Speaker: Yulia Mukhina
Abstract: Differential dynamical systems appear in many applications in modeling and control theory. Frequently, for such dynamical systems, the task is to compute the minimal differential equation satisfied by a chosen coordinate. This task arises in particular in applications where only part of the solution data can be experimentally observed. As such, it is an important special case of more general differential elimination problems.
We will observe two approaches to tackle the computation of such a minimal equation in the evaluation-interpolation fashion.
First, we will present a new result, which provides explicit bounding hyperplanes for the Newton polytope of such a minimal equation. The obtained bounds are based on the degrees of a given dynamical system and are proven to be sharp in “more than half the cases”. We demonstrate an evaluation-interpolation algorithm for computing minimal differential equations for dynamical systems
resulting from these bounds.
Second, we will discuss a new approach of computing so-called mixed fiber polytopes in the problem of polynomial elimination. We demonstrate the increase in practical performance of our algorithm compared to existing methods and discuss an application of our work to differential elimination.
This is joint work with Gleb Pogudin and Rafael Mohr.