Seminar 7.12.2023: Karolina Benkova

[quittner]

Seminár z kvalitatívnej teórie diferenciálnych rovníc
Seminar on Qualitative Theory of Differential Equations

Thursday 7.12.2023 at 14:00 Lecture room M-223

Karolína Benková (The University of Edinburgh):
Numerical Solvers for PDE-constrained optimization in mathematical biology

Abstract:
Many of the mechanisms governing pattern formation in embryonic development
have been identified and described by systems of PDEs.
As some of the parameters or functions in these PDEs may be impossible
to measure in laboratory conditions, we can use optimal control theory,
in particular PDE-constrained optimization, to identify them.
Given experimental data as the desired states, we can pose a minimisation
problem so that the equations in the constraints evolve the state as close
as possible to the desired state while also minimising the amount of control
(or external biological mechanism) applied. In this talk, we will present
a numerical solver for a problem with reaction-diffusion PDEs as constraints,
by making use of a preconditioner for the large-scale saddle-point problems
that arise. Moreover, we will discuss how to solve the numerical problems
that arise when the PDEs are chemotaxis equations, present the flux-corrected
transport technique, and outline how this could be applied
within the optimization setting.