前向傅立叶神经网络系统逼近理论及学习算法

On Forward Fourier Neural Networks System Approximate Theory and Learning Algorithm

定义了傅立叶神经元与傅立叶神经网络,将一组傅立叶基三角函数作为神经网络各隐层单元的激合函数,设计出一类单输入单输出三层前向傅立叶神经网络与双输入单输出四层前向傅立叶神经网络,以及奇、偶傅立叶神经网络,基于三角函数逼近论,讨论了前向傅立叶神经网络的三角插值机理及系统逼近理论,且有严格的数学理论基础,给出了前向傅立叶神经网络学习算法,通过学习,它们分别能逼近于给定的傅立叶函数到预定的精度。仿真实验表明,该学习算法效率高,具有极为重要的理论价值和应用背景。

The concepts of Fourier neurons and Fourier neural networks and firstly proposed.The Fourier base functions can be regarded as neural networks hidden layers of activation functions,and a kind of three layers forwards Fourier neural networks with single input and single output and four layers forward Fourier neural networks with double inputs and single output ,and strange even Fourier neural networks is designed.Base on triangle function approximate theory,the intepolation mechanism of Fourier neural networks is discussed.Which can respectively approximate a given one-variable Fourier function and a given two variable Fourier function satisfying given precision.And have strict mathematical theory.The forward Fourier neural networks learning algorithm is proposed.The simulation results have proven that it has excellent performance of approximating non-linear properoties,and therefore has very important theoretical and practical significance.