N-hidden layer artificial neural network architecture computer code: geophysical application example

Abstract

We provide a MATLAB computer code for training artificial neural network (ANN) with N+1 layer (N-hidden layer) architecture. Currently, the ANN application to solving geophysical problems have been confined to the 2-layer, i.e. 1-hidden layer, architecture because there are no open source software codes for higher numbered layer architecture. The restriction to the 2-layer architecture comes with the attendant model error due to insufficient hidden neurons to fully define the ANN machines. The N-hidden layer ANN has a general architecture whose sensitivity is the accumulation of the backpropagation of the error between the feedforward output and the target patterns. The trained ANN machine can be retrieved by the gradient optimization method namely: Levenberg-Marquardt, steepest descent or conjugate gradient methods. Our test results on the Poisson's ratio (as a function of compressional and shear wave velocities) machines with 2-, 3- and 4-layer ANN architectures reveal that the machines with higher number of layers outperform those with lower number of layers. Specifically, the 3- and 4-layer ANN machines have ≥97% accuracy, predicting the lithology and fluid identification in the oil and gas industry by means of the Poisson's ratio, whereas the 2-layer ANN machines poorly predict the results with as large error as 20%. These results therefore reinforce our belief that this open source code will facilitate the training of accurate N-hidden layer ANN sophisticated machines with high performance and quality delivery of geophysical solutions. Moreover, the easy portability of the functions of the code into other software will enhance a versatile application and further research to improve its performance.