Reduced-Order Modeling Of Hidden Dynamics

ABSTRACT The objective of this paper is to investigate how noisy and incomplete observations can be integrated in the process of building a reduced-order model. This problematic arises in many scientific domains where there exists a need for accurate low-order descriptions of highly-complex phenomena, which can not be directly and/or deterministically observed. Within this context, the paper proposes a probabilistic framework for the construction of "POD-Galerkin" reduced-order models. Assuming a hidden Markov chain, the inference integrates the uncertainty of the hidden states relying on their posterior distribution. Simulations show the benefits obtained by exploiting the proposed framework. Index Terms-- Reduced-order modeling, POD-Galerkin projection, hidden Markov model, uncertainty, optic-flow. 1. INTRODUCTION In many fields of Sciences, one is interested in studying the spatiotemporal evolution of a state variable characterized by a differential equation.