用线性多步法训练神经网络

研究用微分方程数值解法－－线性多步法替代神经网络的学习算法，指出在一定条件下神经网络的BP学习问题与求解一个相应的微分系统在渐近意义下是等价的，从而求解微分动力系统的数值解法也可用于神经网络的学习，给出了训练神经网络的Milne方法和BP－Milne结合算法以及Hamming方法和BP－Hamming结合算法，并以9点两类模式、随机模式识别和石油地质中沉积微相模式识别等3个问题为例进行了实验，实验结果表明利用微分动力系统的数值解法进行神经网络的学习是可行的。

TRAINING NEURAL NETWORKS BY USING THE LINEAR MULTI-STEP METHOD

Training neural networks by using the linear multi-step method is studied, which is a classical numerical method for differential dynamics. It is pointed out that the iteration formula of BP algorithm is equivalent to the Euler method of differential dynamic systems under certain conditions, and the asymptotic solutions of the two formulas are consistent, and thus training a neural network can be converted to computing numerical solution of differential dynamic systems. Two algorithms to train neural networks are presented, namely the Milne method and the Hamming method. Finally three experiment examples are implemented to illustrate the fitness of training neural networks by the numerical method for differential dynamics.