Gleb Pogudin

Hoon Hong, Alexey Ovchinnikov, Gleb Pogudin et al.

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 experiments. 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.

Ilia Ilmer, Alexey Ovchinnikov, Gleb Pogudin et al.

Structural global parameter identifiability indicates whether one can determine a parameter's value from given inputs and outputs in the absence of noise. If a given model has parameters for which there may be infinitely many values, such parameters are called non-identifiable. We present a procedure for accelerating a global identifiability query by eliminating algebraically independent non-identifiable parameters. Our proposed approach significantly improves performance across different computer algebra frameworks.

Yulia Mukhina, Gleb Pogudin

For a polynomial dynamical system, we study the problem of computing the minimal differential equation satisfied by a chosen coordinate (in other words, projecting the system on the coordinate). This problem can be viewed as a special case of the general elimination problem for systems of differential equations and appears in applications to modeling and control. We give a bound for the Newton polytope of such minimal equation. Our bound depends on the dimension of the model and the degrees $d$ and $D$ of the polynomials defining the dynamics of the chosen coordinate and the remaining coordinates, respectively. We show that our bound is sharp if $d \leqslant D$ or the model is planar. We further use this bound to design an algorithm for computing the minimal equation following the evaluation-interpolation paradigm. We demonstrate that our implementation of the algorithm can tackle problems which are out of reach for the state-of-the-art software for differential elimination.