一类随机Lotka-Volterra系统参数的神经网络学习

doi:10.7523/j.ucas.2023.012

中国科学院大学学报 ›› 2025, Vol. 42 ›› Issue (1): 20-25.DOI: 10.7523/j.ucas.2023.012

• 数学与物理学 • 上一篇

一类随机Lotka-Volterra系统参数的神经网络学习

汪展鹏, 王丽瑾

中国科学院大学数学科学学院, 北京 100049

收稿日期:2022-11-02 修回日期:2023-02-17 发布日期:2023-03-21
通讯作者: 王丽瑾,E-mail:ljwang@ucas.ac.cn
基金资助:
Supported by the National Natural Science Foundation of China (11971458,11471310)

Learning the parameters of a class of stochastic Lotka-Volterra systems with neural networks

WANG Zhanpeng, WANG Lijin

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2022-11-02 Revised:2023-02-17 Published:2023-03-21
Supported by:
Supported by the National Natural Science Foundation of China (11971458,11471310)

摘要/Abstract

摘要： 提出一种利用神经网络学习一类随机Lotka-Volterra系统参数的方法。利用随机微分方程的Euler-Maruyama离散近似推导出观测变量的期望和协方差矩阵，并在此基础上建立损失函数。在网络训练过程中，采用随机梯度下降方法进行优化。数值实验验证了该算法的有效性。

关键词: 随机Lotka-Volterra系统, 神经网络, Euler-Maruyama格式, 参数估计

Abstract: In this paper, we propose a neural network approach to learn the parameters of a class of stochastic Lotka-Volterra systems. Approximations of the mean and covariance matrix of the observational variables are obtained from the Euler-Maruyama discretization of the underlying stochastic differential equations (SDEs), based on which the loss function is built. The stochastic gradient descent method is applied in the neural network training. Numerical experiments demonstrate the effectiveness of our method.

Key words: stochastic Lotka-Volterra systems, neural networks, Euler-Maruyama scheme, parameter estimation

中图分类号:

O241.8

汪展鹏, 王丽瑾. 一类随机Lotka-Volterra系统参数的神经网络学习[J]. 中国科学院大学学报, 2025, 42(1): 20-25.

WANG Zhanpeng, WANG Lijin. Learning the parameters of a class of stochastic Lotka-Volterra systems with neural networks[J]. Journal of University of Chinese Academy of Sciences, 2025, 42(1): 20-25.

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一类随机Lotka-Volterra系统参数的神经网络学习

Learning the parameters of a class of stochastic Lotka-Volterra systems with neural networks

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