一类非线性常微分方程参数估计  

Parameter estimation for a class of nonlinear ordinary differential equations

作　　者：孙莹莹 王珺 SUN Yingying;WANG Jun(School of Mathematics&Statistics,Changchun University of Technology,Changchun 130012,China)

机构地区：[1]长春工业大学数学与统计学院,吉林长春130012

出　　处：《长春工业大学学报》2024年第6期557-562,共6页Journal of Changchun University of Technology

基　　金：吉林省科技厅自然科学基金资助项目(20200201273JC)。

摘　　要：针对带有交叉项的非线性常微分方程参数估计问题,利用两阶段方法,首先将最小二乘法和样条展开相结合得到基函数展开的估计,为了提高估计效率,文中提出的方法中采用了积分估计,得到了估计基函数展开的积分;其次将积分结果代入Group LASSO模型,得到参数估计值;最后进行数值模拟。结果表明,文中提出的方法在处理非线性常微分方程参数估计问题时效果良好。In this paper,a two-stage method is used to estimate the parameters of nonlinear ordinary differential equations with cross terms.In the first stage,the least square method is combined with spline expansion to get the estimation of the basis function expansion.At the same time,in order to improve the estimation efficiency,integral estimation is used in the proposed method,and the integral of the expansion of the estimated basis function is obtained.Then the integral results are substituted into the Group LASSO model to get the parameter estimates.Finally,numerical simulation results show that the proposed method is effective in solving nonlinear ordinary differential equation parameter estimation problems.

关 键 词：B样条 非线性常微分方程 变量选择 Group LASSO 

分 类 号：O212[理学—概率论与数理统计]