# Identifiability and numerical algebraic geometry

Autoři: Daniel J. Bates aff001;  Jonathan D. Hauenstein aff002;  Nicolette Meshkat aff003
Působiště autorů: Department of Mathematics, United States Naval Academy, Annapolis, MD, United States of America aff001;  Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, United States of America aff002;  Department of Mathematics and Computer Science, Santa Clara University, Santa Clara, CA, United States of America aff003
Vyšlo v časopise: PLoS ONE 14(12)
Kategorie: Research Article
doi: https://doi.org/10.1371/journal.pone.0226299

## Souhrn

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.

### Klíčová slova:

Blood – Computing methods – Interpolation – Polynomials – Vector spaces – Algebraic geometry – Complex numbers – Compartment models

##### Zdroje

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Článek vyšel v časopise

### PLOS One

2019 Číslo 12
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