Section: New Results

Reduced modeling of unknown trajectories

Participant : Patrick Héas.

This is a collaboration with Cédric Herzet (EPI FLUMINANCE, Inria Rennes–Bretagne Atlantique)

In [12], we deal with model order reduction of parametrical dynamical systems. We consider the specific setup where the distribution of the system's trajectories is unknown but the following two sources of information are available: (i) some “rough” prior knowledge on the system's realisations, and (ii) a set of “incomplete” observations of the system's trajectories. We propose a Bayesian methodological framework to build reduced–order models (ROMs) by exploiting these two sources of information.

We emphasise that complementing the prior knowledge with the collected data provably enhances the knowledge of the distribution of the system's trajectories. We then propose an implementation of the proposed methodology based on Monte Carlo methods. In this context, we show that standard ROM learning techniques, such as proper orthogonal decomposition (POD) or dynamic mode decomposition (DMD), can be revisited and recast within the probabilistic framework considered in this work. We illustrate the performance of the proposed approach by numerical results obtained for a standard geophysical model.