Reduced-Order Modeling Of Hidden Dynamics
This addresses the need for accurate low-order descriptions of complex phenomena in scientific domains where direct observation is limited, but it appears incremental as it builds on existing POD-Galerkin methods.
The paper tackles the problem of building reduced-order models from noisy and incomplete observations by proposing a probabilistic framework that integrates uncertainty in hidden states, showing benefits in simulations.
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.