Algorithm to Find New Identifiable Reparameterizations of Parameteric Rational ODE Models

• 成果类型: Article
• 署名作者: Meshkat, Nicolette; Ovchinnikov, Alexey; Scanlon, Thomas
• 署名单位: Santa Clara University; City University of New York (CUNY) System; City University of New York (CUNY) System; University of California System; University of California Berkeley
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3565058
• 发表日期: 2025
• 页码: 6688-6703
• 关键词: mathematical models; Biological system modeling; lead; data models; Software algorithms; Algebra; POLYNOMIALS; Numerical models; training; observability; Differential algebra; input-output (IO) equations; parameter identifiability; parameteric ODE models

摘要

Structural identifiability concerns the question of which unknown parameters of a model can be recovered from (perfect) input-output (IO) data. If all of the parameters of a model can be recovered from data, then the model is said to be identifiable. However, in many models, there are parameters that can take on an infinite number of values but yield the same input-output data. In this case, those parameters and the model are called unidentifiable. The question is then what to do with an unidentifiable model. One can try to add more input-output data or decrease the number of unknown parameters, if experimentally feasible, or try to find a reparameterization to make the model identifiable. In this article, we take the latter approach. While existing approaches to find identifiable reparameterizations were limited to scaling reparameterizations or were not guaranteed to find a globally identifiable reparameterization even if it exists, we significantly broaden the class of models for which we can find a globally identifiable model with the same input-output behavior as the original one. We also prove that, for linear models, a globally identifiable reparameterization always exists and shows that, for a certain class of linear compartmental models, with and without inputs, an explicit reparameterization formula exists. We illustrate our method on several examples and provide detailed analysis in the Supplementary Material on github.