Power series neural network solution for ordinary differential equations with initial conditions

T. I. Haweel, T. N. Abdelhameed
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引用次数: 4

Abstract

Differential equations are very common in most academic fields. Modern digital control systems require fast on line and sometimes time varying solution schemes for differential equations. This paper presents new nonlinear adaptive numeric solutions for ordinary differential equations (ODE) with initial conditions. The main feature is to implement nonlinear polynomial expansions in a neural network-like adaptive framework. The transfer functions of the employed neural network follow a power series. The proposed technique does not use sigmoid or tanch non-linear transfer functions commonly adopted in conventional neural networks at the output. Instead, linear transfer functions are employed which leads to explicit power series formulae for the ODE solution. This allows extrapolation and interpolation which increase the dynamic numeric range for the solutions. The improved and accurate solutions for the proposed power series neural network (PSNN) are illustrated through simulated examples. It is shown that the performance of the proposed PSNN ODE solution outperforms existing conventional methods.
具有初始条件的常微分方程的幂级数神经网络解
微分方程在大多数学术领域都很常见。现代数字控制系统要求微分方程的快速在线和时变解方案。本文提出一种新的具有初始条件的常微分方程非线性自适应数值解。其主要特点是在类似神经网络的自适应框架中实现非线性多项式展开。所采用的神经网络的传递函数遵循幂级数。该方法不使用传统神经网络中常用的s型或tanch型非线性传递函数作为输出。相反,采用线性传递函数,得到ODE解的显式幂级数公式。这允许外推和内插,从而增加了解决方案的动态数值范围。通过仿真算例说明了所提出的幂级数神经网络(PSNN)的改进解和精确解。结果表明,所提出的PSNN ODE解决方案的性能优于现有的传统方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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