Reduced-Order Modeling Of Hidden Dynamics

TL;DR

This paper introduces a probabilistic framework for building reduced-order models from noisy and incomplete data, effectively capturing hidden dynamics in complex systems.

Contribution

It proposes a novel probabilistic approach to construct POD-Galerkin reduced-order models that incorporate uncertainty in hidden states.

Findings

Improved modeling of hidden dynamics with noisy data

Enhanced accuracy of reduced-order models

Demonstrated benefits through simulations

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.