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On the effect of manifold topology in reduced-order modeling of turbulent combustion

par Zdybał, Kamila;Sutherland, James C.;Parente, Alessandro
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Publication A Paraître, 2023-05-28

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Résumé :

It has been recognized that, under some conditions, reduced-order models (ROMs) of turbulent combustion work very well, but in other can fail dramatically. At the same time, many aspects of data-driven ROMs have not yet been understood. In particular, undesired topological behaviors can be introduced on a data projection through dimensionality reduction. This can hinder the performance of a ROM. The most problematic behavior is an overlap on a projection that leads to non-uniqueness in representing quantities of interest (QoIs). Here, we investigate the effect that low-dimensional manifold (LDM) topologies have on data-driven ROMs. We particularly focus on assessing the effects of steep gradients and non-uniqueness in representing various projection-independent and projection-dependent QoIs. We show how the recently proposed cost function for manifold quality assessment can be used in reduced-order modeling workflows to distinguish between promising and poor manifold topologies. We discuss the effect of severe and subtle differences in manifold topologies. We link those differences with the behavior of a ROM at model runtime and with the mispredictions of the thermo-chemical state variables from the evolved LDM parameters.