A systematic approach for doing an \textit{a priori} identifiability study of dynamical nonlinear models

TL;DR

This paper introduces an automated symbolic computation method to assess and improve the identifiability of parameters in nonlinear dynamical models, considering parameter constraints and aiding in model analysis.

Contribution

It presents a systematic, algebraic approach for a priori identifiability analysis of nonlinear models, incorporating parameter constraints and automating the process.

Findings

Successfully applied to models with up to 12 parameters

Automates the detection of non-identifiable parameters

Provides a practical tool for model identifiability analysis

Abstract

This paper presents a method for investigating, through an automatic procedure, the (lack of) identifiability of parametrized dynamical models. This method takes into account constraints on parameters and returns parameters whose estimations make the model identifiable. It is based on i) an equivalence between an extension of the notion of identifiability and the existence of solutions of algebraic systems, ii) the use of symbolic computations for testing their existence. This method is described in details and is applied to two examples, of which the last one involves 12 parameters.