Calibration and Uncertainty Quantification of Bayesian Convolutional Neural Networks for Geophysical Applications

Deep neural networks offer numerous potential applications across geoscience, for example, one could argue that they are the state-of-the-art method for predicting faults in seismic datasets. In quantitative reservoir characterization workflows, it is common to incorporate the uncertainty of predictions thus such subsurface models should provide calibrated probabilities and the associated uncertainties in their predictions. It has been shown that popular Deep Learning-based models are often miscalibrated, and due to their deterministic nature, provide no means to interpret the uncertainty of their predictions. We compare three different approaches to obtaining probabilistic models based on convolutional neural networks in a Bayesian formalism, namely Deep Ensembles, Concrete Dropout, and Stochastic Weight Averaging-Gaussian (SWAG). These methods are consistently applied to fault detection case studies where Deep Ensembles use independently trained models to provide fault probabilities, Concrete Dropout represents an extension to the popular Dropout technique to approximate Bayesian neural networks, and finally, we apply SWAG, a recent method that is based on the Bayesian inference equivalence of mini-batch Stochastic Gradient Descent. We provide quantitative results in terms of model calibration and uncertainty representation, as well as qualitative results on synthetic and real seismic datasets. Our results show that the approximate Bayesian methods, Concrete Dropout and SWAG, both provide well-calibrated predictions and uncertainty attributes at a lower computational cost when compared to the baseline Deep Ensemble approach. The resulting uncertainties also offer a possibility to further improve the model performance as well as enhancing the interpretability of the models.