反馈神经网络对非线性动力系统的本质逼近能力研究

项目名称： 反馈神经网络对非线性动力系统的本质逼近能力研究

项目编号： No.11261042

项目类型： 地区科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 李风军

作者单位： 宁夏大学

项目金额： 45万元

中文摘要： 目前关于反馈神经网络对非线性动力系统逼近能力的研究基本上集中于稠密性问题，即反馈网络逼近的定性问题。但是，从应用角度来看，反馈神经网络逼近动力系统的定量研究和算法尤为重要。有关反馈神经网络逼近的定量研究, 特别是反映网络的逼近速度与网络拓扑结构之间关系的研究, 最近开始引起人们的强烈关注。本项目将深入研究反馈神经网络对非线性动力系统的本质逼近能力。具体任务包括：设计具有高精度逼近能力的反馈神经网络新模型和新算法；研究该类神经网络对非线性动力系统逼近速度的上、下界估计和本质逼近阶估计；刻画所构造的神经网络对非线性动力系统的本质逼近能力的极限行为与网络拓扑结构、动力系统演化规律的空间性质（元规则的空间性质、支持度及置信度等）之间的相依关系；构造具有较高逼近能力的，结构更简单化的反馈神经网络新模型。另外，设计求解这些模型的优化算法时，必须设计高效、可信的智能优化算法，这是目前相关研究所少有的。

中文关键词： 神经网络；反馈神经网络；非线性动力系统；逼近；

英文摘要： Nonlinear science is a rapidly developing research field. Much attention has been paid all over the world to its promising. Neural networks, which is one of active branches in nonlinear science, has drawn great attention. In application, it involves various areas in natural and social science. Now it has become a powerful tool of exploring and solving many complicated problems in natural science and engineering. In this project, we make a systematic investigation into approximation ability of recurrent neural networks. Neural networks represent a class of functions for the efficient identification and forecasting of dynamical systems. The method of recurrent neural networks approximation is used in nonlinear systems. So far , the study of approximation ability that recurrent neural network works on the nonlinear dynamical systems are basically concentrated on the dense problems，that is, the qualitative issues of the recurrent network approximation. However，from the application point of view, quantitative study of recurrent neural network approximation of dynamical systems and relative algorithms are particularly important. The quantitative study of recurrent neural network approximation, especially the study of reflecting the relationship between network's approximation speed and network topology structure,

英文关键词： recurrent neural network；neural network；nonlinear dynamical system；approxximation；