Detail Seite Kalender

Speaker:
Dr. Jan Bartsch

On 3^rd December 2024 at 15:15, Dr. Jan Bartsch from the University of Konstanz will give a talk.

Abstract: Natural processes inherit noise and uncertainties and are therefore often modeled using stochastic differential equations (SDEs).
Such equations consist of a deterministic part and a stochastic part. The latter one is usually modeled by Brownian motions or Poisson processes, according to whether diffusion or jumps need to be represented.
These SDEs usually include several parameters that must be carefully calibrated to align with experimental data, ensuring the accuracy and reliability of the model.In other cases, the challenge lies in determining optimal external forces to guide the trajectories of the SDEs toward a desired outcome on average.
In this talk, we introduce an adjoint-based optimization method within a microscopic framework. We derive the optimality conditions for both the "discretize-then-optimize" and "optimize-then-discretize" approaches, focusing on the numerical solution of the former.
Next, we extend the analysis to the mesoscopic level by introducing a probability density function, thereby elevating the problem to a partial differential equation (PDE) context. In this setting, we propose a strategy for deriving feedback-like controls that effectively manipulate the evolution of SDEs with jumps, stabilizing them on a desired orbit in phase space.
Finally, we present numerical experiments that demonstrate the effectiveness of the proposed control strategy.