Page 266 - Machine Learning for Subsurface Characterization

230 Machine learning for subsurface characterization

acquire” input logs and the NMR T2 distribution. This two-step training process
increases the robustness of the log synthesis. The fourth model is long short-
term memory network that processes the easy-to-acquire logs as a sequence
and tries to find a corresponding sequence of NMR T2 distribution.

4.1 Variational autoencoder assisted neural network
VAE-NN is trained in two steps. First step uses the variational autoencoder
(VAE) network comprising encoder and decoder networks. VAE learns to
abstract and reconstruct the NMR T2 distribution. The encoder projects the
NMR T2 from training dataset to a 2D or 3D latent space, and the decoder
reconstructs the NMR T2. The decoder takes the encoded latent vector as
input and decodes it into NMR T2 distribution. The goal of the first step is
to reproduce the NMR T2 distribution. The generation of the latent
variable involves a sampling process from Gaussian distribution, the VAE
is trained to project NMR T2 distribution with similar features to similar
space, which reduces the cost of reconstruction. After the first step of
training, the decoder network has learnt to generate a typical NMR
response by processing the latent vectors.
Decoder trained in the first step of training is frozen to preserve the VAE’s
learning related to the NMR T2 distributions in the training dataset. In the
second step of training, a simple fully connected ANN with 3–5 hidden
layers is connected to the trained decoder (Fig. 8.4). The “easy-to-acquire”
input logs are fed to the ANN, and the ANN is trained to generate the latent
vector for the decoder network. The latent vector will be decoded into NMR
T2 distribution by the decoder. In doing so, the second step of training
relates the easy-to-acquire logs to the NMR T2 distribution. Fig. 8.5
illustrates the manifold learned by the VAE in the first step of training. It
basically is an abstraction learnt by the decoder network from the NMR T2
distributions in training set. The gradual and smooth changing NMR T2 in
each of the subplots is what the VAE learned from the training set in the
first step of training. This learnt manifold represents the essential features of
the NMR T2 distribution.

4.2 Generative adversarial network assisted neural network

GAN-NN model follows a two-step training process, with some similarity to
VAE-NN. In the first step, generative adversarial network (GAN) learns
from the NMR T2 distribution in the training dataset; this involves training a
generator network to reconstruct NMR T2 distributions with large similarity
to those in the training dataset. This requires a discriminator network that
evaluates the NMR synthesis achieved by the generator network. In the first
step, the generator and discriminator networks are trained alternatively using
only the NMR T2 distributions in the training dataset. First a random vector