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.

翻译：从稀疏传感器测量中重建高保真流体流场对众多科学与工程应用至关重要，但由于状态空间与观测空间之间的维度差异，该任务仍极具挑战性。这种维度差异导致测量算子呈现病态且不可逆的特性，使得从传感器测量重建流场变得极为困难。尽管稀疏优化与机器学习方法在一定程度上解决了上述问题，但其泛化能力与效率仍存疑，尤其涉及这些模型对离散化方案的依赖性。在此背景下，深度算子学习提供了更优解决方案，该方法通过对无限维函数空间之间的映射进行建模，实现了卓越的泛化能力与离散化无关的重建性能。本文提出FLRONet——一种基于深度算子学习的框架，通过训练实现从稀疏传感器测量重建流体流场。FLRONet采用分支-主干网络架构来表征逆测量算子，该算子将传感器观测映射至原始流场（空间与时间的连续函数）。在CFDBench数据集上的验证表明，即使在传感器测量存在误差或缺失的情况下，FLRONet仍能持续实现高精度与强鲁棒性的重建。此外，算子学习方法赋予FLRONet在空间域与时间域进行零样本超分辨率重建的能力，为快速获取高保真流场提供了解决方案。