FLRONet: Deep Operator Learning for High-Fidelity Fluid Flow Field Reconstruction from Sparse Sensor Measurements
This addresses a critical problem in science and engineering applications like fluid dynamics where sparse sensor data needs to be converted to detailed flow fields, representing a novel method for a known bottleneck rather than incremental improvement.
The paper tackles the problem of reconstructing high-fidelity fluid flow fields from sparse sensor measurements, which is challenging due to dimensional disparities making the measurement operator ill-conditioned. The proposed FLRONet deep operator learning framework achieves high reconstruction accuracy and robustness on the CFDBench dataset, with the capability for zero-shot super-resolution in spatial and temporal domains.
Reconstructing high-fidelity fluid flow fields from sparse sensor measurements is vital for many science and engineering applications but remains challenging because of dimensional disparities between state and observational spaces. Due to such dimensional differences, the measurement operator becomes ill-conditioned and non-invertible, 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 functional spaces, enabling superior generalization and discretization-independent reconstruction. We introduce FLRONet, a deep operator learning framework that is trained to reconstruct fluid flow fields from sparse sensor measurements. FLRONet 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. Validation performed on the CFDBench dataset has demonstrated that FLRONet consistently achieves high levels of reconstruction accuracy and robustness, even in scenarios where sensor measurements are inaccurate or missing. Furthermore, the operator learning approach endows FLRONet with 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.