Page 234 - Machine Learning for Subsurface Characterization

204 Machine learning for subsurface characterization

TABLE 7.1 Summary of few parameters of the deep neural networks.

GAN-NN a VAEc-NN LSTM
Number of 9842 (for GAN) 1825 2071
parameters
Training time – 41.25 s/1000 566.33 s/1000
steps steps
a
Different training schedule is used in GAN-NN. Two models were trained alternatively.

the LSTM network, which relies on the recurrence of the internal state. The
LSTM model takes one of the 10 inversion-derived logs at each timestep to
generate the final form of the intermediate vector. Following that, when
predicting the NMR T2 distribution, the LSTM model predicts one element
of the 64-dimensional NMR T2 sequence at each timestep, which requires
64 updates of all the decoder parameters for the sequential generation of the
entire NMR T2.

5 Application of the VAE-NN model

In the first stage of training the VAE-NN, VAE is trained to memorize and
generalize the sequential and shape-related features in the T2 distribution.
The sparsely distributed 64-dimensional T2 distribution is projected to a
2-dimensional latent. VAE learns the manifold of T2 in the latent space by
minimizing the loss functions. There are infinite points in a 2-dimensional
latent space on which infinite projections of 64-dimensional T2 can be
generated. One hundred samples from the two-dimensional latent space are
shown in Fig. 7.7.In Fig. 7.7, the learned T2 distribution changes gradually
in the 2D latent space with slight successive variations in the number of
peaks, smoothness of the distribution, the positions of the peaks, and heights
and widths of the peaks. VAE learning process ensures that the predictive
model will have robust predictions in the presence of noise in input signals.
Once the VAE is trained to memorize and generalize the dominant features
in the T2 distributions, any new input of T2 distribution is projected to a
corresponding location in the 2D latent space where there already exists a
projection of a similar T2 distribution, which was fed during the prior
training phase. The decoder learns to randomly sample from this latent space
to synthesize realistic NMR T2 distributions.
The trained VAE-NN was applied on the 7 formation mineral content logs
and 3 formation fluid saturation logs from 100 testing depths to synthesize the
NMR T2. VAE-NN-based synthesis of NMR T2 shows good agreement with
the original T2 distributions (Fig. 7.8). Histogram of the coefficient of