Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Application of Gradient Optimization Methodsin Defining Neural Dynamics

Predrag S. Stanimirović
ORCID logo ,
Nataša Tešić
,
Dimitrios Gerontitis
,
Gradimir V. Milovanović
,
Milena J. Petrović
* ORCID logo ,
Vladimir L. Kazakovtsev
,
Vladislav A. Stasiuk
Version 1 : Received: 3 November 2023 / Approved: 6 November 2023 / Online: 6 November 2023 (08:01:40 CET)

A peer-reviewed article of this Preprint also exists.

Stanimirović, P.S.; Tešić, N.; Gerontitis, D.; Milovanović, G.V.; Petrović, M.J.; Kazakovtsev, V.L.; Stasiuk, V. Application of Gradient Optimization Methods in Defining Neural Dynamics. Axioms 2024, 13, 49. Stanimirović, P.S.; Tešić, N.; Gerontitis, D.; Milovanović, G.V.; Petrović, M.J.; Kazakovtsev, V.L.; Stasiuk, V. Application of Gradient Optimization Methods in Defining Neural Dynamics. Axioms 2024, 13, 49.

Abstract

Applications of gradient method for nonlinear optimization in development of Gradient Neural Network (GNN) and Zhang Neural Network (ZNN) are investigated. Particularly, the solution of the matrix equation AXB=D which changes over time is studied using the novel GNN model, termed as GGNN(A,B,D). The GGNN model is developed applying GNN dynamics on the gradient of the error matrix used in the development of the GNN model. The convergence analysis shows that the neural state matrix of the GGNN(A,B,D) design converges asymptotically to the solution of the matrix equation AXB=D, for any initial state matrix. It is also shown that the convergence result is the least square solution which is defined depending on the selected initial matrix. A hybridization of GGNN with analogous modification GZNN of the ZNN dynamics is considered. The Simulink implementation of presented GGNN models is carried out on the set of real matrices.

Keywords

gradient neural network; generalized inverses, Moore-Penrose inverse; linear matrix equations

Subject

Computer Science and Mathematics, Applied Mathematics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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