Stochastic Neural Networks Research Articles

Exponential stability of stochastic inertial neural networks with generalised piecewise constant argument

This paper investigates the exponential stability of stochastic inertial neural networks (SINNs) with generalised piecewise constant argument. By applying variable substitution, the second-order system is transformed into a first-order system. Subsequently, several sufficient conditions are introduced to ensure the existence of a unique solution. Due to the presence of generalised piecewise constant argument, calculus theory is applied to estimate the dynamic effects of network states in current time and deviation function. The global mean-square exponential stability of SINNs with generalised piecewise constant argument is established using the Lyapunov function method. Finally, two numerical examples are provided to verify the validity of derived theoretical results.

Node-to-node clustering asymptotic synchronized discrete stochastic neural networks in time and space with Bernoulli switching delay

The article proposes a new approach to synchronizing space–time discrete stochastic neural networks with random switching delays. This is achieved by employing a control in the boundary, which is based on node-to-node clustering and controlling theories. The design of the control in the boundary for synchronizing space–time discrete stochastic neural networks in the form of clusters is based on the establishment of several significant sequential inequalities and the creation of cluster information. Also, an executable computer algorithm has been developed to streamline the implementation of the findings presented in this paper. The current study represents a pioneering approach in considering spatial discrete factors, providing a solid foundation for future research and offering theoretical and practical guidance.

Finite time stability of nonlinear impulsive stochastic system and its application to neural networks

In this paper, we employ the Lyapunov theory to generalize the finite time stability (FTS) results from general deterministic impulsive systems to impulsive stochastic time-varying systems, which overcomes inherent challenges. Sufficient conditions for the FTS of the system under stabilizing and destabilizing impulses are established by using the method of average dwell interval (ADT). For FTS of stabilizing impulses, we relax the constraint on the differential operator by allowing it to be indefinite rather than strictly negative or semi-negative definite. Furthermore, the theoretical results are applied to impulsive stochastic neural networks. Finally, two numerical examples are given to validate the reliability and practicability of the obtained results.

Observer-Based Asynchronous Boundary Stabilization for Stochastic Markovian Reaction-Diffusion Neural Networks.

This work investigates the observer-based asynchronous boundary stabilization for a kind of stochastic Markovian reaction-diffusion neural networks with exogenous disturbances. Specifically, parameter uncertainties are considered in the drift item. First, a hidden Markov model is introduced that guarantees the observer modes run asynchronously with the system modes. It should be noted that the asynchronous observer constructed in this work only uses the boundary measurement information. Then a nonfragile asynchronous observer-based boundary controller is designed. Taking advantage of inequality techniques and stochastic analysis method, sufficient criterion is provided to satisfy input-to-state exponentially mean-square stability, and the asynchronous boundary observer/controller gains are further derived. As a special case, the synchronous observer-based boundary stabilization is also obtained. Finally, a numerical example is exploited to manifest the validity of the established results.

Retraction Note: Stochastic gradient descent-based convolutional neural network to detect and classify oral cavity cancer

Retraction Note: Stochastic gradient descent-based convolutional neural network to detect and classify oral cavity cancer

A reliable neural network procedure for the novel sixth-order nonlinear singular pantograph differential model

An innovative singular nonlinear sixth-order (SNSO) pantograph differential model (PDM), known as the SNSO-PDM, is the subject of this novel study along with its numerical investigation. The concepts of pantograph and conventional Emden-Fowler have been presented in the design of the novel SNSO-PDM. The models based on Emden–Fowler have huge applications in mathematics and engineering and are always difficult to solve due to singularity. For each class of the innovative SNSO-PDM, the singularity, shape and pantograph factors are described. A reliable stochastic Levenberg-Marquardt backpropagation neural network (LMBPNN) procedure is designed for the SNSO-PDM. The correctness of the SNSOs-PDM is observed through the comparison performances of the achieved and reference outputs. The obtained results of the SNSO-PDM are considered by applying the process of training, certification, and testing to reduce the mean square error. To authenticate the efficacy of the innovative SNSO-PDM, the numerical performances of the solutions are depicted in the sense of regression, error histograms and correlation.

Numerical Performance of the Fractional Direct Spreading Cholera Disease Model: An Artificial Neural Network Approach

The current investigation examines the numerical performance of the fractional-order endemic disease model based on the direct spreading of cholera by applying the neuro-computing Bayesian regularization (BR) neural network process. The purpose is to present the numerical solutions of the fractional-order model, which provides more precise solutions as compared to the integer-order one. Real values based on the parameters can be obtained and one can achieve better results by utilizing these values. The mathematical form of the fractional direct spreading cholera disease is categorized as susceptible, infected, treatment, and recovered, which represents a nonlinear model. The construction of the dataset is performed through the implicit Runge–Kutta method, which is used to lessen the mean square error by taking 74% of the data for training, while 8% is used for both validation and testing. Twenty-two neurons and the log-sigmoid fitness function in the hidden layer are used in the stochastic neural network process. The optimization of BR is performed in order to solve the direct spreading cholera disease problem. The accuracy of the stochastic process is authenticated through the valuation of the outputs, whereas the negligible calculated absolute error values demonstrate the approach’s correctness. Furthermore, the statistical operator performance establishes the reliability of the proposed scheme.

Open-world structured sequence learning via dense target encoding

Structured sequences are popularly used to describe graph data with time-evolving node features and edges. A typical real-world scenario of structured sequences is that unknown class labels continuously arrive and thus the training and testing often across different class spaces. This scenario is also referred to as the open-world learning problem on structured sequences. In this paper, we present a new Dense Open-world Structured Sequence Learning model (DOSSL for short) to learn graph streams in the open-world learning setting. To capture both structural and temporal information, DOSSL uses a GNN-based stochastic recurrent neural network for learning node representation in graph streams, then a truncated Laplacian distribution to describe the latent distribution of graph nodes, and a sampling function is used to generate node representations. Further, DOSSL learns dense target embeddings for the known classes to improve the compactness of known class distribution and reserve enough space for open-world unknown classes. The ultimate open-world classifier is optimized to detect the samples from unknown classes under the constraints of DVAE loss, label loss, class uncertainty loss, and dense target loss. Through empirical analysis conducted on real-world datasets, it has been demonstrated that the advanced technique known as DOSSL exhibits the ability to acquire precise node classifiers by harnessing the power of graph streams.

A Stochastic Recurrent Encoder Decoder Network for Multistep Probabilistic Wind Power Predictions.

In this article, a stochastic recurrent encoder decoder neural network (SREDNN), which considers latent random variables in its recurrent structures, is developed for the first time for the generative multistep probabilistic wind power predictions (MPWPPs). The SREDNN enables the stochastic recurrent model under the encoder-decoder framework to engage exogenous covariates to produce better MPWPP. The SREDNN consists of five components, the prior network, the inference network, the generative network, the encoder recurrent network, and the decoder recurrent network. The SREDNN is equipped with two critical advantages compared with conventional RNN-based methods. First, the integration over the latent random variable builds an infinite Gaussian mixture model (IGMM) as the observation model, which drastically increases the expressiveness of the wind power distribution. Secondly, hidden states of the SREDNN are updated in a stochastic way, which builds an infinite mixture of the IGMM for describing the ultimate wind power distribution and enables the SREDNN to model complex patterns across wind speed and wind power sequences. Computational experiments are conducted on a dataset of a commercial wind farm having 25 wind turbines (WTs) and two publicly assessable WT datasets to verify the advantages and effectiveness of the SREDNN for MPWPP. Experimental results show that the SREDNN achieves a lower negative form of the continuously ranked probability score (CRPS*) as well as a superior sharpness and comparable reliability of prediction intervals by comparing against considered benchmarking models. Results also show the clear benefit gained from considering latent random variables in SREDNN.

Exponential Stability of Impulsive Stochastic Neutral Neural Networks with Lévy Noise Under Non-Lipschitz Conditions

In this paper, the exponential stability issue of stochastic impulsive neutral neural networks driven by Lévy noise is explored. By resorting to the Lyapunov-Krasovskii function that involves neutral time-delay components, the properties of the Lévy process, as well as various inequality approaches, some sufficient exponential stability criteria in non-Lipschitz cases are obtained. Besides, the achieved results depend on the time-delay, noise intensity, and impulse factor. At the end of the paper, two numerical examples with simulations are presented to demonstrate the effectiveness and feasibility of the addressed results

REVIEW ON STOCHASTIC HYBRIDISATION OF FEEDFORWARD NEURAL NETWORK IN STOCK MARKET

The stock market is an example of a stochastic environment in the real world. So, obtaining accurate forecasting models of the stock market can be challenging due to its complex characteristics (noisy environment), which result in uncertainty. Although machine learning models have been widely applied to forecast the market, it fails to capture the presence of stochasticity in it. As a result, a few studies had proposed a hybridization of Multilayer Perceptron and stochastic processes. Hence, this review paper aims to provide a systematic review of these hybridized models, which have been obtained from the scientific databases Scopus and Web of Science. Finally, it was found out that only eight studies had been conducted to forecast the stock market with Stochastic Neural Network (SNN), and all of them concluded that it has better accuracy than the deterministic model. Thus, the development of SNN is worth exploring in the future as there are rooms to explore cross-disciplinary between neural networks and stochastic processes to improve forecasting accuracy.

Adaptive Sliding Mode Fixed-/Preassigned-Time Synchronization of Stochastic Memristive Neural Networks with Mixed-Delays

The paper addresses the fixed-/preassigned-time synchronization of stochastic memristive neural networks (MNNs) with uncertain parameters and mixed delays. Adaptive sliding mode control (ASMC) technology is mainly utilized. First, a proper sliding surface is constructed and the adaptive laws are given. Also, the synchronization control scheme is designed, which can ensure error system to realize fixed-time stability. Second, preassigned-time sliding mode control scheme is mainly provided to realize fast synchronization of MNNs. The presented theoretical methods can guarantee the error system convergence and stability for reaching and sliding mode within preassigned-time. And the synchronization criteria and explicit expression of settling time (ST) are acquired, where ST is not related with initial values and controller parameters but can be predefined perferentially. Finally, the calculation example is offered to interpret the practicability and availability of the innovations in this paper.

Adaptive synchronization of the switching stochastic neural networks with time-dependent delays

Adaptive synchronization of the switching stochastic neural networks with time-dependent delays

Missing Data Filling of Model Based on Neural Network

Today’s society has entered the pace of information development era. All kinds of information are digitized, while the loss of information data also directly affects the normal operation of the application system and has become the biggest obstacle to the development of information technology. The existing missing filling methods do not take into account the time-series information of the data set. Based on the neural network method for filling missing data in time series, an end-to-end missing data filling method for time series based on the residual of regression equation is proposed. Under the assumption that the activation function and the noise diffusion coefficient function are satisfied, the exponential stability of the complex-valued stochastic inertial neural network systems with additive time-varying delays is studied. The bipartite graph model of the time series data missing value filling method of the countermeasure network and the filling cyclic neural unit are generated. According to the end-to-end time series data missing value filling method of the self encoder, the corresponding low-dimensional feature vector can be automatically generated for each time series data. It avoids overfitting by using nonlinear methods directly in low-dimensional space. Experiments show that the method proposed in this paper uses Monte Carlo to fill data missing at different proportions. In data gap filling process, the coefficient variance is less than 0.05, which enhances the rationality of filling data. It is of great research value and practical significance to reasonably fill in the missing values of time series data. The research can accelerate the improvement of big data system, improve the level and effectiveness of database management, and is an important means of computing capacity of existing data centers.

Exponential Synchronization of Stochastic Time-delayed Memristor-based Neural Networks via Pinning Impulsive Control

Exponential Synchronization of Stochastic Time-delayed Memristor-based Neural Networks via Pinning Impulsive Control

Quasi-projective Synchronization Control of Delayed Stochastic Quaternion-Valued Fuzzy Cellular Neural Networks with Mismatched Parameters

Quasi-projective Synchronization Control of Delayed Stochastic Quaternion-Valued Fuzzy Cellular Neural Networks with Mismatched Parameters

Stability analysis of switched stochastic time‐varying delay neural networks with asynchronous switching aperiodic intermittent control

AbstractThis paper is dedicated to studying the mean square exponential stability of switched stochastic time‐varying delay neural networks with asynchronous switching aperiodic intermittent control. By utilizing the Halanay‐type inequality and designing appropriate asynchronous switching aperiodic intermittent control, several novel stability criteria of switched stochastic delay neural networks with asynchronous aperiodic intermittent control are presented under the Lyapunov function method and Lyapunov functional method. Among them, asynchronous switching aperiodic intermittent controllers are more practical and flexible compared to state feedback controllers. Finally, we provide two examples to verify the effectiveness of the theoretical results.

Forecasting Stock Indices: Stochastic and Artificial Neural Network Models

Forecasting Stock Indices: Stochastic and Artificial Neural Network Models

Semiglobal fixed/preassigned-time synchronization of stochastic neural networks with random delay via adaptive control

This paper presents two kinds of novel results about semiglobal synchronization in probability for stochastic systems. To this end, new criteria of semiglobal fixed-time synchronization in probability (SFXTSp) and semiglobal preassigned-time synchronization in probability (SPATSp) are proposed. In contrast to the existing results of semiglobal synchronization in probability, our criteria have wider applicability in SFXTSp and SPATSp due to their flexible forms. Meanwhile, based on the properties of convex functions and Jensen’s inequality, our approaches overcome the issue arising from the non-equivalence between the Lyapunov function and its expectation, making our conclusions more rigorous. In addition, to achieve SFXTSp of stochastic neural networks with random delay (RDSNNs), a unified adaptive controller is developed. By modifying the parameters of the unified controller, RDSNNs reach SPATSp in a predetermined time. Ultimately, numerical simulations are conducted to confirm the practicality and accuracy of the derived outcomes.

Predictive analysis of concrete slump using a stochastic search-consolidated neural network

Attaining a dependable measurement of concrete slump is crucial as it is a valuable indication of concrete workability. On the other hand, complexities associated with costly traditional approaches have driven engineers to use indirect efficient models such as metaheuristic-based machine learning for approximating the slump. While the literature shows promising application of some metaheuristic techniques for this purpose, the large variety of these algorithms calls for evaluating the most capable ones to keep the solution updated. Stochastic fractal search (SFS) is one of the most powerful optimization algorithms in the literature that has not received appropriate attention in analyzing concrete mechanical parameters. In the present research, a multi-layer perceptron neural network (NN-MLP), is enhanced using the SFS. The proposed SFS-NN-MLP model aims to predict the slump based on the amount of ingredients in the mixture, as well as the curing age of specimens. Accuracy assessment revealed that the proposed model can deal with the assigned task with excellent accuracy. It indicates that the SFS could properly tune the parameters required for training the NN-MLP, and consequently, the trained network could reliably calculate the slump of specimens that were not analyzed before. For comparative validation, the SFS was replaced with two similar optimizers, namely elephant herding optimization algorithm (EHO) and slime mould algorithm (SMA). Based on the calculated mean square errors of 5.6526, 6.1129, and 7.3561 along with mean absolute errors of 4.6657, 5.0078, and 6.3066, as well as the percentage-Pearson correlation coefficients of 78.06 %, 73.95 %, and 58.11 %, respectively for the SFS-NN-MLP, EHO–NN–MLP, and SMA–NN–MLP, it was shown that the SFS-NN-MLP is the most accurate predictor. Hereupon, the SFS-NN-MLP model is recommended to be effectively used for obtaining a cost-efficient approximation of concrete slump in real-world projects.