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. © 2020 Wiley Periodicals LLC

Biological processes are often modeled by ordinary differential equations with unknown parameters. The unknown parameters are usually estimated from experimental data. In some cases, due to the structure of the model, this estimation problem does not have a unique solution even in the case of continuous noise-free data. It is therefore desirable to check the uniqueness a priori before carrying out actual experiment. We present a new software SIAN (Structural Identifiability ANalyser) that does this. Our software can tackle problems that could not be tackled by previously developed packages. * All the results presented in the rest of the section are computed with probability of correctness p = 0.99.