Global Identifiability of Differential Models

TL;DR

This paper introduces a new algebraic and randomized algorithm, implemented in software, to determine the global identifiability of parameters in differential equation models, enabling analysis of previously intractable problems.

Contribution

It provides the first rigorous algebraic criterion and a probabilistic algorithm for global identifiability, along with accessible software implementation.

Findings

The algorithm can decide global identifiability efficiently.

Randomization improves computational performance.

Software SIAN is publicly available for practical use.

Abstract

Many real-world processes and phenomena are modeled using systems of ordinary differential equations with parameters. Given such a system, we say that a parameter is globally identifiable if it can be uniquely recovered from input and output data. The main contribution of this paper is to provide theory, an algorithm, and software for deciding global identifiability. First, we rigorously derive an algebraic criterion for global identifiability (this is an analytic property), which yields a deterministic algorithm. Second, we improve the efficiency by randomizing the algorithm while guaranteeing the probability of correctness. With our new algorithm, we can tackle problems that could not be tackled before. A software based on the algorithm (called SIAN) is available at https://github.com/pogudingleb/SIAN.