APPROXIMATION OF DYNAMICAL-SYSTEMS BY CONTINUOUS-TIME RECURRENT NEURAL NETWORKS
APPROXIMATION OF DYNAMICAL-SYSTEMS BY CONTINUOUS-TIME RECURRENT NEURAL NETWORKS
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DOI：
10.1016/s0893-6080(05)80125-x
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发表时间：
1993-01-01
期刊：
影响因子：
7.8
通讯作者：
NAKAMURA, Y
中科院分区：
文献类型：
--
作者：
FUNAHASHI, K;NAKAMURA, Y
本文证明了一个给定的n维动力系统的任意有限时间轨迹都可以由一个具有n个输出单元、若干隐单元和适当初始条件的连续时间递归神经网络的输出单元的内部状态近似实现。证明的基本思想是将n维动力系统嵌入到一个更高维的递归神经网络中。作为推论，我们还证明了任何连续曲线都可以近似于递归神经网络的输出。
In this paper, we prove that any finite time trajectory of a given n-dimensional dynamical system can be approximately realized by the internal state of the output units of a continuous time recurrent neural network with n output units, some hidden units, and an appropriate initial condition. The essential idea of the proof is to embed the n-dimensional dynamical system into a higher dimensional one which defines a recurrent neural network. As a corollary, we also show that any continuous curve can be approximated by the output of a recurrent neural network.