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Reduced-Order Modeling of Hidden Dynamics

Patrick Héas 1 Cédric Herzet 2
1 ASPI - Applications of interacting particle systems to statistics
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
2 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
Inria Rennes – Bretagne Atlantique , IRSTEA - Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture, IRMAR - Institut de Recherche Mathématique de Rennes
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.
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Patrick Héas, Cédric Herzet. Reduced-Order Modeling of Hidden Dynamics. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASPP), Mar 2016, Shangai, China. pp.1268--1272, ⟨10.1109/ICASSP.2016.7471880⟩. ⟨hal-01246074⟩

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