Identifiability and numerical algebraic geometry
Identifiability and numerical algebraic geometry
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DOI：
10.1371/journal.pone.0226299
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发表时间：
2019-12-13
期刊：
影响因子：
3.7
通讯作者：
Meshkat, Nicolette
中科院分区：
文献类型：
--
作者：
Bates, Daniel J.;Hauenstein, Jonathan D.;Meshkat, Nicolette
当分析模型（例如生物过程的数学建模）时的常见问题是确定模型的未知参数是否可以从给定的输入-输出数据确定。可识别模型是这样的模型，使得未知参数可以被确定为具有给定输入-输出数据的有限数量的值。这些值在复数上的总数称为模型的可辨识度。不可识别的模型是这样的模型，未知参数可以有一个给定的输入输出数据的值的无限数量。对于不可识别的模型，一组可识别的功能的参数，以便该模型可以重新参数化的这些功能产生一个可识别的模型。在这项工作中，我们使用数值代数几何，以确定如果一个模型由多项式或有理常微分方程是可识别的或不可识别的。对于可辨识模型，提出了一种新的可辨识度计算方法。对于不可识别的模型，我们提出了一种新颖的数值微分代数技术，旨在计算一组代数独立的可识别函数。通过几个例子来说明新的技术。
A common problem when analyzing models, such as mathematical modeling of a biological process, is to determine if the unknown parameters of the model can be determined from given input-output data. Identifiable models are models such that the unknown parameters can be determined to have a finite number of values given input-output data. The total number of such values over the complex numbers is called the identifiability degree of the model. Unidentifiable models are models such that the unknown parameters can have an infinite number of values given input-output data. For unidentifiable models, a set of identifiable functions of the parameters are sought so that the model can be reparametrized in terms of these functions yielding an identifiable model. In this work, we use numerical algebraic geometry to determine if a model given by polynomial or rational ordinary differential equations is identifiable or unidentifiable. For identifiable models, we present a novel approach to compute the identifiability degree. For unidentifiable models, we present a novel numerical differential algebra technique aimed at computing a set of algebraically independent identifiable functions. Several examples are used to demonstrate the new techniques.