Probabilistic deep learning with variational inference

Abstract

Deep neural networks are used in the petroleum industry to model gas and oil rate. To optimise the production, the uncertainty of the network predictions is desirable. The neural network weights are equipped with prior distributions to be able to quantify the uncertainty of the model predictions within the Bayesian paradigm. To obtain a numerically feasible procedure two different approaches of variational inference are used and compared; black box variational inference and variational inference using the reparameterisation trick. Both approaches are applied to real measurements of gas and oil rate, which were given by Solution Seeker, a company providing production optimisation to the petroleum industry. The results show a more stable convergence using the reparameterisation trick. The uncertainty in predictions is possible to be quantified using variational inference but setting a proper prior distribution is difficult.