Runhai Feng

Recently, machine learning has been widely and successfully used by geoscientists to solve typical inverse problems. However, the uncertainty related to the learned model is not properly analysed, and sometimes a simple activation function is applied to provide posterior probability. To address this problem, variance of machine learning models is calculated that can provide additional information in the accuracy of predictions. Particularly, random forest and convolutional neural networks are used to classify lithofacies and predict porosity that are important parameters to characterize subsurface reservoirs. In the first part for lihtofacies classification, different number of trees in the ensemble forest is used to investigate its influence on the model variance. While the prediction accuracy as measured by the Matthews correlation coefficient does not change with the number of trees, nor the mean probabilities of each lithofacies. The Monte Carlo effect in the variance that arising from a limited number of bootstrap replicates can be eliminated with an increase of trees used in the forest. In the second part of porosity prediction, dropout technique is used to simulate a Bayesian network, and variance of the learned system is decomposed into two parts, in which the aleatoric uncertainty does not change with an increased number of realizations, since it accounts for the randomness in the training data that have been kept the same in the study. On the other hand, the epistemic uncertainty that reflects the variability of model parameters can be explained with an increase in the number of realizations.