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 Gr\"obner 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.

翻译：微分方程系统的符号计算通常计算代价高昂。许多实用微分模型具有多项式或有理ODE系统形式并指定输出函数。分析此类模型的一种基本符号方法是：计算输出函数相对于ODE系统所给向量场的足够多阶Lie导数得到的多项式系统，并对其进行符号处理。本文提出一种方法，通过采用源自ODE模型结构的特定单项式序（包括变量权重）来加速此类多项式系统的Gröbner基计算。我们提供的实证结果表明该方法在不同符号计算框架中均能提升效率，并将其应用于加速ODE模型的结构可辨识性分析。