Special Issue "Numerical Analysis of Artificial Neural Networks"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Network Science".

Deadline for manuscript submissions: 31 October 2021.

Special Issue Editor

Prof. Dr. Miguel Atencia
E-Mail Website
Guest Editor
Escuela de Ingenierías Industriales, Universidad de Málaga, Málaga 29071, Spain
Interests: recurrent neural networks; dynamical systems; numerical optimization; time series; natural language processing

Special Issue Information

Numerical analysis is one of the pillars, computer algebra being the other, of all computational algorithms. Accurate results of machine learning algorithms for classification, regression, and prediction are supported by theoretical features of numerical methods. The list of examples is overwhelming: principal component analysis based upon numerical linear algebra; optimization with Hopfield networks stemming from concepts rooted in dynamical systems; backpropagation that requires numerical optimizers; etc. On the other hand, research on computational intelligence techniques has led to advances in many numerical methods, with stochastic gradient descent being primus inter pares.

In this Special Issue, we aim at fostering the synergy between these two fields, by encouraging the analysis and design of numerical methods for, in, and from machine learning algorithms. We welcome contributions that highlight satisfactory learning results as soundly based on numerical foundations, as well as ground-breaking numerical methods that provide the basis for efficient practical algorithms, at least at the proof-of-concept stage.

The scope of the issue is deliberately broad, including but not limited to numerical techniques from linear algebra, dynamical systems, kernel methods, optimization, spectral methods, and stochastic formulations, as well as algorithms within neural networks, support vector machines, recurrent networks, and clustering methods.

Prof. Dr. Miguel Atencia
Guest Editor

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Numerical linear algebra
  • Numerical methods for dynamical systems
  • Numerical optimization
  • Geometric numerical integration
  • Iterative methods
  • Convergence
  • Machine learning
  • Neural networks 
  • Classification 
  • Time series forecasting 
  • Dimensionality reduction

Published Papers (2 papers)

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Research

Open AccessArticle
Control Method of Flexible Manipulator Servo System Based on a Combination of RBF Neural Network and Pole Placement Strategy
Mathematics 2021, 9(8), 896; https://doi.org/10.3390/math9080896 (registering DOI) - 17 Apr 2021
Abstract
Gravity and flexibility will cause fluctuations of the rotation angle in the servo system for flexible manipulators. The fluctuation will seriously affect the motion accuracy of end-effectors. Therefore, this paper adopts a control method combining the RBF (Radial Basis Function) neural network and [...] Read more.
Gravity and flexibility will cause fluctuations of the rotation angle in the servo system for flexible manipulators. The fluctuation will seriously affect the motion accuracy of end-effectors. Therefore, this paper adopts a control method combining the RBF (Radial Basis Function) neural network and pole placement strategy to suppress the rotation angle fluctuations. The RBF neural network is used to identify uncertain items caused by the manipulator’s flexibility and the time-varying characteristics of dynamic parameters. Besides, the pole placement strategy is used to optimize the PD (Proportional Differential) controller’s parameters to improve the response speed and stability. Firstly, a dynamic model of flexible manipulators considering gravity is established based on the assumed mode method and Lagrange’s principle. Then, the system’s control characteristics are analyzed, and the pole placement strategy optimizes the parameters of the PD controllers. Next, the control method based on the RBF neural network is proposed, and the Lyapunov stability theory demonstrates stability. Finally, numerical analysis and control experiments prove the effectiveness of the control method proposed in this paper. The means and standard deviations of rotation angle error are reduced by the control method. The results show that the control method can effectively reduce the rotation angle error and improve motion accuracy. Full article
(This article belongs to the Special Issue Numerical Analysis of Artificial Neural Networks)
Open AccessArticle
Unpredictable Oscillations for Hopfield-Type Neural Networks with Delayed and Advanced Arguments
Mathematics 2021, 9(5), 571; https://doi.org/10.3390/math9050571 - 07 Mar 2021
Viewed by 322
Abstract
This is the first time that the method for the investigation of unpredictable solutions of differential equations has been extended to unpredictable oscillations of neural networks with a generalized piecewise constant argument, which is delayed and advanced. The existence and exponential stability of [...] Read more.
This is the first time that the method for the investigation of unpredictable solutions of differential equations has been extended to unpredictable oscillations of neural networks with a generalized piecewise constant argument, which is delayed and advanced. The existence and exponential stability of the unique unpredictable oscillation are proven. According to the theory, the presence of unpredictable oscillations is strong evidence for Poincaré chaos. Consequently, the paper is a contribution to chaos applications in neuroscience. The model is inspired by chaotic time-varying stimuli, which allow studying the distribution of chaotic signals in neural networks. Unpredictable inputs create an excitation wave of neurons that transmit chaotic signals. The technique of analysis includes the ideas used for differential equations with a piecewise constant argument. The results are illustrated by examples and simulations. They are carried out in MATLAB Simulink to demonstrate the simplicity of the diagrammatic approaches. Full article
(This article belongs to the Special Issue Numerical Analysis of Artificial Neural Networks)
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