Machine Learning Surrogates for Uncertainty Quantification incorporating Higher Moments in a Flame Spread Application

In this work we implement and compare data driven machine learning surrogates for uncertainty quantification in a flame spread model that captures an experimental setup. We start with a moment independent global sensitivity analysis to choose the most sensitive kinetic and thermophysical parameters affecting the model output. Stochastic uncertainty is then studied in the output over space and time for five most sensitive parameters by analyzing four statistical moments. Different surrogate approaches are compared, namely proper orthogonal decomposition with interpolation (PODI), Gaussian process regression (GPR), Fourier neural operator (FNO), fully connected autoencoder (MLP-AE) and convolutional autoencoder (CAE). Performance of surrogates for both 1D temporal and 2D spatial outputs are analyzed for accuracy and robustness using small to moderate training data sizes. For 1D, all surrogates with the exception of GPR give accurate moment predictions. For 2D, PODI outperforms in capturing expectation and standard deviation but is comparatively weak in approximating higher moments where the CAE shows more promise. FNO is effective for samples hundred and below while GPR exhibits largest errors for the studied case. Considering the empirical importance of the statistical moments, PODI presents the most reliable and robust approach for uncertainty quantification in skewed flame spread profiles.