径向基函数网络在数值计算中的应用

Applications of Radius Basis Function Neural Networks in Numerical Calculation

由经典的函数逼近理论衍生的很多数值算法有共同的缺点:计算量大、适应性差、对模型和数据要求高,在实际应用中受到限制。神经网络可以被用来计算复杂输入与输出结果之间的关系,故神经网络具有很强的函数逼近功能。该文给出了径向基函数网络(RBFNN)的结构及学习过程,重点阐述了RBFNN在函数逼近、求解非线性方程组以及散乱敷据插值中的应用,结合MATLAB神经网络工具箱给出了数值实例,并与BP网络进行了比较。应用结果表明RBFNN是数值计算的一个有力工具,与传统方法比较具有绩程简单、实用的特点,在工程和科学研究上若将其制成软件包则具有很好的使用价值。

Many numeric arithmetics derived from classical function approach theories have some flaws, such as too much complicated computation and so on. So, they are restricted in the real application. Neural networks can be used to compute the relationship between complicated inputs and outputs, so neural networks have a strong ability to approximate functions. Structure and study process of radius basis function neural networks （RBFNN） ,applications of RBFNN in functional approximating, solving nonlinear multivariable equation systems and scattered data interpolation are put forward in the paper. Simultaneously, numerical examples are given combining with the toolbox of MATLAB neural networks and experimental results are compared with the BP neural networks. It is made clear that RBFNN is a powerful tool for numeric computation. It is of great value when RBFNN is made into software package to resolve numerical problems.