数值积分的神经网络算法研究

提出一种求解数值积分的新方法,其基本思想是训练傅立叶基神经网络来逼近被积函数以实现定积分的数值计算.为保证算法的收敛性,提出并证明了神经网络算法的收敛性定理,为学习率的选取提供依据.本算法计算精度较高,对被积函数要求较低,适应性强,并可以计算振荡函数的积分.数值积分算例验证了本算法的有效性,因此在工程实际中有较大的应用价值.

Neural Network Algorithm for Solving Numerical Integration

An algorithm of neural network based on the Fourier series for solving numerical integration was proposed.The basic idea is to use the neural network output to approximate to the integrand.In order to ensure the convergence of algorithm,the convergence theorem of neural network algorithm and the theorem for solving numerical integration were given and proved.This algorithm was validated by the simulation examples of numerical integration.The results show the presented numerical integration algorithm has value in engineering practice.