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To enhance solution accuracy and training efficiency in neural network approximation to partial differential equations, partitioned neural networks can be used as a solution surrogate instead of a single large and deep neural network defined on the whole problem domain. In such a partitioned neural network approach, suitable interface conditions or subdomain boundary conditions are combined to obtain a convergent approximate solution. However, there has been no rigorous study on the convergence and parallel computing enhancement on the partitioned neural network approach. In this paper, iterative algorithms are proposed to enhance parallel computation performance in the partitioned neural network approximation. Our iterative algorithms are based on classical additive Schwarz domain decomposition methods. For the proposed iterative algorithms, their convergence is analyzed under an error assumption on the local and coarse neural network solutions. Numerical results are also included to show the performance of the proposed iterative algorithms. [ABSTRACT FROM AUTHOR]

Forward–backward doubly stochastic differential equations (FBDSDEs) serve as a probabilistic interpretation of stochastic partial differential equations (SPDEs) with diverse applications. Coupled FBDSDEs encounter numerous challenges in numerical approximation compared to forward–backward stochastic differential equations (FBSDEs) and decoupled FBDSDEs, including ensuring the measurability of the numerical solutions, accounting for the mutual influences between forward and backward processes, and considering the relationship with respect to SPDEs rather than PDEs. This paper introduces, for the first time, a numerical method for solving multi-dimensional coupled FBDSDEs. By integrating an optimal control-based approach with deep neural networks, it effectively addresses the coupling-related challenges between forward and backward equations. Computational examples of coupled FBDSDEs with explicit solutions demonstrate that the proposed deep learning-based numerical algorithm achieves commendable performance in terms of both accuracy and efficiency. [ABSTRACT FROM AUTHOR]

Physics-informed neural networks (PINNs) have shown remarkable achievements in solving partial differential equations (PDEs). However, their performance is limited when encountering oscillatory part in the solutions of PDEs. Therefore, this paper proposes a multi-scale deep neural network with periodic activation function to achieve high-frequency to low-frequency conversion, which can capture the oscillation part of the solution of PDEs. Moreover, the use of adaptive sampling method can adaptively change the location and distribution of residual points, improving the performance of the network. Additionally, the gradient-enhanced strategy is also utilized to embed the gradient information of the PDEs into the loss function of the neural network, which further improves the accuracy of PINNs. Through the numerical experiments verification, it is found that our method is better than PINNs in terms of accuracy and efficiency. • A MscaleDNNs structure with periodic activation functions is proposed. • The proposed neural network has better stability and robustness. • The effectiveness of the method was verified through numerical experiments. [ABSTRACT FROM AUTHOR]

The efficient approximation of parametric PDEs is of tremendous importance in science and engineering. In this paper, we show how one can train Galerkin discretizations to efficiently learn quantities of interest of solutions to a parametric PDE. The central component in our approach is an efficient neural-network-weighted Minimal-Residual formulation, which, after training, provides Galerkin-based approximations in standard discrete spaces that have accurate quantities of interest, regardless of the coarseness of the discrete space. [ABSTRACT FROM AUTHOR]

Deep learning methods have gained considerable interest in the numerical solution of various partial differential equations (PDEs). One particular focus is physics-informed neural networks (PINN), which integrate physical principles into neural networks. This transforms the process of solving PDEs into optimization problems for neural networks. To address a collection of advection-diffusion equations (ADE) in a range of difficult circumstances, this paper proposes a novel network structure. This architecture integrates the solver, a multi-scale deep neural networks (MscaleDNN) utilized in the PINN method, with a hard constraint technique known as HCPINN. This method introduces a revised formulation of the desired solution for ADE by utilizing a loss function that incorporates the residuals of the governing equation and penalizes any deviations from the specified boundary and initial constraints. By surpassing the boundary constraints automatically, this method improves the accuracy and efficiency of the PINN technique. To address the "spectral bias" phenomenon in neural networks, a subnetwork structure of MscaleDNN and a Fourier-induced activation function are incorporated into the HCPINN, resulting in a hybrid approach called SFHCPINN. The effectiveness of SFHCPINN is demonstrated through various numerical experiments involving ADE in different dimensions. The numerical results indicate that SFHCPINN outperforms both standard PINN and its subnetwork version with Fourier feature embedding. It achieves remarkable accuracy and efficiency while effectively handling complex boundary conditions and high-frequency scenarios in ADE. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the forward problems on the data-driven rational solitons for the (2+1)-dimensional Kadomtsev–Petviashvili-I (KP-I) equation and spin-nonlinear Schrödinger (spin-NLS) equation via the deep neural networks learning. Moreover, the inverse problems of the (2+1)-dimensional KP-I equation and spin-NLS equation are studied via deep learning. The main idea of the data-driven forward and inverse problems is to use the deep neural networks with the activation function to approximate the solutions of the considered (2+1)-dimensional nonlinear wave equations by optimizing the chosen loss functions related to the considered nonlinear wave equations. • Forward problems of 2D KP-I and spin-NLS equations with rational solitons are studied via deep learning. • Inverse problems of 2D KP-I and spin-NLS equations are discussed via deep learning. • Inverse problems of the 2D combination of NLS and cmKdV equations are explored via deep learning. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the problem of state estimation for fuzzy cellular neural networks (FCNNs) with time delay in the leakage term, discrete and unbounded distributed delays. In this paper, leakage delay in the leakage term is used to unstable the neuron states. It is challenging to develop a delay dependent condition to estimate the unstable neuron states through available output measurements such that the error-state system is globally asymptotically stable. By constructing the Lyapunov–Krasovskii functional which contains a triple-integral term, an improved delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). However, by using the free-weighting matrices method, a simple and efficient criterion is derived in terms of LMIs for estimation. The restriction such as the time-varying delay which was required to be differentiable or even its time-derivative which was assumed to be smaller than one, are removed. Instead, the time-varying delay is only assumed to be bounded. Finally, numerical examples and its simulations are given to demonstrate the effectiveness of the derived results. [Copyright &y& Elsevier]

Abstract: In this paper, a novel approach to adjusting the weightings of fuzzy neural networks using a Real-coded Chaotic Quantum-inspired genetic Algorithm (RCQGA) is proposed. Fuzzy neural networks are traditionally trained by using gradient-based methods, which may fall into local minimum during the learning process. To overcome the problems encountered by the conventional learning methods, RCQGA algorithms are adopted because of their capabilities of directed random search for global optimization. It is well known, however, that the searching speed of the conventional quantum genetic algorithms (QGA) is not satisfactory. In this paper, a real-coded chaotic quantum-inspired genetic algorithm (RCQGA) is proposed based on the chaotic and coherent characters of Q-bits. In this algorithm, real chromosomes are inversely mapped to Q-bits in the solution space. Q-bits probability-guided real cross and chaos mutation are applied to the evolution and searching of real chromosomes. Chromosomes consisting of the weightings of the fuzzy neural network are coded as an adjustable vector with real number components that are searched by the RCQGA. Simulation results have shown that faster convergence of the evolution process in searching for an optimal fuzzy neural network can be achieved. Examples of nonlinear functions approximated by using the fuzzy neural network via the RCQGA are demonstrated to illustrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: The discrete delayed Hopfield neural networks is an extension of the discrete Hopfield neural networks. In this paper, the convergence of discrete delayed Hopfield neural networks is mainly studied, and some results on the convergence are obtained by using Lyapunov function. Several new sufficient conditions for the delayed networks converging towards a limit cycle with period at most 2 are proved in parallel updating mode. Also, some conditions for the delayed networks converging towards a limit cycle with 2-period are investigated in parallel updating mode. All results established in this paper extend the previous results on the convergence of both the discrete Hopfield neural networks, and the discrete delayed Hopfield neural networks in parallel updating mode. [Copyright &y& Elsevier]

Abstract: In this paper, the exponential periodicity and stability of neural networks with Lipschitz continuous activation functions are investigated, without assuming the boundedness of the activation functions and the differentiability of time-varying delays, as needed in most other papers. The neural networks contain reaction-diffusion terms and both variable and unbounded delays. Some sufficient conditions ensuring the existence and uniqueness of periodic solution and stability of neural networks with reaction-diffusion terms and both variable and unbounded delays are obtained by analytic methods and inequality technique. Furthermore, the exponential converging index is also estimated. The methods, which does not make use of Lyapunov functional, is simple and valid for the periodicity and stability analysis of neural networks with variable and/or unbounded delays. The results extend some previous results. Two examples are given to show the effectiveness of the obtained results. [Copyright &y& Elsevier]

Efficient computation of eigenvectors and eigenvalues of a matrix is an important problem in engineering, especially for computing eigenvectors corresponding to largest or smallest eigenvalues of a matrix. This paper proposes a neural network based approach to compute eigenvectors corresponding to the largest or smallest eigenvalues of any real symmetric matrix. The proposed network model is described by differential equations, which is a class of continuous time recurrent neural network model. It has parallel processing ability in an asynchronous manner and can achieve high computing performance. This paper provides a clear mathematical understanding of the network dynamic behaviors relating to the computation of eigenvectors and eigenvalues. Computer simulation results show the computational capability of the network model. [Copyright &y& Elsevier]

A soft computing approach based on artificial neural network (ANN) and optimization is presented for the numerical solution of the unsteady one-dimensional advection–dispersion equation (ADE) arising in contaminant transport through porous media. A length factor ANN method, based on automatic satisfaction of arbitrary boundary conditions (BCs) was chosen for the numerical solution of ADE. The strength of ANN is exploited to construct a trial approximate solution (TAS) for ADE in a way that it satisfies the initial or BCs exactly. An unsupervised error is constructed in approximating the solution of ADE which is minimized by training ANN using gradient descent algorithm (GDA). Two challenging test problems of ADE are considered in this paper, in which, the first problem has steep boundary layers near x = 1 and many numerical methods create non-physical oscillation near steep boundaries. Also for the second problem many numerical schemes suffer from computational noise and instability issues. The proposed method is advantageous as it does not require temporal discretization for the solution of the ADEs as well as it does not suffer from numerical instability. The reliability and effectiveness of the presented algorithm is investigated by sufficient large number of independent runs and comparison of results with other existing numerical methods. The results show that the present method removes the difficulties arising in the solution of the ADEs and provides solution with good accuracy. [ABSTRACT FROM AUTHOR]

Abstract: Several classification tasks in different application domains can be seen as hierarchical classification problems. In order to deal with hierarchical classification problems, the use of existing flat classification approaches is not appropriate. For these reason, there has been a growing number of studies focusing on the development of novel algorithms able to induce classification models for hierarchical classification problems. In this paper we study the performance of a novel algorithm called Hierarchical Classification using a Competitive Neural Network (HC-CNN) and compare its performance against the Global-Model Naïve Bayes (GMNB) on eight protein function prediction datasets. Interestingly enough, the comparison of two global-model hierarchical classification algorithms for single path of labels hierarchical classification problems has never been done before. [Copyright &y& Elsevier]

Abstract: Adaptive networks are a novel class of dynamical networks whose topologies and states coevolve. Many real-world complex systems can be modeled as adaptive networks, including social networks, transportation networks, neural networks and biological networks. In this paper, we introduce fundamental concepts and unique properties of adaptive networks through a brief, non-comprehensive review of recent literature on mathematical/computational modeling and analysis of such networks. We also report our recent work on several applications of computational adaptive network modeling and analysis to real-world problems, including temporal development of search and rescue operational networks, automated rule discovery from empirical network evolution data, and cultural integration in corporate merger. [Copyright &y& Elsevier]

Abstract: This paper addresses the motion tracking control for a class of flexible-joint robotic manipulators actuated by brushed direct current motors. This class of electrically driven flexible-joint robots is perturbed by plant uncertainties and external disturbances. Adaptive neural network systems are employed to approximate the behaviors of uncertain mechanical and electrical dynamics. A reduced-order observer is constructed to estimate the velocity signals. Only the measurements of link position and armature current are required for feedback. Consequently, an adaptive neural network-based dynamic feedback tracking controller without velocity measurements is developed such that all the states and signals of the closed-loop system are bounded and the trajectory tracking errors can be made as small as possible. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control algorithms. [Copyright &y& Elsevier]

Abstract: In this paper, we propose some new results on stability for Takagi–Sugeno fuzzy delayed neural networks with a stable learning method. Based on the Lyapunov–Krasovskii approach, for the first time, a new learning method is presented to not only guarantee the exponential stability of Takagi–Sugeno fuzzy neural networks with time-delay, but also reduce the effect of external disturbance to a prescribed attenuation level. The proposed learning method can be obtained by solving a convex optimization problem which is represented in terms of a set of linear matrix inequalities (LMIs). An illustrative example is given to demonstrate the effectiveness of the proposed learning method. [Copyright &y& Elsevier]

Abstract: This paper proposes a method for efficient power control of Electric Arc Furnaces (EAFs) based on the estimation of the instantaneous value of the flexible cable inductance. In this method, the displacements of the graphite electrodes regulating arc voltages are controlled using instant values of inductances at the secondary side of the EAF in three phases. For on-line estimation of inductance values, an artificial neural network is trained, using a random set of data obtained from an appropriate inductance simulator. The performance of the proposed method is examined by comparing the thermal energy efficiency of a typical EAF for two control schemes, namely, constant and varying flexible cable inductances. It is shown that the proposed method significantly improves the efficiency with negligible changes in harmonic generation and unbalance operation of the EAF. [Copyright &y& Elsevier]

Abstract: Since neural networks have universal approximation capabilities, therefore it is possible to postulate them as solutions for given differential equations that define unsupervised errors. In this paper, we present a wide survey and classification of different Multilayer Perceptron (MLP) and Radial Basis Function (RBF) neural network techniques, which are used for solving differential equations of various kinds. Our main purpose is to provide a synthesis of the published research works in this area and stimulate further research interest and effort in the identified topics. Here, we describe the crux of various research articles published by numerous researchers, mostly within the last 10 years to get a better knowledge about the present scenario. [Copyright &y& Elsevier]

Abstract: A class of simplified background neural networks model with a large number of neurons is proposed. Continuous attractors of the simplified model are studied in this paper. It contains: (1) When the background inputs are set to zero and the excitatory connections are in Gaussian shape, continuous attractors of the new network are obtained under some condition. (2) When the background inputs are nonzero and the excitatory connections are still in Gaussian shape, continuous attractors are achieved under some appropriately selected condition. (3) Discussions and examples are used to illustrate the theories developed. [Copyright &y& Elsevier]

Abstract: Employing the matrix measure approach and Lyapunov function, the author studies the global exponential stability of delayed neural networks with impulses in this paper. Some novel and sufficient conditions are given to guarantee the global exponential stability of the equilibrium point for such delayed neural networks with impulses. Finally, three examples are given to show the effectiveness of the results obtained here. [Copyright &y& Elsevier]

Abstract: In this paper, the problem of neutral-type impulsive bidirectional associative memory neural networks (NIBAMNNs) with time delays are first established by a Takagi–Sugeno (T-S) fuzzy model in which the consequent parts are composed of a set of NIBAMNNs with interval delays and Markovian jumping parameters (MJPs). Sufficient conditions to check the robust exponential stability of the derived model are based on the Lyapunov–Krasovskii functionals (LKFs) containing some novel triple integral terms, Lyapunov stability theory and employing the free-weighting matrix method. The delay-dependent stability conditions are established in terms of linear matrix inequalities (LMIs), which can be very efficiently solved using Matlab LMI control toolbox. Finally, numerical examples and remarks are given to illustrate the effectiveness and usefulness of the derived results. [Copyright &y& Elsevier]

Abstract: There have been many studies on the simultaneous approximation capability of feed-forward neural networks (FNNs). Most of these, however, are only concerned with the density or feasibility of performing simultaneous approximations. This paper considers the simultaneous approximation of algebraic polynomials, employing Taylor expansion and an algebraic constructive approach, to construct a class of FNNs which realize the simultaneous approximation of any smooth multivariate function and all of its derivatives. We also present an upper bound on the approximation accuracy of the FNNs, expressed in terms of the modulus of continuity of the functions to be approximated. [Copyright &y& Elsevier]

Abstract: In this paper, using a linear matrix inequality and a differential inequality, we obtain an exponentially robust stability criterion for interval fuzzy Cohen–Grossberg type neural networks with time-varying delays. The criterion can be easily applied to the design of fuzzy general neural networks. [Copyright &y& Elsevier]

Abstract: The problem of stability analysis of stochastic BAM neural networks with time delays and impulse effects is investigated in this paper. Using the Lyapunov technique and the generalized Hanalay inequality, we characterize theoretically the aggregated effects of impulse and stability properties of the impulse-free version. The present approaches allow us to estimate the feasible upper bounds of impulse strengths and can also extend to the more general impulsive nonlinear systems with delays. [Copyright &y& Elsevier]

Abstract: This paper introduces a novel neural network based approach for extracting the eigenvalues with the largest or smallest modulus of real skew-symmetric matrices, as well as the corresponding eigenvectors. To this end, unlike the previous neural network based methods that can be summarized by some -dimensional ordinary differential equations (ODEs), where is the order of the given skew-symmetric matrix, our proposed approach corresponds to an ODE of order , instead of . Hence, the scale of networks can be reduced a lot. Simulations verify the computational capability of such approach. [ABSTRACT FROM AUTHOR]

Abstract: Accurate remaining useful life (RUL) prediction of machines is important for condition based maintenance (CBM) to improve the reliability and cost of maintenance. This paper proposes artificial neural network (ANN) as a method to improve accurate RUL prediction of bearing failure. For this purpose, ANN model uses time and fitted measurements Weibull hazard rates of root mean square (RMS) and kurtosis from its present and previous points as input. Meanwhile, the normalized life percentage is selected as output. By doing that, the noise of a degradation signal from a target bearing can be minimized and the accuracy of prognosis system can be improved. The ANN RUL prediction uses FeedForward Neural Network (FFNN) with Levenberg Marquardt of training algorithm. The results from the proposed method shows that better performance is achieved in order to predict bearing failure. [ABSTRACT FROM AUTHOR]

Abstract: This paper describes the implementation of a genetic algorithm to evolve the population of weight matrices for storing and recalling the patterns in a Hopfield type neural network model. In the Hopfield type neural network of associative memory, the appropriate arrangement of synaptic weights provides an associative function in the network. The energy function associated with the stable state of this model represents the appropriate storage of the input patterns. The aim is to obtain the optimal weight matrix for efficient recall of any prototype input pattern. For this, we explore the population generation technique (mutation and elitism), crossover and the fitness evaluation function for generating the new population of the weight matrices. This process continues until the selection of the last weight matrix or matrices has been performed. The experiments incorporate a neural network trained with multiple numbers of patterns using the Hebbian learning rule. In most cases, the recalling of patterns using a genetic algorithm seems to give better results than the conventional recalling with the Hebbian rule. The simulated results suggest that the genetic algorithm is the better searching technique for recalling noisy prototype input patterns. [ABSTRACT FROM AUTHOR]

Abstract: In actual industrial fields, data for modelling are usually generated gradually, which requires that the data-based prediction model has the online learning capability. Although many online learning algorithms have been proposed, the generalization performance needs to be improved further. In this paper, a structure-adjustable online learning neural network (SAO-ELM) based on the extreme learning machine (ELM) with quicker learning speed and better generalization performance is proposed. Firstly, ELM is changed into a structure-adjustable learning machine, in which the number of nodes in its single hidden layer can be adjusted. Then, a special strategy is developed to handle the difficulty that the new added hidden nodes’ outputs corresponding to the discarded training data cannot be obtained. After that, an iterative equation is presented to update the output matrix when hidden nodes are added. Results of numerical comparison based on data from the real world benchmark problems and an actual continuous casting process show that the performance of SAO-ELM has significant advantages over that of the typical online learning algorithms on generalization performance. In addition, SAO-ELM retains the merit of quick learning characteristic of ELM. [Copyright &y& Elsevier]

Abstract: In this paper, the problem of global exponential stability for cellular neural networks (CNNs) with time-varying delays and fixed moments of impulsive effect is studied. A new sufficient condition has been presented ensuring the global exponential stability of the equilibrium points by using piecewise continuous Lyapunov functions and the Razumikhin technique combined with Young’s inequality. The results established here extend those given previously in the literature. Compared with the method of Lyapunov functionals as in most previous studies, our method is simpler and more effective for stability analysis. [Copyright &y& Elsevier]

Abstract: In this paper, the existence and global exponential stability of periodic solutions for a class of numerical discretization neural networks are considered. Using coincidence degree theory and the Lyapunov method, sufficient conditions for the existence and global exponential stability of periodic solutions are obtained. A numerical simulation is given to illustrate the results. [Copyright &y& Elsevier]

Abstract: This paper presents an automated method to help us assess the speech quality of a dysarthric speaker, in place of laborious and subjective manual methods. The assessment result can be used as a good indicator for predicting the accuracy of speech recognition. The so-called speech confusion index is proposed to measure the speech disorder severity of a speaker in terms of how easily his/her speech signal may be misrecognized to other unintended words. Based on signal processing without any high-level information, the dynamic-time-warping technique incorporated with adaptive slope constraint and accumulative mismatch score is used to measure a distance between any two speech signals of a same word or two different words. Compared to the articulatory and intelligibility tests, the proposed indicator was shown to have more predictability on the recognition rates obtained from the Hidden Markov Model (HMM) and Artificial Neural Networks (ANN). Based on three evaluation criteria, namely root-mean-square difference, correlation coefficient and rank-order inconsistency, the experimental results on a phoneme-balance set showed that achieved better prediction than both articulatory and intelligibility tests. Another experiment on a reduced training set is made to investigate the robustness of the proposed indicator. Finally, a detailed analysis of speech confusion is done at the phoneme level. [Copyright &y& Elsevier]

Abstract: A model describing the dynamics of Cohen-Grossberg neural networks with time-delays and impulses is considered. By means of Lyapunov functionals and a differential inequality technique, criteria on global exponential stability of this model are derived. Many adjustable parameters are introduced in the criteria to provide flexibility for the design and analysis of the system. The results of this paper are new and they supplement previously known results. [Copyright &y& Elsevier]

Abstract: In this paper, we study qualitative properties of equilibrium points in a class of interval fuzzy neural networks, and obtain an estimate on the domain of robust attraction of locally exponentially stable equilibrium points. Both the conditions and the estimate are formulated in terms of the parameter intervals, so they are easily verifiable. The result can be used for the evaluation of fault-tolerance capability for interval fuzzy neural networks. [Copyright &y& Elsevier]

Abstract: In this paper, Cohen–Grossberg neural networks (CGNNs) with delays are considered. Some new sufficient conditions for the existence and exponential stability of anti-periodic solutions are established. [Copyright &y& Elsevier]

Abstract: In this paper, the global asymptotic stability of Hopfield neural networks with delays is investigated. Distinct differences from other analytical approaches lie in transforming to an equivalent system by using a parameterized transformation which allows free variables in an operator. A novel, less conservative and restrictive criterion than those established in the earlier references is given in terms of several matrix inequalities by utilizing the Lyapunov theory and matrix inequality framework. The results are related to the size of delays. Numerical examples are given to show the effectiveness of our proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, we discuss impulsive high-order Hopfield type neural networks. Investigating their global asymptotic stability, by using Lyapunov function method, sufficient conditions that guarantee global asymptotic stability of networks are given. These criteria can be used to analyse the dynamics of biological neural systems or to design globally stable artificial neural networks. Two numerical examples are given to illustrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the global exponential stability of impulsive high-order Hopfield type neural networks with delays. By establishing the impulsive delay differential inequalities and using the Lyapunov method, two sufficient conditions that guarantee global exponential stability of these networks are given, and the exponential convergence rate is also obtained. A numerical example is given to demonstrate the validity of the results. [Copyright &y& Elsevier]

Abstract: In this paper, we obtain some sufficient conditions for determining the asymptotic stability of discrete-time non-autonomous delayed Hopfield neural networks by utilizing the Lyapunov functional method. An example is given to show the validity of the results. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate a novel delayed chaotic neural model, in which a non-monotonously increasing transfer function is employed as activation function. Local stability and existence of Hopf bifurcation are analyzed in details. Chaos behavior of the neuron model is observed in computer simulations. An electronic implementation of the neuron is also considered. The dynamical behavior of the designed circuits is closely similar to the results simulated by numerical experiments. [Copyright &y& Elsevier]

Abstract: In this paper, by using nonsmooth analysis approach, linear matrix inequality (LMI) technique, topological degree theory and Lyapunov–Krasovskii function method, the issue of global exponential stability is investigated for a class of generalized Cohen–Grossberg neural networks possessing inverse Lipschitz neuron activations and nonsmooth behaved functions. Several novel delay-dependent sufficient conditions are established towards the existence, uniqueness and global exponential stability of the equilibrium point, which are shown in terms of LMIs. It is noted that the results above require neither the Lipschitz continuity of the activation functions, nor the smoothness of the behaved functions. Also, for the case of the activation function that satisfies not only the inverse Lipschitz conditions but also the Lipschitz conditions, some conditions are derived which generalize the previous results. Finally, two examples with their simulations are given to show the effectiveness of the theoretical results. [Copyright &y& Elsevier]

Abstract: In this paper, by utilizing the Lyapunov functional method, applying M-matrix, Young inequality technique and other analysis techniques, we analyze the exponential stability and the existence of periodic solutions for non-autonomous hybrid BAM neural networks with distributed delays and impulses. Sufficient conditions are obtained for the global exponential stability and the existence of periodic solutions for non-autonomous hybrid bidirectional associative memory (BAM) neural networks with Lipschitzian activation functions without assuming their boundedness, monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time. Finally, two examples are also provided to demonstrate the effectiveness of the results obtained. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate a class of impulsive BAM neural networks with time-varying delays. By establishing the delay differential inequality with impulsive initial conditions and employing -matrix theory, we find some new sufficient conditions ensuring the existence, uniqueness and global exponential stability of the equilibrium point for impulsive BAM neural networks with time-varying delays. In particular, the estimate of the exponential convergence rate is also provided, which depends on the system parameters. An example is given to show the effectiveness of the results obtained here. [Copyright &y& Elsevier]

Abstract: In this paper, by using the fixed point theorem of differential inclusion theory and constructing suitable Lyapunov functions, the existence, uniqueness and global exponential stability of the periodic solution for BAM neural networks with discontinuous neuron activations are investigated. Moreover, the global convergence in finite time of the networks is discussed. The conditions that ensure the existence and stability of periodic solution are given. The obtained results extend previous work on global stability of BAM neural networks with Lipschitz continuous neuron activations but without delays, and show that Forti’s conjecture is true for BAM neural networks without delays. [Copyright &y& Elsevier]

Abstract: In this paper high-order Hopfield neural networks (HHNNs) with time-varying delays are considered. Sufficient conditions for the existence and exponential stability of anti-periodic solutions are established, which are new and complement previously known results. [Copyright &y& Elsevier]

Abstract: The stability of a class of stochastic Recurrent Neural Networks with time-varying delays is investigated in this paper. With the help of the Lyapunov function and the Dini derivative of the expectation of “along” the solution of the model, a set of novel sufficient conditions on mean square exponential stability has been established. An example is also given to illustrate the effectiveness of our results. [Copyright &y& Elsevier]

Abstract: This paper investigates the robust control problem for a class of neural networks subject to bounded uncertainties and time-varying delays. A memoryless decentralized variable structure control law with dead-zone input for guaranteeing global asymptotical system stability is derived. The results demonstrate that the derived control law does not restrict the derivative of the time-varying delays even if dead-zone nonlinearity occurs in the control input. Such a control law can be used to stabilize Cohen–Grossberg neural networks, cellular neural networks and Hopfield neural networks; all of which have bounded uncertainties and time-varying delays. Two examples are provided to illustrate the effectiveness and validity of the proposed control scheme. [Copyright &y& Elsevier]

Abstract: Minor component analysis (MCA) is an important statistical tool for signal processing and data analysis. Neural networks can be used to extract online minor component from input data. Compared with traditional algebraic approaches, a neural network method has a lower computational complexity. Stability of neural networks learning algorithms is crucial to practical applications. In this paper, we propose a stable MCA neural networks learning algorithm, which has a more satisfactory numerical stability than some existing MCA algorithms. Dynamical behaviors of the proposed algorithm are analyzed via deterministic discrete time (DDT) method and the conditions are obtained to guarantee convergence. Simulations are carried out to illustrate the theoretical results achieved. [Copyright &y& Elsevier]

Abstract: In this paper, we study simple algorithms for tracking objects in a video sequence, based on the selection of landmark points representative of the moving objects in the first frame of the sequence to be analyzed. The movement of these points is estimated using a sparse optical-flow method. Methods of this kind are fast, but they are not very robust. Particularly, they are not able to handle the occlusion of the moving objects in the video. To improve the performance of optical flow-based methods, we propose the use of adaptive filters and neural networks to predict the expected instantaneous velocities of the objects, using the predicted velocities as indicators of the performance of the tracking algorithm. The efficiency of these strategies in handling occlusion problems are tested with a set of synthetic and real video sequences. [Copyright &y& Elsevier]

Abstract: This paper presents a Fuzzy Neural Network (FNN) based local to overall thermal sensation model for prediction of clothing thermal function in functional textile design system. Unlike previous experimental and regression analysis approaches, this model depends on direct factors of human thermal response — body core and skin temperatures. First the local sensation is predicted by a FNN network using local body part skin temperatures, their change rates, and core temperature as inputs; then the overall sensation is predicted. This is also performed by a FNN network. The FNN networks are developed on the basis of the Feed-Forward Back-Propagation (FFBP) network; the advantage of using fuzzy logic here is to reduce the requirement of training data. The simulation result shows a good correlation between predicted and the traditional experimental data. [Copyright &y& Elsevier]

In this paper linear and quadratic programming problems are solved using a novel recurrent artificial neural network. The new model is simpler and converges very fast to the exact primal and dual solutions simultaneously. The model is based on a nonlinear dynamical system, using arbitrary initial conditions. In order to construct an economy model, here we avoid using analog multipliers. The dynamical system is a time dependent system of equations with the gradient of specific Lyapunov energy function in the right hand side. Block diagram of the proposed neural network model is given. Fourth order Runge–Kutta method with controlled step size is used to solve the problem numerically. Global convergence of the new model is proved, both theoretically and numerically. Numerical simulations show the fast convergence of the new model for the problems with a unique solution or infinitely many. This model converges to the exact solution independent of the way that we may choose the starting points, i.e. inside, outside or on the boundaries of the feasible region. [Copyright &y& Elsevier]