Explores the generalization error of fuzzy neural network, analyzes the reason for occurrence and presents the equation of calculating error by the confidence interval approach. In addition, a generalization error tra...Explores the generalization error of fuzzy neural network, analyzes the reason for occurrence and presents the equation of calculating error by the confidence interval approach. In addition, a generalization error transfering(GET) method of improving the generalization error is proposed. The simulation experimental results of heating furnance show that the GET scheme is efficient.展开更多
A fuzzy modeling method for complex systems is studied. The notation of general stochastic neural network (GSNN) is presented and a new modeling method is given based on the combination of the modified Takagi and Suge...A fuzzy modeling method for complex systems is studied. The notation of general stochastic neural network (GSNN) is presented and a new modeling method is given based on the combination of the modified Takagi and Sugeno's (MTS) fuzzy model and one-order GSNN. Using expectation-maximization(EM) algorithm, parameter estimation and model selection procedures are given. It avoids the shortcomings brought by other methods such as BP algorithm, when the number of parameters is large, BP algorithm is still difficult to apply directly without fine tuning and subjective tinkering. Finally, the simulated example demonstrates the effectiveness.展开更多
This paper discusses the general decay synchronization problem for a class of fuzzy competitive neural networks with time-varying delays and discontinuous activation functions. Firstly, based on the concept of Filippo...This paper discusses the general decay synchronization problem for a class of fuzzy competitive neural networks with time-varying delays and discontinuous activation functions. Firstly, based on the concept of Filippov solutions for right-hand discontinuous systems, some sufficient conditions for general decay synchronization of the considered system are obtained via designing a nonlinear feedback controller and applying discontinuous differential equation theory, Lyapunov functional methods and some inequality techniques. Finally, one numerical example is given to verify the effectiveness of the proposed theoretical results. The general decay synchronization considered in this article can better estimate the convergence rate of the system, and the exponential synchronization and polynomial synchronization can be seen as its special cases.展开更多
A fairly comprehensive analysis is presented for the gradient descent dynamics for training two-layer neural network models in the situation when the parameters in both layers are updated.General initialization scheme...A fairly comprehensive analysis is presented for the gradient descent dynamics for training two-layer neural network models in the situation when the parameters in both layers are updated.General initialization schemes as well as general regimes for the network width and training data size are considered.In the overparametrized regime,it is shown that gradient descent dynamics can achieve zero training loss exponentially fast regardless of the quality of the labels.In addition,it is proved that throughout the training process the functions represented by the neural network model are uniformly close to those of a kernel method.For general values of the network width and training data size,sharp estimates of the generalization error are established for target functions in the appropriate reproducing kernel Hilbert space.展开更多
With the remarkable empirical success of neural networks across diverse scientific disciplines,rigorous error and convergence analysis are also being developed and enriched.However,there has been little theoretical wo...With the remarkable empirical success of neural networks across diverse scientific disciplines,rigorous error and convergence analysis are also being developed and enriched.However,there has been little theoretical work focusing on neural networks in solving interface problems.In this paper,we perform a convergence analysis of physics-informed neural networks(PINNs)for solving second-order elliptic interface problems.Specifically,we consider PINNs with domain decomposition technologies and introduce gradient-enhanced strategies on the interfaces to deal with boundary and interface jump conditions.It is shown that the neural network sequence obtained by minimizing a Lipschitz regularized loss function converges to the unique solution to the interface problem in H2 as the number of samples increases.Numerical experiments are provided to demonstrate our theoretical analysis.展开更多
In this paper, an intelligent control system based on recurrent neural fuzzynetwork is presented for complex, uncertain and nonlinear processes, in which a recurrent neuralfuzzy network is used as controller (RNFNC) t...In this paper, an intelligent control system based on recurrent neural fuzzynetwork is presented for complex, uncertain and nonlinear processes, in which a recurrent neuralfuzzy network is used as controller (RNFNC) to control a process adaptively and a recurrent neuralnetwork based on recursive predictive error algorithm (RNNM) is utilized to estimate the gradientinformation partial deriv y/partial deriv u for optimizing the parameters of controller. Comparedwith many neural fuzzy control systems, it uses recurrent neural network to realize the fuzzycontroller. Moreover, recursive predictive error algorithm (RPE) is implemented to construct RNNM online. Lastly, in order to evaluate the performance of the proposed control system, the presentedcontrol system is applied to continuously stirre'd tank reactor (CSTR). Simulation comparisons,based on control effect and output error, with general fuzzy controller and feed-forward neuralfuzzy network controller (FNFNC), are conducted. In addition, the rates of convergence of RNNMrespectively using RPE algorithm and gradient learning algorithm are also compared. The results showthat the proposed control system is better for controlling uncertain and nonlinear processes.展开更多
文摘Explores the generalization error of fuzzy neural network, analyzes the reason for occurrence and presents the equation of calculating error by the confidence interval approach. In addition, a generalization error transfering(GET) method of improving the generalization error is proposed. The simulation experimental results of heating furnance show that the GET scheme is efficient.
文摘A fuzzy modeling method for complex systems is studied. The notation of general stochastic neural network (GSNN) is presented and a new modeling method is given based on the combination of the modified Takagi and Sugeno's (MTS) fuzzy model and one-order GSNN. Using expectation-maximization(EM) algorithm, parameter estimation and model selection procedures are given. It avoids the shortcomings brought by other methods such as BP algorithm, when the number of parameters is large, BP algorithm is still difficult to apply directly without fine tuning and subjective tinkering. Finally, the simulated example demonstrates the effectiveness.
文摘This paper discusses the general decay synchronization problem for a class of fuzzy competitive neural networks with time-varying delays and discontinuous activation functions. Firstly, based on the concept of Filippov solutions for right-hand discontinuous systems, some sufficient conditions for general decay synchronization of the considered system are obtained via designing a nonlinear feedback controller and applying discontinuous differential equation theory, Lyapunov functional methods and some inequality techniques. Finally, one numerical example is given to verify the effectiveness of the proposed theoretical results. The general decay synchronization considered in this article can better estimate the convergence rate of the system, and the exponential synchronization and polynomial synchronization can be seen as its special cases.
基金supported by a gift to Princeton University from i Flytek and the Office of Naval Research(ONR)(Grant No.N00014-13-1-0338)。
文摘A fairly comprehensive analysis is presented for the gradient descent dynamics for training two-layer neural network models in the situation when the parameters in both layers are updated.General initialization schemes as well as general regimes for the network width and training data size are considered.In the overparametrized regime,it is shown that gradient descent dynamics can achieve zero training loss exponentially fast regardless of the quality of the labels.In addition,it is proved that throughout the training process the functions represented by the neural network model are uniformly close to those of a kernel method.For general values of the network width and training data size,sharp estimates of the generalization error are established for target functions in the appropriate reproducing kernel Hilbert space.
基金the National Natural Science Foundation of China(Grant Nos.11771435,22073110 and 12171466).
文摘With the remarkable empirical success of neural networks across diverse scientific disciplines,rigorous error and convergence analysis are also being developed and enriched.However,there has been little theoretical work focusing on neural networks in solving interface problems.In this paper,we perform a convergence analysis of physics-informed neural networks(PINNs)for solving second-order elliptic interface problems.Specifically,we consider PINNs with domain decomposition technologies and introduce gradient-enhanced strategies on the interfaces to deal with boundary and interface jump conditions.It is shown that the neural network sequence obtained by minimizing a Lipschitz regularized loss function converges to the unique solution to the interface problem in H2 as the number of samples increases.Numerical experiments are provided to demonstrate our theoretical analysis.
基金The author is now working as a research fellow in the Department of Chemical & Biomolecular Engineering,Faculty of Engineering,National University of Singapore,Singapore,119260.
文摘In this paper, an intelligent control system based on recurrent neural fuzzynetwork is presented for complex, uncertain and nonlinear processes, in which a recurrent neuralfuzzy network is used as controller (RNFNC) to control a process adaptively and a recurrent neuralnetwork based on recursive predictive error algorithm (RNNM) is utilized to estimate the gradientinformation partial deriv y/partial deriv u for optimizing the parameters of controller. Comparedwith many neural fuzzy control systems, it uses recurrent neural network to realize the fuzzycontroller. Moreover, recursive predictive error algorithm (RPE) is implemented to construct RNNM online. Lastly, in order to evaluate the performance of the proposed control system, the presentedcontrol system is applied to continuously stirre'd tank reactor (CSTR). Simulation comparisons,based on control effect and output error, with general fuzzy controller and feed-forward neuralfuzzy network controller (FNFNC), are conducted. In addition, the rates of convergence of RNNMrespectively using RPE algorithm and gradient learning algorithm are also compared. The results showthat the proposed control system is better for controlling uncertain and nonlinear processes.
