An assessment of the coupling between principal component analysis and nonlinear transformation in data-driven reduced-order models for combustion simulations

Data-driven reduced-order models (ROMs) enable efficient combustion simulations when resolving all chemical species is computationally prohibitive. Principal component analysis (PCA) is often employed to compress chemical composition space and, in some cases, combined with nonlinear transformations such as a Box–Cox function to improve regression accuracy in ignition problems. However, the interaction between PCA-based linear compression and nonlinear data transformation, as well as its combined effect on regression accuracy in combustion ROMs, has rarely been investigated. This study systematically assesses the coupling of PCA with nonlinear transformations in ROM frameworks across a series of compression ignition problems involving large hydrocarbon fuels. The results show that while PCA is effective at low ranks where truncation error dominates, combining PCA with nonlinear transformations can degrade regression performance especially at higher ranks, in association with nonlinear cross-term coupling among retained principal components. The findings clarify when PCA remains advantageous and provide guidance for developing robust, data-driven ROMs for complex ignition problems. Novelty and significance statement This work provides the first systematic clarification of a previously unresolved question in data-driven combustion ROMs: how PCA-based dimensionality reduction interacts with nonlinear transformations commonly used to train surrogate models for ignition problems. It identifies a rank-dependent trade-off between PCA truncation benefits and transformation-induced regression complexity, showing that PCA transport can be less reliable than direct subset transport at sufficiently high rank. This finding is significant for designing robust ROM frameworks that mitigate time-accumulated errors in ignition simulations involving wide-ranging thermochemical states.