Levenberg-Marquardt training algorithm

The performance of an ANN is measured by the root-mean-square error (RMSE) which is also the function to be minimised. The Levenberg-Marquardt optimization algorithm (Marquardt, 1963) and resilient propagation algorithm (RPROP) (Riedmiller Braun, 1993) were used to train the neural networks in this study. 

The above-related situation can also be improved by using a different algorithm for training. One of the most efficient minimization algorithms is the Levenberg-Marquardt (LM) [56,59]. It is between 10 and 100 times faster than gradient-descent, given it employs a second-derivative approach, while GDM employs only first-derivative terms. As the calculation of the Hessian matrix (matrix of the second derivatives of the error in... 

To construct and train the network, pulse current intensity (I), pulse-on time (t,) and pulse-off time (tg) are used as the input parameters and corresponding fractal dimension (D) is used as the output. Only one hidden layer is used in the networks. The numbers of neurons are varied to select best network based on the minimum mean squared error (MSB). For training of the network, Levenberg-Marquardt algorithm is used. All the observations of the FCC design are used in the training of the networks. 

Training algorithm Levenberg- Marquardt Bayesian Regulation... 

Commercially available software [15] was used for the ANN calculations. The Levenberg-Marquardt algorithm was used to accelerate the training procedure. 

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