Comparison of Machine Learning Algorithms in the Interpolation and Extrapolation of Flame Describing Functions

Abstract

This paper examines and compares the commonly used machine learning algorithms in their performance in interpolation and extrapolation of flame describing function (FDFs), based on experimental and simulation data. Algorithm performance is evaluated by interpolating and extrapolating FDFs and then the impact of errors on the limit cycle amplitudes are evaluated using the extended FDF (xFDF) framework. The best algorithms in interpolation and extrapolation were found to be the widely used cubic spline interpolation, as well as the Gaussian processes (GPs) regressor. The data itself were found to be an important factor in defining the predictive performance of a model; therefore, a method of optimally selecting data points at test time using Gaussian processes was demonstrated. The aim of this is to allow a minimal amount of data points to be collected while still providing enough information to model the FDF accurately. The extrapolation performance was shown to decay very quickly with distance from the domain and so emphasis should be put on selecting measurement points in order to expand the covered domain. Gaussian processes also give an indication of confidence on its predictions and are used to carry out uncertainty quantification, in order to understand model sensitivities. This was demonstrated through application to the xFDF framework.