Page 133 - Machine Learning for Subsurface Characterization

Stacked neural network architecture Chapter 4 109

When there are multiple targets (outputs), a general practitioner either uses
one ANN to simultaneously predict all the targets or uses one ANN model to
individually predict each target by processing all the features (none of the tar-
gets) as inputs to the ANN model. In both the cases, the relationships/dependen-
cies between the available targets are not fully used when training the ANN
model. In other words, a traditional ANN model is not trained to process few
of the available targets along with all the features as inputs to the ANN model
for predicting the rest of the targets.
The stacking of ANN models in the SNN model is such that the 8 ANN
models implemented in the second step for the synthesis of the 8 DD logs
(Fig. 4.1) are sequentially trained, wherein the ith ANN model that synthesizes
the ith ranked DD log is fed with all the previously predicted or measured
higher-ranked DD logs (i ¼ 1to i 1) and the 15 conventional logs. Conse-
quently, the SNN model learns to synthesize each target by processing 15 con-
ventional logs along with few other targets as inputs. Notably, when training the
SNN model, the measured values of targets (DD logs) and measured values of
features (15 conventional logs) are fed as inputs to each ANN model implemen-
ted in the second step, whereas when testing and deploying the SNN model, the
predicted values of targets (DD logs) and measured values of features (15 con-
ventional logs) are fed as inputs to each ANN model implemented in the second
step. This avoids contamination between training and testing dataset, and
ensures that the testing dataset is used in a way that is similar to the deploy-
ment/new dataset. Due to the physics of charge polarization, conductivity is
related to permittivity at each frequency, and the conductivity/permittivity at
one frequency is related to conductivity/permittivity at another frequency. Such
relationships are inherent in any dispersive property with a causal behavior. The
SNN architecture used in this study is designed to learn these physical relation-
ships as a function of frequency and phase difference.
A simple multivariate linear regression (MLR) model and a traditional ANN
model were also trained to synthesize the 8 DD logs one at a time by processing
the 15 conventional logs as features/inputs. This evaluation was performed to
check the performance of MLR model and ANN model in comparison with the
SNN model in the DD log-synthesis task. The prediction performance of the
MLR model and ANN model is 20% lower and 10% lower, respectively, com-
pared with that of the SNN model. It can be concluded that the inherent depen-
dencies among the targets can be utilized by using few targets as some of the
inputs to synthesize the rest of the targets.

2.3 Evaluation metric/measure for log-synthesis model

A key aspect in the development of data-driven model is the selection and
proper interpretation of the evaluation metrics used for measuring and deter-
mining the model performances on the training and testing dataset. There are
various evaluation metrics for model evaluation. A user should be aware of