论文标题
更快的Gröbner基地通过单订单的ODE系统的谎言衍生物
Faster Gröbner bases for Lie derivatives of ODE systems via monomial orderings
论文作者
论文摘要
微分方程系统的符号计算通常在计算上很昂贵。许多实用的差异模型具有具有指定输出的多项式或有理ODE系统的形式。分析这些模型的一种基本符号方法是计算，然后象征性地处理由ODE系统给出的矢量字段的足够多个谎言衍生物获得的多项式系统。 在本文中，我们提出了一种通过使用特定的单一秩序（包括变量的权重）来加速此类多项式系统的Gröbner基础计算的方法，来自ODE模型的结构。我们提供的经验结果显示了不同符号计算框架之间的改进，并应用了该方法来加快ODE模型的结构可识别性分析。
Symbolic computation for systems of differential equations is often computationally expensive. Many practical differential models have a form of polynomial or rational ODE system with specified outputs. A basic symbolic approach to analyze these models is to compute and then symbolically process the polynomial system obtained by sufficiently many Lie derivatives of the output functions with respect to the vector field given by the ODE system. In this paper, we present a method for speeding up Gröbner basis computation for such a class of polynomial systems by using specific monomial ordering, including weights for the variables, coming from the structure of the ODE model. We provide empirical results that show improvement across different symbolic computing frameworks and apply the method to speed up structural identifiability analysis of ODE models.
