Mining Goes Digital – Mueller et al. (Eds)
© 2019 Taylor & Francis Group, London, ISBN 978-0-367-33604-2
168
Recursive convolutional neural networks in a multiple-point
statistics framework
Sebastian Avalos & Julian M. Ortiz
The Robert M. Buchan Department of Mining, Queen’s University, Canada
ABSTRACT: This work proposes a new technique for Multiple-Point Statistics simulation
based on a Recursive Convolutional Neural Network approach (RCNN). A study on the
architecture of the network is done to ensure that the spatial structure of the phenomenon
inferred from a training image and its associated uncertainty are properly captured.
A sensitivity analysis over the main architecture parameters is performed on a two dimensional
binary image. Statistical and spatial metrics are determined to quantify the impact of each
parameter as well as the ability to capture the underlying phenomenon.
Keywords: Geostatistics, Deep Learning, Training Image, Categorical Variable
1 INTRODUCTION
Multiple-point statistics (MPS) simulation has seen an explosive development since Strebelle’s
seminal paper in 2002 (Strebelle, 2002). Many different approaches have been proposed (Arpat &
Caers, 2007; Mariethoz et al., 2010; Parra & Ortiz, 2011) and some have reached industrial
applications (Mariethoz et al., 2010). The methods associated to MPS are intimately related
to image and texture analysis (Daly, 2004; Parra & Ortiz, 2011; Zahner et al., 2015). Excellent
reviews of multiple-point simulation methods are available (Tahmasebi, 2018) and further
theoretical and practical details can be found (Mariethoz & Caers, 2014).
This paper is motivated by the possibilities offered by deep learning methods, particularly
Convolutional Neural Networks (CNNs) (LeCun et al., 1998) which have shown extraordinary performances in image analysis, including classification, reconstruction, segmentation,
labeling and more (Dosovitskiy et al., 2015; Eilertsen et al., 2017; Gatys et al., 2016; He et al.,
2016). The main aim is to create a bridge between CNNs and MPS. This is done by proposing
a Recursive Convolutional Neural Network (RCNN) approach that enables the architecture
to learn features of an underlying phenomenon from a training image and then perform
simulations on different domains reproducing the phenomenon complexity.
2 RELATED WORK
MPS simulation provides a framework for spatial modeling of variables in geoscience problems. The reproduction of complex patterns and spatial uncertainty assessment are their
main goals. They can be applied for continuous or categorical variables and the methods can
be extended to the multivariate case, suiting applications in diverse fields (oil and gas, hydrological reservoirs, ore deposits).
CNNs belong to a set of deep learning architectures with great abilities on image analysis.
Their features extraction properties, from raw images, have made them suitable for a variety
of image analysis applications. Connecting neural networks with MPS is not new (Caers &
Journel, 1998) however deep learning techniques have only recently been connected to MPS
(Laloy et al., 2018).
© 2019 Taylor & Francis Group, London, ISBN 978-0-367-33604-2
168
Recursive convolutional neural networks in a multiple-point
statistics framework
Sebastian Avalos & Julian M. Ortiz
The Robert M. Buchan Department of Mining, Queen’s University, Canada
ABSTRACT: This work proposes a new technique for Multiple-Point Statistics simulation
based on a Recursive Convolutional Neural Network approach (RCNN). A study on the
architecture of the network is done to ensure that the spatial structure of the phenomenon
inferred from a training image and its associated uncertainty are properly captured.
A sensitivity analysis over the main architecture parameters is performed on a two dimensional
binary image. Statistical and spatial metrics are determined to quantify the impact of each
parameter as well as the ability to capture the underlying phenomenon.
Keywords: Geostatistics, Deep Learning, Training Image, Categorical Variable
1 INTRODUCTION
Multiple-point statistics (MPS) simulation has seen an explosive development since Strebelle’s
seminal paper in 2002 (Strebelle, 2002). Many different approaches have been proposed (Arpat &
Caers, 2007; Mariethoz et al., 2010; Parra & Ortiz, 2011) and some have reached industrial
applications (Mariethoz et al., 2010). The methods associated to MPS are intimately related
to image and texture analysis (Daly, 2004; Parra & Ortiz, 2011; Zahner et al., 2015). Excellent
reviews of multiple-point simulation methods are available (Tahmasebi, 2018) and further
theoretical and practical details can be found (Mariethoz & Caers, 2014).
This paper is motivated by the possibilities offered by deep learning methods, particularly
Convolutional Neural Networks (CNNs) (LeCun et al., 1998) which have shown extraordinary performances in image analysis, including classification, reconstruction, segmentation,
labeling and more (Dosovitskiy et al., 2015; Eilertsen et al., 2017; Gatys et al., 2016; He et al.,
2016). The main aim is to create a bridge between CNNs and MPS. This is done by proposing
a Recursive Convolutional Neural Network (RCNN) approach that enables the architecture
to learn features of an underlying phenomenon from a training image and then perform
simulations on different domains reproducing the phenomenon complexity.
2 RELATED WORK
MPS simulation provides a framework for spatial modeling of variables in geoscience problems. The reproduction of complex patterns and spatial uncertainty assessment are their
main goals. They can be applied for continuous or categorical variables and the methods can
be extended to the multivariate case, suiting applications in diverse fields (oil and gas, hydrological reservoirs, ore deposits).
CNNs belong to a set of deep learning architectures with great abilities on image analysis.
Their features extraction properties, from raw images, have made them suitable for a variety
of image analysis applications. Connecting neural networks with MPS is not new (Caers &
Journel, 1998) however deep learning techniques have only recently been connected to MPS
(Laloy et al., 2018).