A new class of neural networks for NCPs using smooth perturbations of the natural residual function

2022 ◽  
pp. 114092
Author(s):  
Jan Harold Alcantara ◽  
Jein-Shan Chen
Keyword(s):  
Neural Networks ◽  
Residual Function ◽  
New Class

CHAOS AND HYPERCHAOS IN A CLASS OF SIMPLE CELLULAR NEURAL NETWORKS MODELED BY O.D.E.

2006 ◽  
Vol 16 (09) ◽  
pp. 2729-2736 ◽  
Author(s):  
XIAO-SONG YANG ◽  
YAN HUANG
Keyword(s):  
Neural Networks ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Lyapunov Exponents ◽  
Cellular Neural Networks ◽  
New Class ◽  
Connection Matrices ◽  
Low Dimensional

This paper presents a new class of chaotic and hyperchaotic low dimensional cellular neural networks modeled by ordinary differential equations with some simple connection matrices. The chaoticity of these neural networks is indicated by positive Lyapunov exponents calculated by a computer.

COMPUTER ASSISTED VERIFICATION OF CHAOS IN THREE-NEURON CELLULAR NEURAL NETWORKS

2007 ◽  
Vol 17 (12) ◽  
pp. 4381-4386 ◽  
Author(s):  
QUAN YUAN ◽  
XIAO-SONG YANG
Keyword(s):  
Neural Networks ◽  
Topological Entropy ◽  
Chaotic Behavior ◽  
Cellular Neural Networks ◽  
Computer Assisted ◽  
Topological Horseshoe ◽  
Poincaré Maps ◽  
New Class ◽  
Numerical Studies ◽  
Connection Matrices

In this paper, we study a new class of simple three-neuron chaotic cellular neural networks with very simple connection matrices. To study the chaotic behavior in these cellular neural networks demonstrated in numerical studies, we resort to Poincaré section and Poincaré map technique and present a rigorous verification of the existence of horseshoe chaos using topological horseshoe theory and the estimate of topological entropy in derived Poincaré maps.

scholarly journals Stochastic Memristive Quaternion-Valued Neural Networks with Time Delays: An Analysis on Mean Square Exponential Input-to-State Stability

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 815 ◽  
Author(s):  
Usa Humphries ◽  
Grienggrai Rajchakit ◽  
Pramet Kaewmesri ◽  
Pharunyou Chanthorn ◽  
Ramalingam Sriraman ◽  
...  
Keyword(s):  
Neural Networks ◽  
Continuous Time ◽  
Lyapunov Functional ◽  
Time Delays ◽  
System Model ◽  
Mean Square ◽  
New Class ◽  
Quaternion Multiplication ◽  
The Mean ◽  
Theoretical Results

In this paper, we study the mean-square exponential input-to-state stability (exp-ISS) problem for a new class of neural network (NN) models, i.e., continuous-time stochastic memristive quaternion-valued neural networks (SMQVNNs) with time delays. Firstly, in order to overcome the difficulties posed by non-commutative quaternion multiplication, we decompose the original SMQVNNs into four real-valued models. Secondly, by constructing suitable Lyapunov functional and applying It o ^ ’s formula, Dynkin’s formula as well as inequity techniques, we prove that the considered system model is mean-square exp-ISS. In comparison with the conventional research on stability, we derive a new mean-square exp-ISS criterion for SMQVNNs. The results obtained in this paper are the general case of previously known results in complex and real fields. Finally, a numerical example has been provided to show the effectiveness of the obtained theoretical results.

scholarly journals An Algorithm for Producing Fuzzy Negations via Conical Sections

Algorithms ◽  
2019 ◽  
Vol 12 (5) ◽  
pp. 89 ◽  
Author(s):  
Souliotis ◽  
Papadopoulos
Keyword(s):  
Artificial Intelligence ◽  
Neural Networks ◽  
Structural Element ◽  
Specific Field ◽  
New Class ◽  
Fuzzy Implications ◽  
Classical Negation ◽  
Geometrical Concepts ◽  
Computational Processes

In this paper we introduced a new class of strong negations, which were generated via conical sections. This paper focuses on the fact that simple mathematical and computational processes generate new strong fuzzy negations, through purely geometrical concepts such as the ellipse and the hyperbola. Well-known negations like the classical negation, Sugeno negation, etc., were produced via the suggested conical sections. The strong negations were a structural element in the production of fuzzy implications. Thus, we have a machine for producing fuzzy implications, which can be useful in many areas, as in artificial intelligence, neural networks, etc. Strong Fuzzy Negations refers to the discrepancy between the degree of difficulty of the effort and the significance of its results. Innovative results may, therefore, derive for use in literature in the specific field of mathematics. These data are, moreover, generated in an effortless, concise, as well as self-evident manner.

Edge-aware filtering with Siamese neural networks

2020 ◽  
Vol 39 (10) ◽  
pp. 711-717
Author(s):  
Mehdi Aharchaou ◽  
Michael Matheney ◽  
Joe Molyneux ◽  
Erik Neumann
Keyword(s):  
Neural Networks ◽  
Seismic Data ◽  
Learning Ability ◽  
Seismic Exploration ◽  
Data Sets ◽  
3D Seismic ◽  
New Class ◽  
Seismic Image ◽  
Siamese Networks ◽  
Seismic Images

Recent demands to reduce turnaround times and expedite investment decisions in seismic exploration have invited new ways to process and interpret seismic data. Among these ways is a more integrated collaboration between seismic processors and geologist interpreters aiming to build preliminary geologic models for early business impact. A key aspect has been quick and streamlined delivery of clean high-fidelity 3D seismic images via postmigration filtering capabilities. We present a machine learning-based example of such a capability built on recent advances in deep learning systems. In particular, we leverage the power of Siamese neural networks, a new class of neural networks that is powerful at learning discriminative features. Our novel adaptation, edge-aware filtering, employs a deep Siamese network that ranks similarity between seismic image patches. Once the network is trained, we capitalize on the learned features and self-similarity property of seismic images to achieve within-image stacking power endowed with edge awareness. The method generalizes well to new data sets due to the few-shot learning ability of Siamese networks. Furthermore, the learning-based framework can be extended to a variety of noise types in 3D seismic data. Using a convolutional architecture, we demonstrate on three field data sets that the learned representations lead to superior filtering performance compared to structure-oriented filtering. We examine both filtering quality and ease of application in our analysis. Then, we discuss the potential of edge-aware filtering as a data conditioning tool for rapid structural interpretation.

CHAOS, BIFURCATION AND ROBUSTNESS OF A CLASS OF HOPFIELD NEURAL NETWORKS

2011 ◽  
Vol 21 (03) ◽  
pp. 885-895 ◽  
Author(s):  
WEN-ZHI HUANG ◽  
YAN HUANG
Keyword(s):  
Neural Networks ◽  
Dynamical Systems ◽  
Chaotic Behavior ◽  
Robustness Analysis ◽  
Original System ◽  
Hopfield Neural Networks ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Computer Assisted ◽  
New Class

Chaos, bifurcation and robustness of a new class of Hopfield neural networks are investigated. Numerical simulations show that the simple Hopfield neural networks can display chaotic attractors and limit cycles for different parameters. The Lyapunov exponents are calculated, the bifurcation plot and several important phase portraits are presented as well. By virtue of horseshoes theory in dynamical systems, rigorous computer-assisted verifications for chaotic behavior of the system with certain parameters are given, and here also presents a discussion on the robustness of the original system. Besides this, quantitative descriptions of the complexity of these systems are also given, and a robustness analysis of the system is presented too.

A new class of neural networks and its applications

2017 ◽  
Vol 249 ◽  
pp. 28-47 ◽  
Author(s):  
Kais Bouallegue
Keyword(s):  
Neural Networks ◽  
New Class

scholarly journals Delay-Dependent Stability Analysis for Recurrent Neural Networks with Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Shu Lv ◽  
Junkang Tian ◽  
Shouming Zhong
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Activation Functions ◽  
New Class ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper concerns the problem of delay-dependent stability criteria for recurrent neural networks with time varying delays. By taking more information of states and activation functions as augmented vectors, a new class of the Lyapunov functional is proposed. Then, some less conservative stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.

scholarly journals The Problem of Constructing the GMDH Neural Networks with Active Neurons

2021 ◽  
pp. 45-54
Author(s):  
Olha G. Moroz ◽  
Keyword(s):  
Complex System ◽  
Neural Networks ◽  
Computational Intelligence ◽  
Statistical Data ◽  
System Models ◽  
New Class ◽  
Advantages And Disadvantages ◽  
Inductive Construction ◽  
The Creation

Characteristics of the existing neural networks of GMDH with active neurons are given and their main advantages and disadvantages are analyzed. An approach to increasing the efficiency of inductive construction of complex system models from statistical data based on the creation of a new class of GMDH neural networks with active neurons using methods of computational intelligence is proposed.

scholarly journals The duality between particle methods and artificial neural networks

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
A. Alexiadis ◽  
M. J. H. Simmons ◽  
K. Stamatopoulos ◽  
H. K. Batchelor ◽  
I. Moulitsas
Keyword(s):  
Artificial Intelligence ◽  
Neural Networks ◽  
Molecular Dynamics ◽  
Artificial Neural Networks ◽  
Particle Methods ◽  
Luminal Content ◽  
Physical Systems ◽  
Reward Function ◽  
New Class ◽  
Artificial Neurons

Abstract The algorithm behind particle methods is extremely versatile and used in a variety of applications that range from molecular dynamics to astrophysics. For continuum mechanics applications, the concept of ‘particle’ can be generalized to include discrete portions of solid and liquid matter. This study shows that it is possible to further extend the concept of ‘particle’ to include artificial neurons used in Artificial Intelligence. This produces a new class of computational methods based on ‘particle-neuron duals’ that combines the ability of computational particles to model physical systems and the ability of artificial neurons to learn from data. The method is validated with a multiphysics model of the intestine that autonomously learns how to coordinate its contractions to propel the luminal content forward (peristalsis). Training is achieved with Deep Reinforcement Learning. The particle-neuron duality has the advantage of extending particle methods to systems where the underlying physics is only partially known, but we have observations that allow us to empirically describe the missing features in terms of reward function. During the simulation, the model evolves autonomously adapting its response to the available observations, while remaining consistent with the known physics of the system.

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