Convolutional neural networks (CNN) for feature-based model calibration under uncertain geologic scenarios

This paper presents convolutional neural network architectures for integration of dynamic flow response data to reduce the uncertainty in geologic scenarios and calibrate subsurface flow models. The workflow consists of two steps, where in the first step the solution search space is reduced by eliminating unlikely geologic scenarios using distinguishing salient flow data trends. The first step serves as a pre-screening to remove unsupported scenarios from the full model calibration process in the second step. For this purpose, a convolutional neural network (CNN) with a cross-entropy loss function is designed to act as a classifier in predicting the likelihood of each scenario based on the observed flow responses. In the second step, the selected geologic scenarios are used in another CNN with an ℓ2-loss function (as a regression model) to perform model calibration. The regression CNN model (step 2) learns the inverse mapping from the production data space to the low-rank representation of the model realizations within the feasible set. Once the model is trained off-line, a fast feed-forward operation on the observed historical production data (input) is used to reconstruct a calibrated model. The presented approach offers an opportunity to utilize flow data in identifying plausible geologic scenarios, results in an off-line implementation that is conveniently parallellizable, and can generate calibrated models in real time, i.e., upon availability of data and without in-depth technical expertise about model calibration. Several synthetic Gaussian and non-Gaussian examples are used to evaluate the performance of the method.