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Comparison of Second Order Algorithms for Function Approximation with Neural Networks

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Boutalbi E., Ait Gougam L., Mekideche-Chafa F.

Acta Physica Polonica A

2015

vol. 128

issue 2B

B-271-B-272

The Neural networks are massively parallel, distributed processing systems representing a new computational technology built on the analogy to the human information processing system. They are usually considered as naturally parallel computing models. The combination of wavelets with neural networks can hopefully remedy each other's weaknesses, resulting in wavelet based neural network capable of approximating any function with arbitrary precision. A wavelet based neural network is a nonlinear regression structure that represents nonlinear mappings as the superposition of dilated and translated versions of a function, which is found both in the space and frequency domains. The desired task is usually obtained by a learning procedure which consists in adjusting the "synaptic weights". For this purpose, many learning algorithms have been proposed to update these weights. The convergence for these learning algorithms is a crucial criterion for neural networks to be useful in different applications. In this paper, we use different training algorithms for feed forward wavelet networks used for function approximation. The training is based on the minimization of the least-square cost function. The minimization is performed by iterative first and second order gradient-based methods. We make use of the Levenberg-Marquardt algorithm to train the architecture of the chosen network and, then, the training procedure starts with a simple gradient method which is followed by a BFGS (Broyden, Fletcher, Glodfarb et Shanno) algorithm. The conjugate gradient method is then used. The performances of the different algorithms are then compared. It is found that the advantage of the last training algorithm, namely, conjugate gradient method, over many of the other optimization algorithms is its relative simplicity, efficiency and quick convergence.

Neurocomputing Techniques to Predict the 2D Structures by Using Lattice Dynamics of Surfaces

100%

Belayadi A., Bourahla B., Mekideche-Chafa F.

Acta Physica Polonica A

2017

vol. 132

issue 4

1314-1319

A theoretical study of artificial neural network modelling, based on vibrational dynamic data for 2D lattice, is proposed in this paper. The main purpose is to establish a neurocomputing model able to predict the 2D structures of crystal surfaces. In material surfaces, atoms can be arranged in different possibilities, defining several 2D configurations, such as triangular, square lattices, etc. To describe these structures, we usually employ the Wood notations, which are considered as the simplest manner and the most frequently used to spot the surfaces in physics. Our contribution consists to use the vibration lattice of perfect 2D structures along with the matrix and Wood notations to build up an input-output set to feed the neural model. The input data are given by the frequency modes over high symmetry points and the group velocity. The output data are given by the basis vectors corresponding to surface reconstruction and the rotation angle which aligns the unit cell of the reconstructed surface. Results showed that the method of collecting the dataset was very suitable for building a neurocomputing model that is able to predict and classify the 2D surface of the crystals. Moreover, the model was able to generate the lattice spacing for a given structure.

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2 Acta Physica Polonica A

1 2017

1 2015

2 Mekideche-Chafa F.

1 Ait Gougam L.

1 Belayadi A.

1 Bourahla B.

1 Boutalbi E.

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Comparison of Second Order Algorithms for Function Approximation with Neural Networks

Neurocomputing Techniques to Predict the 2D Structures by Using Lattice Dynamics of Surfaces