Page 228 - Machine Learning for Subsurface Characterization

198 Machine learning for subsurface characterization

of the NMR T2 distribution, which is processed as a 64-dimensional 1D vector.
The training schematic for the VAEc-NN architecture is presented in Fig. 7.5.
In the first stage of training the VAEc-NN (Fig. 7.5), the VAEc learns to
reproduce the measured NMR T2 distributions. The encoder network of the
VAEc projects the 64-dimensional T2 data to 3-dimensional latent space.
Subsequently the decoder upscales the latent vectors sampled from the
latent spacetoreconstruct themeasuredT2data,which was fedtothe
encoder network. VAEc comprises 8 layers, namely, one 64-dimensional
input layer, one 64 16 convolutional layer, one 16 16 max-pooling
layer, 16-dimensional fully connected hidden layer, one 3-dimensional
probabilistic latent layer, and finally the 3-layered decoder network
comprising fully connected 3-dimensional and 16-dimensional hidden
layers and 64-dimensional output layer.
The original NMR T2 are first fed into the 64-dimensional input layer of the
encoder. The 64 16 convolutional layer is then generated by filtering the
64-dimensional input layer using 16 filters (kernels) of size 3 1. VAEc
training aims at finding the mathematical forms of these 16 filters most
suited for extracting features from the NMR T2 that can later be used for the
NMR T2 synthesis. Unlike a fully connected layer that learns features from
all the combinations of the features of the previous layer, a convolutional
layer relies on local spatial coherence within a small receptive field, as

FIG. 7.5 Schematic for training the VAEc-NN architecture. The number of hidden layers in each
network and the number of neurons in each hidden layer are determined by hyperparameter
optimization.