Uncertainty quantification of a deep learning fuel property prediction model

Deep learning models are being widely used in the field of combustion. Given the black-box nature of typical neural network based models, uncertainty quantification (UQ) is critical to ensure the reliability of predictions as well as the training datasets, and for a principled quantification of noise and its various sources. However, the uncertainties of the developed models are seldom quantified, which is primarily attributed to the huge incremental cost of adding UQ to already computationally expensive deep learning models. In this work, UQ methods with different ranges of computational cost are applied in the context of fuel property prediction. Deep learning surrogate models for predicting properties of chemical compounds and mixtures have been recently shown to be promising for enabling data-driven fuel design and optimization, with the ultimate goal of improving efficiency and lowering emissions from combustion engines. In this study, UQ is performed on one such multi-task deep learning model that simultaneously predicts the research octane number (RON), Motor Octane Number (MON), and Yield Sooting Index (YSI) of pure components and multicomponent blends. The deep learning model is comprised of three smaller networks: Extractor 1, Extractor 2, and Predictor, and a mixing operator. The molecular fingerprint is encoded via Extractor 1 and Extractor 2, the mixing operator generates mixture fingerprints based on linear operation, and the predictor maps fingerprints to the target properties. Two different classes of UQ methods, monte-Carlo ensemble methods and Bayesian neural networks, are employed for quantifying the epistemic uncertainty. Combinations of Bernoulli and Gaussian distributions with DropConnect and DropOut techniques are explored as ensemble methods. All the DropConnect, DropOut and Bayesian layers are applied to the predictor network. Aleatoric uncertainty is modeled by assuming that each data point has an independent uncertainty associated with it. Although this study is confined to UQ of fuel property prediction, the methodologies and findings are applicable to other deep learning frameworks that are being widely used in the combustion community.