In the present article, delay and system of delay differential equations are treated using feed-forward artificial neural networks. We have solved multiple problems using neural network architectures with different depths. The neural networks are trained using the extreme learning machine algorithm for the satisfaction of delay differential equations and associated initial/boundary conditions. Further, numerical rates of convergence of the proposed algorithm are reported based on variation of error in the obtained solution for different number of training points. Emphasis is on analysing whether deeper network architectures trained with extreme learning machine algorithm can perform better than shallow network architectures for approximating the solutions of delay differential equations.

在本文中，使用前馈人工神经网络处理时滞和时滞微分方程组。我们已经使用不同深度的神经网络架构解决了多个问题。使用极限学习机算法对神经网络进行训练，以使它们满足延迟微分方程和相关的初始/边界条件的要求。此外，基于获得的解决方案中针对不同数量的训练点的误差变化，报告了所提出算法的收敛速度数值。重点在于分析用极限学习机算法训练的较深的网络体系结构在近似延迟微分方程解方面是否能比浅层的网络体系结构更好地执行。