Global stability of Cohen-Grossberg neural networks with time-varying and distributed delays

In this paper, the global asymptotic stability is investigated for a class of Cohen-Grossberg neural networks with time-varying and distributed delays. By using the Lyapunov-Krasovskii functional and equivalent descriptor form of the considered system, several delay-dependent sufficient conditions are obtained to guarantee the asymptotic stability of the addressed systems. These conditions are dependent on both time-varying and distributed delays and presented in terms of LMIs and therefore, the stability criteria of such systems can be checked readily by resorting to the Matlab LMI toolbox. Finally, an example is given to show the effectiveness and less conservatism of the proposed methods.

Analysis for Cohen-Grossberg neural networks with multiple delays

The stability analysis of Cohen-Grossberg neural networks with multiple delays is given. An approach combining the Lyapunov functional with the linear matrix inequality （LMI） is taken to obtain the sufficient conditions for the globally asymptotic stability of equilibrium point. By using the properties of matrix norm, a practical corollary is derived. All results are established without assuming the differentiability and monotonicity of activation functions. The simulation samples have proved the effectiveness of the conclusions.

Global exponential stability of Cohen-Grossberg neural networks with time-varying delays and impulses

In this paper, the Cohen-Grossberg neural networks with time-varying delays and impulses are considered. New sufficient conditions for the existence and global exponential stability of a unique equilibrium point are established by using the fixed point theorem and Lyapunov functional. An example is given to demonstrate the effectiveness of our results.

Global exponential stability of Cohen-Grossberg neural networks with variable delays

A class of generalized Cohen-Grossberg neural networks（CGNNs） with variable de- lays are investigated. By introducing a new type of Lyapunov functional and applying the homeomorphism theory and inequality technique, some new conditions axe derived ensuring the existence and uniqueness of the equilibrium point and its global exponential stability for CGNNs. These results obtained are independent of delays, develop the existent outcome in the earlier literature and are very easily checked in practice.

Multiple Lagrange stability and Lyapunov asymptotical stability of delayed fractional-order Cohen-Grossberg neural networks

This paper addresses the coexistence and local stability of multiple equilibrium points for fractional-order Cohen-Grossberg neural networks(FOCGNNs)with time delays.Based on Brouwer's fixed point theorem,sufficient conditions are established to ensure the existence of Πi=1^n(2Ki+1)equilibrium points for FOCGNNs.Through the use of Hardy inequality,fractional Halanay inequality,and Lyapunov theory,some criteria are established to ensure the local Lagrange stability and the local Lyapunov asymptotical stability of Πi=1^n(Ki+1)equilibrium points for FOCGNNs.The obtained results encompass those of integer-order Hopfield neural networks with or without delay as special cases.The activation functions are nonlinear and nonmonotonic.There could be many corner points in this general class of activation functions.The structure of activation functions makes FOCGNNs could have a lot of stable equilibrium points.Coexistence of multiple stable equilibrium points is necessary when neural networks come to pattern recognition and associative memories.Finally,two numerical examples are provided to illustrate the effectiveness of the obtained results.

Stability Analysis of Cohen-Grossberg Neural Networks with Time-Varying Delays

The global exponential stability of Cohen-Grossberg neural networks with time-varying delays is studied. By constructing several suitable Lyapunov functionals and utilizing differential in-equality techniques, some sufficient criteria for the global exponential stability and the exponential convergence rate of the equilibrium point of the system are obtained. The criteria do not require the activation functions to be differentiable or monotone nondecreasing. Some stability results from previous works are extended and improved. Comparisons are made to demonstrate the advantage of our results.

μ-stability of multiple equilibria in Cohen-Grossberg neural networks and its application to associative memory

In this paper, the μ-stability of multiple equilibrium points(EPs) in the Cohen-Grossberg neural networks(CGNNs) is addressed by designing a kind of discontinuous activation function(AF). Under some criteria, CGNNs with this AF are shown to possess at least 5^(n)EPs, of which 3^(n)EPs are locally μ-stable. Compared with the saturated AF or the sigmoidal AF, CGNNs with the designed AF can produce many more total/stable EPs. Therefore, when CGNNs with the designed discontinuous AF are applied to associative memory, they can store more prototype patterns. Moreover, the AF is expanded to a more general version to further increase the number of total/stable equilibria. The CGNNs with the expanded AF are found to produce(2k+3)^(n)EPs, of which (k+2)^(n)EPs are locally μ-stable. By adjusting two parameters in the AF, the number of sufficient conditions ensuring the μ-stability of multiple equilibria can be decreased. This finding implies that the computational complexity can be greatly reduced.Two numerical examples and an application to associative memory are illustrated to verify the correctness of the obtained results.

Pluggable multitask diffractive neural networks based on cascaded metasurfaces

Optical neural networks have significant advantages in terms of power consumption,parallelism,and high computing speed,which has intrigued extensive attention in both academic and engineering communities.It has been considered as one of the powerful tools in promoting the fields of imaging processing and object recognition.However,the existing optical system architecture cannot be reconstructed to the realization of multi-functional artificial intelligence systems simultaneously.To push the development of this issue,we propose the pluggable diffractive neural networks(P-DNN),a general paradigm resorting to the cascaded metasurfaces,which can be applied to recognize various tasks by switching internal plug-ins.As the proof-of-principle,the recognition functions of six types of handwritten digits and six types of fashions are numerical simulated and experimental demonstrated at near-infrared regimes.Encouragingly,the proposed paradigm not only improves the flexibility of the optical neural networks but paves the new route for achieving high-speed,low-power and versatile artificial intelligence systems.

Activation Redistribution Based Hybrid Asymmetric Quantization Method of Neural Networks

The demand for adopting neural networks in resource-constrained embedded devices is continuously increasing.Quantization is one of the most promising solutions to reduce computational cost and memory storage on embedded devices.In order to reduce the complexity and overhead of deploying neural networks on Integeronly hardware,most current quantization methods use a symmetric quantization mapping strategy to quantize a floating-point neural network into an integer network.However,although symmetric quantization has the advantage of easier implementation,it is sub-optimal for cases where the range could be skewed and not symmetric.This often comes at the cost of lower accuracy.This paper proposed an activation redistribution-based hybrid asymmetric quantizationmethod for neural networks.The proposedmethod takes data distribution into consideration and can resolve the contradiction between the quantization accuracy and the ease of implementation,balance the trade-off between clipping range and quantization resolution,and thus improve the accuracy of the quantized neural network.The experimental results indicate that the accuracy of the proposed method is 2.02%and 5.52%higher than the traditional symmetric quantization method for classification and detection tasks,respectively.The proposed method paves the way for computationally intensive neural network models to be deployed on devices with limited computing resources.Codes will be available on https://github.com/ycjcy/Hybrid-Asymmetric-Quantization.

A data-driven model of drop size prediction based on artificial neural networks using small-scale data sets

An artificial neural network(ANN)method is introduced to predict drop size in two kinds of pulsed columns with small-scale data sets.After training,the deviation between calculate and experimental results are 3.8%and 9.3%,respectively.Through ANN model,the influence of interfacial tension and pulsation intensity on the droplet diameter has been developed.Droplet size gradually increases with the increase of interfacial tension,and decreases with the increase of pulse intensity.It can be seen that the accuracy of ANN model in predicting droplet size outside the training set range is reach the same level as the accuracy of correlation obtained based on experiments within this range.For two kinds of columns,the drop size prediction deviations of ANN model are 9.6%and 18.5%and the deviations in correlations are 11%and 15%.

A Review of Computing with Spiking Neural Networks

Artificial neural networks(ANNs)have led to landmark changes in many fields,but they still differ significantly fromthemechanisms of real biological neural networks and face problems such as high computing costs,excessive computing power,and so on.Spiking neural networks(SNNs)provide a new approach combined with brain-like science to improve the computational energy efficiency,computational architecture,and biological credibility of current deep learning applications.In the early stage of development,its poor performance hindered the application of SNNs in real-world scenarios.In recent years,SNNs have made great progress in computational performance and practicability compared with the earlier research results,and are continuously producing significant results.Although there are already many pieces of literature on SNNs,there is still a lack of comprehensive review on SNNs from the perspective of improving performance and practicality as well as incorporating the latest research results.Starting from this issue,this paper elaborates on SNNs along the complete usage process of SNNs including network construction,data processing,model training,development,and deployment,aiming to provide more comprehensive and practical guidance to promote the development of SNNs.Therefore,the connotation and development status of SNNcomputing is reviewed systematically and comprehensively from four aspects:composition structure,data set,learning algorithm,software/hardware development platform.Then the development characteristics of SNNs in intelligent computing are summarized,the current challenges of SNNs are discussed and the future development directions are also prospected.Our research shows that in the fields of machine learning and intelligent computing,SNNs have comparable network scale and performance to ANNs and the ability to challenge large datasets and a variety of tasks.The advantages of SNNs over ANNs in terms of energy efficiency and spatial-temporal data processing have been more fully exploited.And the development of programming and deployment tools has lowered the threshold for the use of SNNs.SNNs show a broad development prospect for brain-like computing.

Prediction of Porous Media Fluid Flow with Spatial Heterogeneity Using Criss-Cross Physics-Informed Convolutional Neural Networks

Recent advances in deep neural networks have shed new light on physics,engineering,and scientific computing.Reconciling the data-centered viewpoint with physical simulation is one of the research hotspots.The physicsinformedneural network(PINN)is currently the most general framework,which is more popular due to theconvenience of constructing NNs and excellent generalization ability.The automatic differentiation(AD)-basedPINN model is suitable for the homogeneous scientific problem;however,it is unclear how AD can enforce fluxcontinuity across boundaries between cells of different properties where spatial heterogeneity is represented bygrid cells with different physical properties.In this work,we propose a criss-cross physics-informed convolutionalneural network(CC-PINN)learning architecture,aiming to learn the solution of parametric PDEs with spatialheterogeneity of physical properties.To achieve the seamless enforcement of flux continuity and integration ofphysicalmeaning into CNN,a predefined 2D convolutional layer is proposed to accurately express transmissibilitybetween adjacent cells.The efficacy of the proposedmethodwas evaluated through predictions of several petroleumreservoir problems with spatial heterogeneity and compared against state-of-the-art(PINN)through numericalanalysis as a benchmark,which demonstrated the superiority of the proposed method over the PINN.

Reconfigurable optical neural networks with Plug-and-Play metasurfaces

In a very recent study,Prof.Lingling Huang and co-workers proposed and demonstrated reconfigurable optical neural networks based on cascaded metasurfaces.By fixing one metasurface and switching the other pluggable metasurfaces,the neural networks,which operate at near-infrared wavelengths,can perform distinct recognition tasks for handwritten digits and fashion products.This innovative device opens up an avenue for all-optical,high-speed,low-power,and multifunctional artificial intelligence systems.

Application of Convolutional Neural Networks in Classification of GBM for Enhanced Prognosis

The lethal brain tumor “Glioblastoma” has the propensity to grow over time. To improve patient outcomes, it is essential to classify GBM accurately and promptly in order to provide a focused and individualized treatment plan. Despite this, deep learning methods, particularly Convolutional Neural Networks (CNNs), have demonstrated a high level of accuracy in a myriad of medical image analysis applications as a result of recent technical breakthroughs. The overall aim of the research is to investigate how CNNs can be used to classify GBMs using data from medical imaging, to improve prognosis precision and effectiveness. This research study will demonstrate a suggested methodology that makes use of the CNN architecture and is trained using a database of MRI pictures with this tumor. The constructed model will be assessed based on its overall performance. Extensive experiments and comparisons with conventional machine learning techniques and existing classification methods will also be made. It will be crucial to emphasize the possibility of early and accurate prediction in a clinical workflow because it can have a big impact on treatment planning and patient outcomes. The paramount objective is to not only address the classification challenge but also to outline a clear pathway towards enhancing prognosis precision and treatment effectiveness.

Predicting microseismic,acoustic emission and electromagnetic radiation data using neural networks

Microseism,acoustic emission and electromagnetic radiation(M-A-E)data are usually used for predicting rockburst hazards.However,it is a great challenge to realize the prediction of M-A-E data.In this study,with the aid of a deep learning algorithm,a new method for the prediction of M-A-E data is proposed.In this method,an M-A-E data prediction model is built based on a variety of neural networks after analyzing numerous M-A-E data,and then the M-A-E data can be predicted.The predicted results are highly correlated with the real data collected in the field.Through field verification,the deep learning-based prediction method of M-A-E data provides quantitative prediction data for rockburst monitoring.

A Pooling Method Developed for Use in Convolutional Neural Networks

In convolutional neural networks,pooling methods are used to reduce both the size of the data and the number of parameters after the convolution of the models.These methods reduce the computational amount of convolutional neural networks,making the neural network more efficient.Maximum pooling,average pooling,and minimum pooling methods are generally used in convolutional neural networks.However,these pooling methods are not suitable for all datasets used in neural network applications.In this study,a new pooling approach to the literature is proposed to increase the efficiency and success rates of convolutional neural networks.This method,which we call MAM(Maximum Average Minimum)pooling,is more interactive than other traditional maximum pooling,average pooling,and minimum pooling methods and reduces data loss by calculating the more appropriate pixel value.The proposed MAM pooling method increases the performance of the neural network by calculating the optimal value during the training of convolutional neural networks.To determine the success accuracy of the proposed MAM pooling method and compare it with other traditional pooling methods,training was carried out on the LeNet-5 model using CIFAR-10,CIFAR-100,and MNIST datasets.According to the results obtained,the proposed MAM pooling method performed better than the maximum pooling,average pooling,and minimum pooling methods in all pool sizes on three different datasets.

Event-based nonfragile state estimation for memristive recurrent neural networks with stochastic cyber-attacks and sensor saturations

This paper addresses the issue of nonfragile state estimation for memristive recurrent neural networks with proportional delay and sensor saturations. In practical engineering, numerous unnecessary signals are transmitted to the estimator through the networks, which increases the burden of communication bandwidth. A dynamic event-triggered mechanism,instead of a static event-triggered mechanism, is employed to select useful data. By constructing a meaningful Lyapunov–Krasovskii functional, a delay-dependent criterion is derived in terms of linear matrix inequalities for ensuring the global asymptotic stability of the augmented system. In the end, two numerical simulations are employed to illustrate the feasibility and validity of the proposed theoretical results.

MetaPINNs:Predicting soliton and rogue wave of nonlinear PDEs via the improved physics-informed neural networks based on meta-learned optimization

Efficiently solving partial differential equations(PDEs)is a long-standing challenge in mathematics and physics research.In recent years,the rapid development of artificial intelligence technology has brought deep learning-based methods to the forefront of research on numerical methods for partial differential equations.Among them,physics-informed neural networks(PINNs)are a new class of deep learning methods that show great potential in solving PDEs and predicting complex physical phenomena.In the field of nonlinear science,solitary waves and rogue waves have been important research topics.In this paper,we propose an improved PINN that enhances the physical constraints of the neural network model by adding gradient information constraints.In addition,we employ meta-learning optimization to speed up the training process.We apply the improved PINNs to the numerical simulation and prediction of solitary and rogue waves.We evaluate the accuracy of the prediction results by error analysis.The experimental results show that the improved PINNs can make more accurate predictions in less time than that of the original PINNs.

Multi-Scale-Matching neural networks for thin plate bending problem

Physics-informed neural networks are a useful machine learning method for solving differential equations,but encounter challenges in effectively learning thin boundary layers within singular perturbation problems.To resolve this issue,multi-scale-matching neural networks are proposed to solve the singular perturbation problems.Inspired by matched asymptotic expansions,the solution is decomposed into inner solutions for small scales and outer solutions for large scales,corresponding to boundary layers and outer regions,respectively.Moreover,to conform neural networks,we introduce exponential stretched variables in the boundary layers to avoid semiinfinite region problems.Numerical results for the thin plate problem validate the proposed method.

Multi-Material Topology Optimization of 2D Structures Using Convolutional Neural Networks

In recent years,there has been significant research on the application of deep learning(DL)in topology optimization(TO)to accelerate structural design.However,these methods have primarily focused on solving binary TO problems,and effective solutions for multi-material topology optimization(MMTO)which requires a lot of computing resources are still lacking.Therefore,this paper proposes the framework of multiphase topology optimization using deep learning to accelerate MMTO design.The framework employs convolutional neural network(CNN)to construct a surrogate model for solving MMTO,and the obtained surrogate model can rapidly generate multi-material structure topologies in negligible time without any iterations.The performance evaluation results show that the proposed method not only outputs multi-material topologies with clear material boundary but also reduces the calculation cost with high prediction accuracy.Additionally,in order to find a more reasonable modeling method for MMTO,this paper studies the characteristics of surrogate modeling as regression task and classification task.Through the training of 297 models,our findings show that the regression task yields slightly better results than the classification task in most cases.Furthermore,The results indicate that the prediction accuracy is primarily influenced by factors such as the TO problem,material category,and data scale.Conversely,factors such as the domain size and the material property have minimal impact on the accuracy.