基于人工神经网络的三阶龙格库塔法建模

M. Dehghanpour, A. Rahati, E. Dehghanian
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引用次数: 3

摘要

世界上常见的规律(量子物理、电子学、计算化学和天文学)在微分方程的语言中找到了它们的正常数学解释,因此寻找这些方程的最佳数值解方法是非常重要的。本文利用人工神经网络(ANN)设计了一种求解特定微分方程组的数值方法,使得人工神经网络在训练过程中计算出三阶龙格库塔法系数的最优值。为了验证我们的方法,我们进行了一些实验,通过使用人工神经网络获得的系数和另外两个众所周知的系数(Classical和Heun)来解决两个体问题。结果表明,与其他两种方法相比,人工神经网络方法具有更好的性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
ANN-based modeling of third order runge kutta method
The world's common rules (Quantum Physics, Electronics, Computational Chemistry and Astronomy) find their normal mathematical explanation in language of differential equations, so finding optimum numerical solution methods for these equations are very important. In this paper, using an artificial neural network (ANN) a numerical approach is designed to solve a specific system of differential equations such that the training process of the ANN  calculates the  optimal values for the coefficients of third order Runge Kutta method. To validate our approach, we performed some experiments by solving two body problem using coefficients obtained by ANN and also two other well-known coefficients namely Classical and Heun. The results show that the ANN approach has a better performance in compare with two other approaches.
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