山西大学学报（自然科学版）2024，Vol.47Issue(6)：1136-1147,12.DOI:10.13451/j.sxu.ns.2023160
深度学习下随机基因开关模型的概率密度函数估计
Probability Density Function Estimation of Stochastic Gene Switching Model Under Deep Learning
摘要
Abstract
In the process of solving the probability density function(PDF)of stochastic gene switching model,the commonly used methods are difficult to solve theoretically,and the accurate solutions can only be obtained under some very strict conditions.The re-sults are relatively rough,with low accuracy and long time consumption,and the accuracy may be limited by sample path length and mesh subdivision degree.In response to these issues,this paper uses neural network to estimate the PDF of this model.In the re-search process,penalty factors were introduced to overcome local optimization,and corresponding setting criteria were provided.Normalization conditions were also used as supervisory conditions to avoid approximate solutions of zero.Our final results show that the deep learning method is very feasible and effective to estimate the PDF of stochastic gene switching model,and this method does not require any interpolation or coordinate transformation.Compared with the Monte Carlo method,the time consumption is re-duced by at least 50 seconds,and the obtained results have higher accuracy.The effects of the number of hidden layers and nodes were also studied,indicating that the computational performance of machine learning can be improved by appropriately constructing neural network.关键词
概率密度函数/蒙特卡罗模拟/神经网络/惩罚因子/高斯白噪声/随机基因开关模型Key words
probability density function/Monte Carlo simulation/neural network/penalty factor/Gaussian white noise/stochastic gene switching model分类
数理科学引用本文复制引用
石昊楠,马晋忠..深度学习下随机基因开关模型的概率密度函数估计[J].山西大学学报（自然科学版）,2024,47(6):1136-1147,12.基金项目
国家自然科学基金(12102237) （12102237）
山西省基础研究计划(20210302124387) （20210302124387）
