Hydro
Convolutional Neural Networks with Encoder-decoder structure for predicting Hydraulic tomography
In this work, we discuss the capabilities of using a deep learning algorithm with Conventional Neural Network concept to characterize the hydraulic properties of aquifers. Designed to directly approximate the inverse operator of hydraulic tomography, the algorithm (CNN-HT) is trained with a synthetic dataset where hydraulic head records are associated with pumping tests in a randomized hydraulic transmissivity field.
Encoder-Decoder architecture with 31 layers.
This approach relies on an adaptation of SegNet neural network, which was initially developed for understanding real traffic scenes in urban streets. SegNet consists of encoder-decoders network. In the encoder, sequential operations with multiple filters such as convolution, batch normalization, and max-pooling are performed to identify feature maps of the input data. In the decoder, the up-sampling, convolution, batch normalization, and regression operators are used to prepare the output by recovering the loss of spatial resolution that occurred in the encoder process. In this fitting, we used the iterative least squares formulation at the first interpretation with the Jacobian matrix to fit the size of the hydraulic head data to the size of the output (transmissivity field).
This protocol was applied to hydraulic head data computed numerically by solving the groundwater flow equation for a given transmissivity field generated geostatistically with Gaussian and spherical variograms. Part of this data was used to train the network and the other unseen part to test its performance. The testing step confirmed the effectiveness of this tool in reconstructing the main heterogeneities of the hydraulic properties, the effectiveness being related to the nature and amount of training data.
CNN-HT method provided mapping results of the same quality as those obtained with the Gauss-Newton algorithm employing a computation of the Jacobian matrix. While this new method performs each interpretation instantly compared to hours by a conventional approach.
