Low-order empirical modeling of distributed parameter systems using temporal and spatial eigenfunctions

We provide a methodology for retrieving spatial and temporal eigenfunctions from an ensemble of data, using Proper Orthogonal Decomposition (POD). Focusing on a Newtonian fluid flow problem, we illustrate that the efficiency of these two families of eigenfunctions can be different when used in model reduction projections. The above observation can be of critical importance for low-order modeling of Distributed Parameter Systems (DPS) in on-line control applications, due to the computational savings that are introduced. Additionally, for the particular fluid flow problem, we introduce the use of the entropy of the data ensemble as the criterion for choosing the appropriate eigenfunction family.