Dual Neural Network Architecture for Determining Epistemic and Aleatoric Uncertainties

Deep learning techniques have been shown to be extremely effective for various classification and regression problems, but quantifying the uncertainty of their predictions and separating them into the epistemic and aleatoric fractions is still considered challenging. In oil and gas exploration projects, tools consisting of seismic, sonic, magnetic resonance, resistivity, dielectric and/or nuclear sensors are sent downhole through boreholes to probe the earth's rock and fluid properties. The measurements from these tools are used to build reservoir models that are subsequently used for estimation and optimization of hydrocarbon production. Machine learning algorithms are often used to estimate the rock and fluid properties from the measured downhole data. Quantifying uncertainties of these properties is crucial for rock and fluid evaluation and subsequent reservoir optimization and production decisions. These machine learning algorithms are often trained on a "ground-truth" or core database. During the inference phase which involves application of these algorithms to field data, it is critical that the machine learning algorithm flag data as out of distribution from new geologies that the model was not trained upon. It is also highly important to be sensitive to heteroscedastic aleatoric noise in the feature space arising from the combination of tool and geological conditions. Understanding the source of the uncertainty and reducing them is key to designing intelligent tools and applications such as automated log interpretation answer products for exploration and field development. In this paper we describe a methodology consisting of a system of dual networks comprising of the combination of a Bayesian Neural Network (BNN) and an Artificial Neural Network (ANN) addressing this challenge for geophysical applications.