Uncertainty Quantification in Deep Learning through Stochastic Maximum Principle

In this paper, we introduce an efficient computational framework to quantify the uncertainty of a class of deep neural networks (DNNs). The DNN has emerged from machine learning and becomes one of the most extensively studied research topics in scientific computing and data science. As a type of artificial neural network with multiple layers, the DNN is capable to model complex systems and its applications cover wide range among various scientific and engineering disciplines. However, despite phenomenal success, the deterministic output of DNNs can not produce probabilistic predictions for the uncertain nature of scientific research. Therefore, it's difficult to apply DNNs to solve real-world scientific problems since there are typically uncertainties involved in scientific models and observed data are always perturbed by noises.