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 training data. In this paper, we show that PCA applied in local clusters of data (local PCA) is capable of detecting physically meaningful 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 n-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. We shed the light on how data-driven techniques, such as local PCA, can be enhanced by using the available knowledge of the system.

Keywords

• Local principal component analysis
• Low-dimensional manifolds
• Physically interpretable models
• Data parameterization
• Data clustering
• Semi-supervised learning