Local manifold learning and its link to domain-based physics knowledge

Abstract

In many reacting flow systems, the thermo-chemical state-space is known or assumed to evolve close to a low-dimensional manifold (LDM). Various approaches are available to obtain those manifolds and subsequently express the original high-dimensional space with fewer parameterizing variables. Principal component analysis (PCA) is one of the dimensionality reduction methods that can be used to obtain LDMs. PCA does not make prior assumptions about the parameterizing variables and retrieves them empirically from the training data. In this paper, we show that PCA applied in local clusters of data (local PCA) is capable of detecting the intrinsic parameterization of the thermo-chemical state-space. We first demonstrate that utilizing three common combustion models of varying complexity: the Burke-Schumann model, the chemical equilibrium model and the homogeneous reactor. Parameterization of these models is known a priori which allows for benchmarking with the local PCA approach. We further extend the application of local PCA to a more challenging case of a turbulent non-premixed -heptane/air jet flame for which the parameterization is no longer obvious. Our results suggest that meaningful parameterization can be obtained also for more complex datasets. We show that local PCA finds variables that can be linked to local stoichiometry, reaction progress and soot formation processes.

Automated adaptive chemistry for Large Eddy Simulations of turbulent reacting flows

“…Local Principal Component Analysis (LPCA) is a dimensionality reduction technique, proposed by Kambhatla et al [37], based on the projection of high-dimensional data onto k sets of lower-dimensional manifolds. Although this algorithm was originally proposed for dimensionality reduction, it has been frequently utilized for clustering tasks in the last years [38][39][40][41]. In addition, it has been shown that, when applied to reacting flow databases, LPCA can ensure a better partitioning with respect to popular unsupervised algorithms such as k-Means and Self-Organzing Maps (SOMs) [32].…”

“…• Initialization: the clusters' centers of mass (centroids) Additional information on the PCA decomposition and reconstruction error, as well as the on LPCA partitioning algorithm, can be found in [38][39][40][41].…”