Input-output equivalence and identifiability: some simple generalizations of the differential algebra approach

TL;DR

This paper explores simple generalizations of the differential algebra approach to input-output equivalence and identifiability, providing practical methods for analyzing complex models and extending existing techniques.

Contribution

It introduces a straightforward observation linking input-output equivalence to identifiability, with implications for model analysis, reduction, and equation generation.

Findings

Input-output equivalence can determine identifiability.

Extensions to non-first order ODE models are possible.

Methods for generating input-output equations are expanded.

Abstract

In this paper, we give an overview of the differential algebra approach to identifiability, and then note a very simple observation about input-output equivalence and identifiability, that describes the identifiability equivalence between input-output equivalent models. We then give several simple consequences of this observation that can be useful in showing identifiability, including examining non-first order ODE models, nondimensionalization and rescaling, model reducibility, and a modular approach to evaluating identifiability. We also examine how input-output equivalence can allow us to generate input output equations in the differential algebra approach through a wider range of methods (e.g. substitution and differential or standard Groebner basis approaches).