Entropy of spatiotemporal data as a dynamic truncation indicator for model reduction applications

We have provided a methodology for retrieving spatial and temporal eigenfunctions from an ensemble of data. Focusing on a Newtonian fluid flow problem, we illustrate that the efficacy 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 in on-line control applications, due to the computational savings that are introduced. 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. Finally, we examine the use of the entropy as a dynamic truncation indicator.