Robust reconstruction of flow fields from limited measurements

In many applications it is important to estimate the structure of a flow field from limited and possibly corrupt measurements. Many current methods in flow estimation use least squares regression to reconstruct the flow field, which searches for the minimum-energy solution that is consistent with the measured data. However, this approach is known to be prone to overfitting and is sensitive to noise. To address these challenges we instead seek a sparse representation of the data in a library of examples rather than a minimum-energy solution. Sparse representation has been widely used in image recognition and reconstruction examples, and is well-suited to structured data with limited measurements, corruption, and outliers. We demonstrate sparse representation for flow reconstruction using various fluid data sets, including vortex shedding past a cylinder at low Reynolds number, a mixing layer, and two geophysical flows. In particular we find considerable improvements in overall estimation accuracy and robustness compared with least squares methods such as gappy POD. Sparse representation is a promising framework for extracting useful information from complex flow fields with realistic measurements.