Inverting subsurface flow data for geologic scenarios selection with convolutional neural networks

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Subsurface flow model calibration against dynamic response data is often constrained by a prior conceptual model of geologic scenario that specifies the expected spatial variability and geologic patterns in the solution. However, several sources of uncertainty exist in developing a conceptual geological model, including data limitation, process-based modeling assumptions, and subjective interpretations. Therefore, it is prudent to consider the uncertainty in geologic scenarios during model calibration and to utilize the flow response data in supporting or rejecting the proposed scenarios. We present a novel framework whereby dynamic response data is used to screen a set of proposed geologic scenarios by combining gradient-based inversion for feature extraction and convolutional neural networks for feature recognition. To compactly represent the salient features of each scenario, an extremely low-rank parameterization with the leading elements of the Principal Components Analysis (PCA) is adopted. The PCA basis elements of different scenarios are combined to define the search space for feature extraction, which is implemented via an iterative least-squares inversion formulation to match the observed data. The inversion solution is obtained by selectively combining the PCA representations from different scenarios, and contains the dominant spatial patterns that are needed to match the observed data. Feature recognition to identify the relevant geologic scenarios based on the reconstructed spatial solution of feature extraction inversion is performed using a pre-trained convolutional neural network (CNN). The method offers several advantages, including an efficient implementation that does not require extensive forward simulation runs, use of flow data to identify pertinent geologic scenarios, and the ability to combine geologic scenarios if supported by data. The performance of the proposed approach is evaluated using numerical experiments from pumping tests in groundwater aquifers.