Alternative to Ritt's Pseudodivision for finding the input-output equations in algebraic structural identifiability analysis

TL;DR

This paper introduces a simplified algorithm using Gr"obner Bases as an alternative to Ritt's pseudodivision for deriving input-output equations in algebraic structural identifiability analysis, improving efficiency and reducing derivative requirements.

Contribution

The paper proposes a novel Gr"obner Bases-based method as a simpler, more efficient alternative to Ritt's pseudodivision for finding input-output equations in identifiability analysis.

Findings

The new algorithm is effective on biosystem models.

It reduces the derivative order needed in calculations.

The method is mathematically proven to be valid.

Abstract

Differential algebra approaches to structural identifiability analysis of a dynamic system model in many instances heavily depend upon Ritt's pseudodivision at an early step in analysis. The pseudodivision algorithm is used to find the characteristic set, of which a subset, the input-output equations, is used for identifiability analysis. A simpler algorithm is proposed for this step, using Gr\"obner Bases, along with a proof of the method that includes a reduced upper bound on derivative requirements. Efficacy of the new algorithm is illustrated with two biosystem model examples.