Layer-wise relevance propagation for backbone identification in discrete fracture networks

Berrone, Stefano; Santa, Francesco Della; Mastropietro, Antonio; Pieraccini, Sandra; Vaccarino, Francesco

doi:10.1016/j.jocs.2021.101458

Cited by 4 publications

(4 citation statements)

References 37 publications

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“…The use of DNNs as surrogate models for UQ is still a novel approach that requires deep investigations but is very promising. To the best of the authors' knowledge, other than [35][36][37], there are no works in the literature that train DNNs to perform flux regression tasks on DFNs and, in particular, that use these NNs in the context of UQ as in [35]. While the results illustrated in [35] are very promising, the ones presented in Section 3 of this work concerns the use of NN reduced models as a practical possibility in the UQ framework for flow analyses of a subsurface network of fractures.…”

Section: Discussionmentioning

confidence: 99%

“…Some recent contributions involving ML and NNs applied to DFN flow simulations or UQ analysis are proposed in [30][31][32][33][34][35]. To the best of the authors' knowledge, other than [35][36][37] there are no works in the literature that involve the use of NNs as a model reduction method for DFN simulations. In particular, in [35], multi-task deep neural networks are trained to predict the fluxes of DFNs with fixed geometry, given the fracture transmissivities.…”

Section: Introductionmentioning

confidence: 99%

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

Berrone

Santa

2021

Geosciences

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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.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Berrone

Santa

2021

Geosciences

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“…Graph models [9][10][11][12][13][14][15][16][17][18] are arguably the most widely used tools for molecular representations in molecular dynamics simulation, coarse-grained models, elastic network models, QSAR/QSPR, graph neural networks, etc. In general, a molecule (or a molecular complex) is modeled as a graph with each vertex representing an atom, an amino acid, a domain, or an entire molecule, and edge representing covalent-bond, non-covalent-bond, or more general interaction.…”

Section: Introductionmentioning

confidence: 99%

Persistent Dirac for molecular representation

Wee¹,

Bianconi²,

Xia³

2023

Preprint

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Molecular representations are of fundamental importance for the modeling and analysis of molecular systems. Representation models and in general approaches based on topological data analysis (TDA) have demonstrated great success in various steps of drug design and materials discovery.Here we develop a mathematically rigorous computational framework for molecular representation based on the persistent Dirac operator. The properties of the spectrum of the discrete weighted and unweighted Dirac matrices are systemically discussed and used to demonstrate the geometric and topological properties of both non-homology and homology eigenvectors of real molecular structures. This allows us to asses the influence of weighting schemes on the information encoded in the Dirac eigenspectrum. A series of physical persistent attributes, which characterize the spectrum of the Dirac matrices across a filtration, are proposed and used as efficient molecular fingerprints. Finally, our persistent Dirac-based model is used for clustering molecular configurations from nine types of organic-inorganic halide perovskites. We found that our model can cluster the structures very well, demonstrating the representation and featurization power of the current approach.

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“…7.7] in [14]), network interdiction models (NIMs) [15], and flux regression problems in underground fractured media [16,17]. A classic multi-layer perceptron (MLP), or its suitable variants, can perform this regression task on the graph data with a good performance [16,17], implicitly learning the node relationships during the training (see [18,19]). On the other hand, the current GCNs in the literature are not comparable to MLPs for such a regression task; indeed, as mentioned above, they are designed mainly for other kinds of tasks and, in practice, they cannot exploit deep architectures.…”

Section: Introductionmentioning

confidence: 99%

Graph-Informed Neural Networks for Regressions on Graph-Structured Data

et al. 2022

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In this work, we extend the formulation of the spatial-based graph convolutional networks with a new architecture, called the graph-informed neural network (GINN). This new architecture is specifically designed for regression tasks on graph-structured data that are not suitable for the well-known graph neural networks, such as the regression of functions with the domain and codomain defined on two sets of values for the vertices of a graph. In particular, we formulate a new graph-informed (GI) layer that exploits the adjacent matrix of a given graph to define the unit connections in the neural network architecture, describing a new convolution operation for inputs associated with the vertices of the graph. We study the new GINN models with respect to two maximum-flow test problems of stochastic flow networks. GINNs show very good regression abilities and interesting potentialities. Moreover, we conclude by describing a real-world application of the GINNs to a flux regression problem in underground networks of fractures.

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Layer-wise relevance propagation for backbone identification in discrete fracture networks

Cited by 4 publications

References 37 publications

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

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

Persistent Dirac for molecular representation

Graph-Informed Neural Networks for Regressions on Graph-Structured Data

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