一种调整型径向基网络偏微分方程解法

基于径向基神经网络（RBFN）的偏微分方程（PDE）求解算法中，仪通过搜索最佳权值逼近方程解，精度有限。实际上在建立的RBFN中可能存在对求解PDE贡献很小的但是增加算法复杂度的神经元，或者缺少对方程解贡献很大的辅助神经元。基于这个事实提出一种新的算法：在搜索最佳权值同时调整RBFN结构，删除对方程解贡献小的神经元，增加对方程解贡献大的辅助神经元；采用最小均方误羔梯度下降法得到最优权值；最后得到PDE的逼近解。仿真实验表明新算法较传统的RBFN算法，精度更高，误差收敛速度更快；可广泛应用于工程实践。

A Numerical Solution of Differential Equation Based on Adapted Radial Bases Function Network

The radial basis function network(RBFN) is popular to solute the partial differential equation(PDE).But the accuracy of Solution is limited,only by searching optimal weights in RBFN.In fact,some neurons contribution to the solution of PDE is small and that of others is great in RBFN.Basing that fact,a algorithm is proposed: when searching optimal weights in RBFN,Neurons contributing to solution less are deleted from RBFN and Ancillary neurons contributing to solution more are added to RBFN.Optimal weights are achieved by gradient descent method.