Real-Time Reduced Order Modeling Using Time Dependent Subspaces

We present real-time reduced-order models for deterministic/stochastic systems constructed by projection of the full-dimensional dynamics onto a time-dependent basis. To this end, we leverage a scalable algorithm to extract time dependent modes from highly transient data sets. We will present two case studies for the reduced-order modeling of: (1) transient instabilities in Kuramoto-Sivashinsky equation, and (2) transient flow over a bump. The results will be compared to a reduced-order model constructed using static (i.e. time invariant) POD modes.