Modal Analysis of Spatiotemporal Data via Multi-fidelity Multi-variate Gaussian Processes

Abstract

Modal analysis has become an essential tool to understand the coherent structure of complex flows. The classical modal analysis methods, such as dynamic mode decomposition (DMD) and spectral proper orthogonal decomposition (SPOD), rely on a sufficient amount of data that is regularly sampled in time. However, often one needs to deal with sparse temporally irregular data, e.g., due to experimental measurements and simulation algorithm. To overcome the limitations of data scarcity and irregular sampling, we propose a novel modal analysis technique using multi-variate Gaussian process regression (MVGPR). We first establish the connection between MVGPR and the existing modal analysis techniques, DMD and SPOD, from a linear system identification perspective. Next, leveraging this connection, we develop a MVGPR-based modal analysis technique that addresses the aforementioned limitations. The capability of MVGPR is endowed by its judiciously designed kernel structure for correlation function, that is derived from the assumed linear dynamics. Subsequently, the proposed MVGPR