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Subsurface flow model calibration is commonly performed by assuming that a known conceptual model of geologic continuity is available and can be used to constrain the solution search space. In real applications, however, the knowledge about geologic continuity is far from certain and subjective interpretations can lead to multiple distinct plausible geologic scenarios. Conventional parameterization methods that are widely used in model calibration, such as the Principal Component Analysis, encounter difficulty in capturing diverse spatial patterns from distinct geologic scenarios. We propose a special type of deep learning architecture, known as variational auto-encoder, for robust dimension-reduced parameterization of spatially distributed aquifer properties, such as hydraulic conductivity, in solving model calibration problems under uncertain geostatistical models. We show that convolutional autoencoders offer the versatility and robustness required for nonlinear parameterization of complex subsurface flow property distributions when multiple distinct geologic scenarios are present. The robustness of these models results, in part, from the use of many convolutional filters that afford the redundancy needed to extract, classify and encode very diverse spatial patterns at different abstraction levels/scales into the low-dimensional latent variables. The resulting latent variables control the salient spatial patterns in different geologic continuity models and are effective for parameterization of model calibration problems under uncertainty in geologic continuity, a task that is not trivial to accomplish using traditional parameterization methods. Several numerical experiments are used to demonstrate the robustness of convolutional deep learning models for reduced-order parameterization of flow model calibration problems when alternative plausible geologic continuity models are present.

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