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Article

Performance Analysis of Multi-Task Deep Learning Models for Flux Regression in Discrete Fracture Networks

1
Dipartimento di Scienze Matematiche (DISMA), Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
2
[email protected] Center, Politecnico di Torino, 10138 Torino, Italy
*
Author to whom correspondence should be addressed.
Academic Editors: Chaoshui Xu and Jesus Martinez-Frias
Geosciences 2021, 11(3), 131; https://doi.org/10.3390/geosciences11030131
Received: 18 January 2021 / Revised: 8 March 2021 / Accepted: 9 March 2021 / Published: 12 March 2021
(This article belongs to the Special Issue Quantitative Fractured Rock Hydrology)
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. View Full-Text
Keywords: discrete fracture networks; neural networks; deep learning; uncertainty quantification discrete fracture networks; neural networks; deep learning; uncertainty quantification
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MDPI and ACS Style

Berrone, S.; Della Santa, F. Performance Analysis of Multi-Task Deep Learning Models for Flux Regression in Discrete Fracture Networks. Geosciences 2021, 11, 131. https://doi.org/10.3390/geosciences11030131

AMA Style

Berrone S, Della Santa F. Performance Analysis of Multi-Task Deep Learning Models for Flux Regression in Discrete Fracture Networks. Geosciences. 2021; 11(3):131. https://doi.org/10.3390/geosciences11030131

Chicago/Turabian Style

Berrone, Stefano, and Francesco Della Santa. 2021. "Performance Analysis of Multi-Task Deep Learning Models for Flux Regression in Discrete Fracture Networks" Geosciences 11, no. 3: 131. https://doi.org/10.3390/geosciences11030131

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