Identifiable specializations for ODE models

TL;DR

This paper proves that any dynamical system model can be reparametrized to be locally identifiable through a partial specialization of parameters, maintaining the model's structure and providing an algorithmic approach.

Contribution

It introduces a constructive proof that guarantees the existence of a locally identifiable reparameterization for any model, extending beyond linear cases.

Findings

Existence of locally identifiable models via parameter specialization.

Reparameterizations preserve the monomial structure of the original model.

An algorithmic method for reparameterization is provided and illustrated.

Abstract

The parameter identifiability problem for a dynamical system is to determine whether the parameters of the system can be found from data for the outputs of the system. Verifying whether the parameters are identifiable is a necessary first step before a meaningful parameter estimation can take place. Non-identifiability occurs in practical models. To reparametrize a model to achieve identifiability is a challenge. The existing approaches have been shown to be useful for many important examples. However, these approaches are either limited to linear models and scaling parametrizations or are not guaranteed to find a reparametrization even if it exists. In the present paper, we prove that there always exists a locally identifiable model with the same input-output behaviour as the original one obtained from a given one by a partial specialization of the parameters. As an extra feature of our approach, the resulting (at least) locally identifiable reparameterization has the same shape: the monomials in the new state variables in the new model are formed in the same way as in the original model. Furthermore, we give a sufficient observability condition for the existence of a state space transformation from the original model to the new one. Our proof is constructive and can be translated to an algorithm, which we illustrate by several examples.