A Meshless Method To Compute The POD And Its Variants From Scattered Data

The Proper Orthogonal Decomposition (POD) is one of the most popular methods for discovering patterns from data in fluid mechanics. When the data is available on a uniform grid, such as in cross-correlation-based particle image velocimetry, the POD is equivalent to a Singular Value Decomposition (SVD) of the matrix containing the measurement. When the data is scattered, as in particle tracking velocimetry, the POD computation first requires interpolation onto a grid. Such interpolation degrades spatial resolution and limits the benefits of PTV over correlation-based methods. In this work, we propose a method to compute the POD from scattered data that circumvents the need for interpolation. The method uses physics-constrained Radial Basis Function (RBFs) regression to compute inner products in space and time. We demonstrate that this method is more accurate than the traditional interpolation or binning-based approaches. Since the method does not require the definition of a mesh and produces results that are analytic and mesh-independent, we refer to our method as meshless POD.