Guiding diffusion models to reconstruct flow fields from sparse data
This work addresses a crucial challenge in engineering applications like Computational Fluid Dynamics by improving flow field reconstruction from limited data, though it is incremental as it builds on existing diffusion models.
The authors tackled the problem of reconstructing unsteady flow fields from sparse measurements by introducing a novel sampling method for diffusion models that guides the reverse process with sparse data and incorporates physics knowledge during training. Their method outperformed other diffusion-based approaches in predicting fluid structure and pixel-wise accuracy on 2D and 3D turbulent flow data.
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.