Constrained reduced-order modeling using bounded Gaussian processes for physically consistent reacting flow predictions

Abstract

Reduced-order models offer a cost-effective and accurate approach to analyzing high-dimensional combustion problems. These surrogate models are built in a data-driven manner by combining computational fluid dynamics simulations with Proper Orthogonal Decomposition (POD) for dimensionality reduction and Gaussian Process Regression (GPR) for nonlinear regression. However, these models can yield physically inconsistent results, such as negative mass fractions. As a linear decomposition method, POD complicates the enforcement of constraints in the reduced space, while GPR lacks inherent provisions to ensure physical consistency. To address these challenges, this study proposes a novel constrained reduced-order model framework that enforces physical consistency in predictions. Dimensionality reduction is achieved by downsampling the dataset through low-cost Singular Value Decomposition (lcSVD) using optimal sensor placement, ensuring that the retained data points preserve physical information in the reduced space. We integrate finite-support parametric distribution functions, such as truncated Gaussian and beta distribution scaled to the interval $[a,b]$, into the GPR framework. These bounded likelihood functions explicitly model the observational noise in the bounded space and use variational inference to approximate analytically intractable posterior distributions, producing GP estimations that satisfy physical constraints by construction. We validate the proposed methods using a synthetic dataset and a benchmark case of one-dimensional laminar NH₃/H₂ flames. The results show that the thermo-chemical state predictions comply with physical constraints while maintaining the high accuracy of unconstrained reduced-order models.