Space-time POD as a unifying framework for modal decomposition

Modal decompositions, which seek to extract meaningful structures from flow data or governing equations, are widely used in fluid mechanics to explore physical processes and develop reduced-complexity models. Many such methods are currently in use, but the connections between them and the appropriate choice of method for a given application are not always clear. In this presentation, we show how a space-time formulation of proper orthogonal decomposition (POD) provides a framework for understanding most available modal decomposition methods. In particular, we show how standard POD, spectral POD (SPOD), dynamic mode decomposition (DMD), resolvent analysis, and Hankel singular value decomposition can all be understood as special cases of space-time POD obtained in certain limits. Moreover, we discuss how this unified viewpoint is helpful, e.g., we show how it motivates alternatives to Hankel singular value decomposition with improved convergence properties.