Deep Operator Learning for High-Fidelity Fluid Flow Field Reconstruction From Sparse Sensor Measurements

Abstract Reconstructing high-fidelity fluid flow fields from sparse sensor measurements is vital for many science and engineering applications but remains challenging because of the dimensional disparities between state and observational spaces. Due to such dimensional differences, the measurement operator becomes ill conditioned and noninvertible, making the reconstruction of flow fields from sensor measurements extremely difficult. Although sparse optimization and machine learning address the above problems to some extent, questions about their generalization and efficiency remain, particularly regarding the discretization dependence of these models. In this context, deep operator learning offers a better solution as this approach models mappings between infinite-dimensional function spaces, enabling superior generalization and discretization-independent reconstruction. We introduce a deep operator-learning model that is trained to reconstruct fluid flow fields from sparse sensor measurements. Our deep-learning model employs a branch–trunk network architecture to represent the inverse measurement operator that maps sensor observations to the original flow field, a continuous function of both space and time. Our validation has demonstrated that the proposed deep-learning method consistently achieves high levels of reconstruction accuracy and robustness, even in scenarios where sensor measurements are inaccurate or missing. Furthermore, the operator-learning approach enables the capability to perform zero-shot super-resolution in both spatial and temporal domains, offering a solution for rapid reconstruction of high-fidelity flow fields.