Abstract

The purpose of this paper is to introduce a new method based on the deep neural network method (DNN) for finding numerical solution of a novel class of stochastic biological systems. DNN utilizes the Morgan-Voyce even Lucas polynomials and \(\sinh\) function as activation functions of the deep structure. To train this neural network, we utilize the standard Brownian motion, Gauss–Legendre quadrature, and classical optimization algorithm. In the proposed method, acceptable approximate solutions are achieved by employing only a few number of the basis functions. Furthermore, we show convergence of the computational technique. Finally, the numerical technique is implemented for a stochastic biological system to illustrate the effectiveness of the presented strategy.

中文翻译：

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用于求解随机生物系统的深度神经网络

摘要

本文的目的是介绍一种基于深度神经网络方法（DNN）的新方法，用于寻找一类新型随机生物系统的数值解。DNN 利用 Morgan-Voyce 甚至 Lucas 多项式和\(\sinh\)函数作为深层结构的激活函数。为了训练这个神经网络，我们利用标准布朗运动、高斯-勒让德求积和经典优化算法。在所提出的方法中，仅使用少量的基函数即可获得可接受的近似解。此外，我们展示了计算技术的收敛性。最后，对随机生物系统实施数值技术，以说明所提出策略的有效性。