Input-Output Equations and Identifiability of Linear ODE Models

• 成果类型: Article
• 署名作者: Ovchinnikov, Alexey; Pogudin, Gleb; Thompson, Peter
• 署名单位: City University of New York (CUNY) System; City University of New York (CUNY) System; New York University; HSE University (National Research University Higher School of Economics); Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Linkoping University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3145571
• 发表日期: 2023
• 页码: 812-824
• 关键词: mathematical models; Biological system modeling; Transfer functions; data models; computer science; computational modeling; Analytical models; Identifiable functions; input-output (IO) equations; linear compartment models; structural parameter identifiability

摘要

Structural identifiability is a property of a differential model with parameters that allows for the parameters to be determined from the model equations in the absence of noise. The method of input-output (IO) equations is one method for verifying structural identifiability. This method stands out in its importance because the additional insights it provides can be used to analyze and improve models. However, its complete theoretical grounds and applicability are still to be established. A subtlety and key for this method to work correctly is knowing whether the coefficients of these equations are identifiable. In this article, to address this, we prove identifiability of the coefficients of IO equations for types of differential models that often appear in practice, such as linear models with one output and linear compartment models in which, from each compartment, one can reach either a leak or an input. This shows that checking identifiability via IO equations for these models is legitimate, and as we prove, that the field of identifiable functions is generated by the coefficients of the IO equations. Finally, we exploit a connection between IO equations and the transfer function matrix to show that, for a linear compartment model with an input and strongly connected graph, the field of all identifiable functions is generated by the coefficients of the transfer function matrix even if the initial conditions are generic.