Dual guidance: ROM-informed field reconstruction with generative models

2025/06/16 by Sajad Salavatidezfouli, Salavatidezfouli, Sajad, Henrik Karstoft +5
Computer Science · Engineering · #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Image Processing and 3D Reconstruction #Numerical Analysis (math.NA) #Robotics and Sensor-Based Localization

paper · pdf · doi:10.48550/arxiv.2506.13369

openalex publication_date 2025/06/16 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28

Abstract

We present a dual-guided framework for reconstructing unsteady incompressible flow fields using sparse observations. The approach combines optimized sensor placement with a physics-informed guided generative model. Sensor locations are selected using mutual information theory applied to a reduced-order model of the flow, enabling efficient identification of high-information observation points with minimal computational cost. These sensors, once selected, provide targeted observations that guide a denoising diffusion probabilistic model conditioned by physical constraints. Extensive experiments on 2D laminar cylinder wake flows demonstrate that under sparse sensing conditions, the structured sensor layouts fail to capture key flow dynamics, yielding high reconstruction errors. In contrast, our optimized sensor placement strategy achieves accurate reconstructions with L2 errors as low as 0.05, even with a limited number of sensors, confirming the effectiveness of the proposed approach in data-limited regimes. When the number of sensors is higher than a threshold, however, both methods perform comparably. Our dual-guided approach bridges reduced order model-based sensor position optimization with modern generative modeling, providing accurate, physics-consistent reconstruction from sparse data for scientific machine-learning problems.

Citations

• Physics vs Distributions: Pareto Optimal Flow Matching with Physics Constraints
• Text2PDE: Latent Diffusion Models for Accessible Physics Simulation
• Generative Learning of the Solution of Parametric Partial Differential Equations Using Guided Diffusion Models and Virtual Observations
• Physics-Informed Diffusion Models
• CoNFiLD: Conditional Neural Field Latent Diffusion Model Generating Spatiotemporal Turbulence
• CoCoGen: Physically-Consistent and Conditioned Score-based Generative Models for Forward and Inverse Problems
• Denoising Diffusion Bridge Models
• Diffusion Models Beat GANs on Image Classification
• A Variational Perspective on Solving Inverse Problems with Diffusion Models
• Diffusion Posterior Sampling for General Noisy Inverse Problems
• Elucidating the Design Space of Diffusion-Based Generative Models
• Diffusion Models Beat GANs on Image Synthesis
• Score-Based Generative Modeling through Stochastic Differential Equations

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• Learning Turbulent Flows with Generative Models: Super-resolution, Forecasting, and Sparse Flow Reconstruction