Modal Analysis of Spatiotemporal Data via Multivariate Gaussian Process
  Regression
Jiwoo Song Daning Huang
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 method is benchmarked against DMD and SPOD on a range of
examples, from academic and synthesized data to unsteady airfoil aerodynamics.
The results demonstrate MVGPR as a promising alternative to classical modal
analysis methods, especially in the scenario of scarce and temporally irregular
data.