175
5.4 Recursiveness
Section 3 discusses the theoretical benefits of the recursive approach, where CNN 1 is trained
to infer the closest IP from a finite number of hard data while CNN i i
| >1 learns how to remediate the lack of previous information by improving the quality of the inferred IP.
D
1 has some artefacts due to the lack of information but on D
4 the structures get connected and almost every artefact has been erased. Realizations go from failing to reproduce
the two-points statistics at D
1 to suitably reproduce the GT variogram at D
4 . The pixel error
decreases considerably from D
1 to D
4 . The binary proportion does not seem to improve
after D
2 . Figure 5 shows E-types at each domain using 100 realizations and the base case
parameters.
6 CONCLUSIONS
RCNN, a Recursive Convolutional Neural Network approach to perform Multiple-Point
Statistics simulations was presented. The focus was mainly on the architecture of RCNN,
and the training and simulation methodology to provide a clear understanding of the novel
approach and a simple guide to define CNN inner architectures. Excellent results were
achieved over a two dimensional binary case, showing the benefits of bringing deep learning
techniques into the classical MPS framework.
By means of visualizations, variographic analysis and statistical metrics of continuity,
the relevance of the amount of neurons at the classification zone has been stablished suggesting 5000 neurons, as well as the advantage of keeping a simple model with a depth in
the hidden layers in the extraction feature zone of 16, and a search grid and inner pattern
of 19 × 19.
Although no sensitivities on the amount of nested CNN were carried out, the benefits
of using a RCNN with 4 nested CNN were clearly established suggesting the further use of
at least four recursive CNN. Results are promising and further work must be carried out to
achieve better results with less information.
Figure 4. One realization, E-type, variance map and variographic analysis over D
4
, using optimum
parameters.
Figure 5. E-types over each domain using 100 realizations using the base case.
On e realization
E-type
Var i ance map
E- type D 1
E - t ype D 2
E - type D 3
0 . 25
Experimental variogram
Reas - Ver
0 . 4
Reas-Ho r
0 . 3
0 . 2
0 . 1
Distance
E- type D 4
5.4 Recursiveness
Section 3 discusses the theoretical benefits of the recursive approach, where CNN 1 is trained
to infer the closest IP from a finite number of hard data while CNN i i
| >1 learns how to remediate the lack of previous information by improving the quality of the inferred IP.
D
1 has some artefacts due to the lack of information but on D
4 the structures get connected and almost every artefact has been erased. Realizations go from failing to reproduce
the two-points statistics at D
1 to suitably reproduce the GT variogram at D
4 . The pixel error
decreases considerably from D
1 to D
4 . The binary proportion does not seem to improve
after D
2 . Figure 5 shows E-types at each domain using 100 realizations and the base case
parameters.
6 CONCLUSIONS
RCNN, a Recursive Convolutional Neural Network approach to perform Multiple-Point
Statistics simulations was presented. The focus was mainly on the architecture of RCNN,
and the training and simulation methodology to provide a clear understanding of the novel
approach and a simple guide to define CNN inner architectures. Excellent results were
achieved over a two dimensional binary case, showing the benefits of bringing deep learning
techniques into the classical MPS framework.
By means of visualizations, variographic analysis and statistical metrics of continuity,
the relevance of the amount of neurons at the classification zone has been stablished suggesting 5000 neurons, as well as the advantage of keeping a simple model with a depth in
the hidden layers in the extraction feature zone of 16, and a search grid and inner pattern
of 19 × 19.
Although no sensitivities on the amount of nested CNN were carried out, the benefits
of using a RCNN with 4 nested CNN were clearly established suggesting the further use of
at least four recursive CNN. Results are promising and further work must be carried out to
achieve better results with less information.
Figure 4. One realization, E-type, variance map and variographic analysis over D
4
, using optimum
parameters.
Figure 5. E-types over each domain using 100 realizations using the base case.
On e realization
E-type
Var i ance map
E- type D 1
E - t ype D 2
E - type D 3
0 . 25
Experimental variogram
Reas - Ver
0 . 4
Reas-Ho r
0 . 3
0 . 2
0 . 1
Distance
E- type D 4