神经网络在动力学系统建模中的理论研究

动力学系统可以看成是映输入空间到输出空间的一个算子，在特定时刻动力学系统的输出可以看成是其输入空间上的一个泛函，这样动力学系统建模就可以看作是表征系统映射关系的算子或泛函的逼近问题。研究了多层神经网络的非线性映射能力，给出了多层网络可一致逼近有限维空间Ｒｎ紧集上的连续函数、无穷维函数空间紧集上的连续泛函和连续算子的理论证明。得出的几个一般性结论为在动力学系统建模等领域应用神经网络准备了理论工具。

Theoretical research on neural networks in application to dynamic system modeling

A dynamic system can be viewed as an operator which maps an input space to an output space. The output of a dynamic system at any particular time can be viewed as a functional defined on the input space. Thus the dynamic system modeling is in fact a problem of approximating an operator or a functional which represents the mapping relationship of the system. In this paper, the nonlinear mapping capability of multilayer neural networks is studied. A proof of multilayer network consistent approximation to continuous functions defined on some compact set in R n (a space of finite dimensions), continuous functionals and operators defined on some compact set of a function space (a space of infinite dimensions) is given. Several strong results on neural network approximation capability obtained provide a theory tool useful for the applications of neural networks in the areas such as dynamic system modeling etc.