A comparative study of back-propagation algorithms: Levenberg-Marquart and BFGS for the formation of multilayer neural networks for estimation of fluoride

Abstract

This paper compares and contrasts two back-propagation algorithms: the Levenberg-Marquardt (LM) and the Broyden Fletcher Goldfarb Shanno (BFGS). The concentrations of sixteen physicochemical factors were used to predict Fluoride in the Inaouène basin using artificial neural networks (ANN) of the multilayer perceptron type (MLP). We created many models based on the evolution of activation functions and the number of neurons in the hidden layer. The mean square error (MSE) and correlation coefficient were used to assess the effectiveness of the various ANN model training procedures (R). The LM training algorithms outperform the BFGS training algorithm, according to the results. The statistical indicators (R = 0.99 and MSE = 0.135 for LM and R = 0.95 and MSE = 41.22 for BFGS) highlight the efficacy of the LM algorithm for Fluoride prediction when compared to the BFGS method utilizing MLP type neural networks.