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Manifold-informed state vector subset for reduced-order modeling

par Zdybal, Kamila ;Sutherland, James;Parente, Alessandro
Référence Combura Symposium 2021(2021-11-10: Soesterberg, The Netherlands)
Publication Publié, 2021-10-29

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Résumé :

Reduced-order models (ROMs) for turbulent combustion rely on identifying a small number of parameters that can effectively describe the complexity of reacting flows. With the advent of data-driven approaches, ROMs can be trained on data sets representing the evolution of the thermo-chemical state-space in simple systems. For low-Mach flows, the full state vector that serves as a training data set is typically composed of temperature and chemical composition. The data set is projected onto a lower-dimensional basis and the evolution of the complex system is tracked on the low-dimensional manifold. This approach allows for substantial dimensionality reduction, but the quality of the manifold topology is a decisive aspect in successful modeling. To mitigate manifold challenges, several authors advocate reducing the state vector to only a subset of major variables when training ROMs. However, this subsetting is often done ad hoc and without giving detailed insights into the effect of removing certain variables on the resulting low-dimensional data projection. In this work, we present a quantitative manifold-informed method for selecting the best subset of state variables that minimizes unwanted behaviors in manifold topologies.