Probabilistic machine learning framework for chemical source term integration with Gaussian Processes: H<inf>2</inf>/air auto-ignition case

Abstract

The integration of chemistry poses a major bottleneck in numerical combustion modelling, as a significant amount of simulation time is consumed in the direct integration (DI) of differential equations into thermochemistry modelling. In this work, a probabilistic machine learning (ML) framework, using Gaussian processes (GPs), is developed as a chemical source term integrator to replace DI for the prediction of a H2/air auto-ignition case. In this context, two algorithms, namely Gaussian Process Regression (GPR) and Gaussian Process Autoregressive Regression (GPAR), are investigated. The training dataset is generated using zero-dimensional (0D) isobaric H2/air auto-ignition simulations in Cantera. To address the scalability issue of the GPs, the variational inducing points method is used. This method leverages a subset of the original data for training, allowing sparse approximations. The performances of the GPR and GPAR are compared to a standard artificial neural network (ANN) model. A priori comparison with direct integration shows that both GPR (Rtest2=0.997) and GPAR (Rtest2=0.998) outperform the ANNs (Rtest2=0.988) by capturing latent dynamics of the chemistry when working with small datasets. Additionally, GP models offer the capability to quantify the uncertainty of each prediction, providing deeper insights into the model's limitations. It is also shown that the inference with GP-based models is slower than ANNs with speed-up factors of 1.9-2.1 relative to the 0D reactor model, whereas the ANN speed-up factor goes up to 3.0.