Even if a model fails to be structurally identifiable, some useful information about the parameters can still be determined, which is the main motivation for this paper. ![]() For this reason, structural identifiability is often referred to as a priori identifiability. This is a necessary condition for the practical or numerical identifiability problem, which involves parameter estimation with real, and often noisy, data. ![]() In this paper, we address structural identifiability, which concerns whether the parameters of a model can be determined from perfect input-output data, i.e., noise-free and of any time duration required. Parameter identifiability analysis for dynamical system models consisting of ordinary differential equations (ODEs) addresses the question of which unknown parameters can be determined from given input-output data. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Ĭompeting interests: The authors have declared that no competing interests exist. JDH was supported by Army ( ) YIP W911NF-15-1-0219, National Science Foundation ( ACI-1460032, and Sloan Research Fellowship ( ) BR2014-110 TR14. įunding: DJB was supported by National Science Foundation ( ACI-1440467 and National Science Foundation ( DMS-1719658. The work is made available under the Creative Commons CC0 public domain dedication.ĭata Availability: All data files are publicly available at. This is an open access article, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. Received: Accepted: NovemPublished: December 13, 2019 Several examples are used to demonstrate the new techniques.Ĭitation: Bates DJ, Hauenstein JD, Meshkat N (2019) Identifiability and numerical algebraic geometry. For unidentifiable models, we present a novel numerical differential algebra technique aimed at computing a set of algebraically independent identifiable functions. For identifiable models, we present a novel approach to compute the identifiability degree. 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 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. ![]() Unidentifiable models are models such that the unknown parameters can have an infinite 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. Identifiable models are models such that the unknown parameters can be determined to have a finite number of values given input-output data. 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.
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