基于神经网络的常微分方程数值计算方法

A Numerical Method for Solving Ordinary Differential Equations by Using Neural Network

科学与工程应用中常用微分方程来建模,提出了一种基于余弦基神经网格的计算微分方程的新方法,其基本思想是以神经网络的输出来近似初值问题中的解析解.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,为神经网络学习率的选择提供了依据.通过实例证明了该算法的有效性.

Differential equations are used to model problems in science and engineering, most of these problems require the solution to an initial-value problem. A new method for solving initial-value problems in ordinary differential equations （ ODEs ） is proposed. The basic idea is to use the out-put of neural network to approximate to the solution of the initial-value problems in ODEs. The convergence theorem of neural networks algorithm is given and proved. The accurac and efficiency of the proposed method are validated by the simulation examples of＇initial-value problems in ODE.