Dual guidance: ROM-informed field reconstruction with generative models

TL;DR

This paper introduces a dual-guided framework that combines physics-informed sensor placement with generative models to accurately reconstruct unsteady flow fields from sparse observations, outperforming traditional methods especially in data-limited scenarios.

Contribution

It proposes a novel integration of reduced-order model-based sensor placement with generative modeling for flow reconstruction, enhancing accuracy with limited data.

Findings

Optimized sensor placement reduces reconstruction error to 0.05 L2 error.

Structured sensor layouts perform poorly under sparse sensing conditions.

The dual-guided approach outperforms traditional sensor placement methods in data-limited regimes.

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.