Constrained reduced-order modeling of reacting flows using bounded Gaussian process likelihoods: application to a furnace operating under MILD conditions

Abstract

This study explores the application of a novel constrained reduced-order modeling framework to analyze a furnace operating under Moderate and Intense Low-oxygen Dilution (MILD) combustion conditions. The methodology employs low-cost Singular Value Decomposition (lcSVD) with optimal sensor placement for data compression and reconstruction, followed by Gaussian Process Regression (GPR) with bounded likelihood functions – truncated Gaussian and beta distributions – to ensure physically admissible outputs in high-dimensional combustion simulations. We test these models by predicting the unexplored thermo-chemical states of three-dimensional CH₄/H₂ simulation samples, with varying equivalence ratio, fuel composition (ranging from pure methane to pure hydrogen), and air injector diameter. Results indicate that the beta likelihood constrains species mass fraction predictions to the $0$–$1$ interval by construction, yielding higher accuracy for species with localized distributions. Meanwhile, the truncated Gaussian enhances robustness by respecting realistic thermo-chemical ranges, reducing the influence of outliers, and improving model reliability in sparse or noisy data regions. These models demonstrate computational efficiency and scalability while delivering high-accuracy, physically consistent predictions.