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236 Machine learning for subsurface characterization

Figs. 8.9 and 8.10 compare the original and synthesized NMR T2
distributions obtained by processing the inversion-derived and raw logs,
respectively, using the deep learning models. Deep learning models exhibit
better NMR T2 synthesis as compared to the shallow-learning models. The
synthetic NMR T2 is smooth and appears physically consistent.

4.6 Cross validation
Because of the limited size of the training dataset, the deep learning models
were trained with fixed training steps. To ensure the deep learning models
do not overfit, it is recommended to use the cross-validation method. In our
study, we test the efficacy of the cross validation on the VAE-NN model. A
validation set is built by randomly selecting 100 samples from the 300-ft
interval of the shale formation. The training set contains 375 samples. The
validation loss is monitored during training, and when the validation loss
increases, the training is automatically stopped to prevent overfitting. The
VAE-NN model so trained exhibits a R2 score of 0.60 on the testing dataset
containing 100 samples. Notably the cross validation led to decrease in the
testing/generalization performance due to the reduction in data size under the
limited data available to us for this study. For our case, having a separate
validation set reduces the training set size resulting in the poorly trained,
highly biased deep learning model. Cross validation is suitable when the
model has access to large training dataset; in those cases the model can use
the validation set to monitor overfitting.

5 Comparison of the performances of the deep
and shallow models

Both shallow- and deep learning models can be implemented for NMR T2 log
synthesis. Shallow models are easier to apply due to their simplicity in
architecture, lower training-resource requirements, and relatively easier
explainability. Log-synthesis performance of shallow models in terms of the
R2 score is in the range of 0.6–0.75. A simple ANN with two hidden layers
exhibits the best performance among the shallow-learning models in terms
of R2; nonetheless, ANN performs poorly in terms of the generalization of
the NMR T2 distribution to ensure that the synthesis is physically
consistent (Figs. 8.2 and 8.3).
The four deep learning models implemented in this study process the same
dataset as the shallow-learning models. The two-step training process used for
VAE-, VAEc-, and GAN-based deep neural networks leads to stable and
physically consistent NMR T2 distributions, which resemble those in
the training set (Figs. 8.5 and 8.6). The performance of the four deep
learning models is better than that of shallow-learning models. The average
R2 score for the log synthesis accomplished by the deep models ranges from