of-the-art performance—outperforming existing diffusion models in structural fidelity, vortex core localization accuracy, and pixel-level metrics (PSNR and SSIM). This work establishes a novel paradigm for physics-informed generative modeling and CFD data assimilation.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Natural Language Processing: Generation

Application Category

• Web Mining and Content Analysis: Web data generation and simulation
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity in solving this problem due to their ability to learn complex patterns from data and generalize across diverse conditions. Among these, diffusion models have emerged as particularly powerful in generative tasks, producing high-quality samples by iteratively refining noisy inputs. In contrast to other methods, these generative models are capable of reconstructing the smallest scales of the fluid spectrum. In this work, we introduce a novel sampling method for diffusion models that enables the reconstruction of high-fidelity samples by guiding the reverse process using the available sparse data. Moreover, we enhance the reconstructions with available physics knowledge using a conflict-free update method during training. To evaluate the effectiveness of our method, we conduct experiments on 2 and 3-dimensional turbulent flow data. Our method consistently outperforms other diffusion-based methods in predicting the fluid's structure and in pixel-wise accuracy. This study underscores the remarkable potential of diffusion models in reconstructing flow field data, paving the way for their application in Computational Fluid Dynamics research.

Problem

• Reconstructing unsteady flow fields from sparse measurements
• Guiding diffusion models with physics knowledge for reconstruction
• Enhancing accuracy in turbulent flow field predictions

Innovation

• Guided diffusion models reconstruct flow fields
• Physics knowledge enhances reconstructions via conflict-free update
• Method outperforms others in fluid structure prediction