In several applications concerning underground flow simulations in fractured media, the fractured rock matrix is modeled by means of the Discrete Fracture Network (DFN) model. The fractures are typically described through stochastic parameters sampled from known distributions. In this framework, it is worth considering the application of suitable complexity reduction techniques, also in view of possible uncertainty quantification analyses or other applications requiring a fast approximation of the flow through the network. Herein, we propose the application of Neural Networks to flux regression problems in a DFN characterized by stochastic trasmissivities as an approach to predict fluxes.
In this work, we investigate the sensitivity of a family of multi-task Deep Neural Networks (DNN) trained to predict fluxes through given Discrete Fracture Networks (DFNs), stochastically varying the fracture transmissivities. In particular, detailed performance and reliability analyses of more than two hundred Neural Networks (NN) are performed, training the models on sets of an increasing number of numerical simulations made on several DFNs with two fixed geometries (158 fractures and 385 fractures) and different transmissibility configurations. A quantitative evaluation of the trained NN predictions is proposed, and rules fitting the observed behavior are provided to predict the number of training simulations that are required for a given accuracy with respect to the variability in the stochastic distribution of the fracture transmissivities. A rule for estimating the cardinality of the training dataset for different configurations is proposed. From the analysis performed, an interesting regularity of the NN behaviors is observed, despite the stochasticity that imbues the whole training process. The proposed approach can be relevant for the use of deep learning models as model reduction methods in the framework of uncertainty quantification analysis for fracture networks and can be extended to similar geological problems (for example, to the more complex discrete fracture matrix models). The results of this study have the potential to grant concrete advantages to real underground flow characterization problems, making computational costs less expensive through the use of NNs.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.