Elimination of unknowns in a system of differential equations is often required when analysing (possibly nonlinear) dynamical systems models, where only a subset of variables are observable. One such analysis, identifiability, often relies on computing input-output relations via differential algebraic elimination. Determining identifiability, a natural prerequisite for meaningful parameter estimation, is often prohibitively expensive for medium to large systems due to the computationally expensive task of elimination. We propose an algorithm that computes a description of the set of differential-algebraic relations between the input and output variables of a dynamical system model. The resulting algorithm outperforms general-purpose software for differential elimination on a set of benchmark models from literature. We use the designed elimination algorithm to build a new randomized algorithm for assessing structural identifiability of a parameter in a parametric model. A parameter is said to be identifiable if its value can be uniquely determined from input-output data assuming the absence of noise and sufficiently exciting inputs. Our new algorithm allows the identification of models that could not be tackled before. Our implementation is publicly available as a Julia package at https://github.com/SciML/StructuralIdentifiability.jl.
翻译:在分析(可能是非线性的非线性)动态系统模型时,往往需要消除差异方程式系统中的未知数,因为只有一组变量可以观测到。其中一种分析,即可识别性,往往依赖通过不同的代数消除方法计算输入输出关系。确定可识别性,这是有意义的参数估计的自然先决条件,对于中大系统来说,由于计算成本高昂的消除任务,对于中大系统来说,确定可识别性往往成本极高。我们建议一种算法,对动态系统模型的输入和输出变量之间的一组差异-代数关系进行描述。由此产生的算法,在文献基准模型的一套基准模型上形成用于区别消除的通用软件。我们使用设计的消除算法来建立一个新的随机化算法,用以评估参数在参数中的结构性可识别性。一个参数如果其价值能够根据假定没有噪音和足够刺激性的投入数据的独特性来确定,是可以确定的。我们的新算法可以确定以前无法处理的模型。我们的实施在 https://gifilable.SML/commexical /comm。