New elimination algorithms for differential dynamical systems

Differential parametric dynamical systems appear in many applications in modeling and control theory. Frequently, the task is to compute the minimal differential equation satisfied by experimentally observed data, which is an important special case of the more general differential elimination problem. In this talk, we present how to tackle this computation in an evaluation interpolation framework, gaining efficiency over classical methods by avoiding intermediate expression swell. First, we provide explicit bounds on the Newton polytope of the minimal equation in terms of the degrees of the dynamical system, and prove these bounds to be sharp in more than half the cases. Second, we show how convex geometry can be further exploited in the sparse setting. Finally, we show how to use the structure of input dynamical systems by designing an algorithm that, through a careful choice of evaluation points, reduces the problem to solving a block-triangular linear system. Based on joint work with Gleb Pogudin, Rafael Mohr and Maxime Despréaux.