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Simulating 2D flow in fractured crystalline rock requires 2D stochasticdiscrete-fracture matrix (DFM) models. To obtain the simulation statistics ofinterest at an affordable computational cost, we aim to use the multilevelMonte Carlo method. To use this multiscale approach, one needs to upscale thehydraulic conductivity of the fractures by numerical homogenization. In thiswork, we substitute numerical homogenization with a surrogate model to speed upthe computations. In particular, we resort to a deep convolutional neuralnetwork (CNN) connected to a deep feed-forward neural network. The equivalenthydraulic conductivity tensor $K_{eq}$ is predicted based on an input spatialrandom field (SRF) of hydraulic conductivity tensors, cross-section, andhydraulic conductivity of fractures. Three independent surrogates with the samearchitecture are trained using data from DFM models with three different ratiosof hydraulic conductivities of fracture and bulk $K_f/K_b$. As the $K_f/K_b$ratio increases, the multivariate $K_{eq}$ distribution becomes more complex,and thus, the prediction accuracy of the trained surrogates deteriorates.Regardless of $K_f/K_b$, however, an improvement in the prediction accuracy ofthe trained surrogates is noted as the considered fracture density of themodeling setup decreases. We also investigate prediction accuracy on input SRFsof different correlation lengths. Upscaling by numerical homogenization and bysurrogate modeling is compared on two practical problems: upscaling of thehydraulic conductivity tensor and groundwater flow through a given surface. Weobtained equally accurate results for the equivalent hydraulic tensorcalculation of upscaled DFM models regardless of the upscaling method. For thegroundwater flow problem, the accuracy of quantity of interest imitates theaccuracy of $K_{eq}$ predictions.

Deep learning surrogate for predicting hydraulic conductivity tensors from stochastic discrete fracture-matrix models