Praktikum am Fachbereich Mathematik - Januar 2022
Schülerinnen und Schüler der 9. bis 12. Klasse absolvieren ihr zweiwöchiges Schulpraktikum am Fachbereich Mathematik an der TU Kaiserslautern. Vom 17. bis 28. Januar haben sie die Möglichkeit, spannende Einblicke in die Welt der Mathematik zu bekommen. Neben einem Besuch von Vorlesungen lernen sie mathematische Konzepte kennen, die ihnen in Vorträgen und Workshops von Mitarbeitern und Mitarbeiterinnen des Fachbereichs Mathematik nähergebracht werden. Außerdem arbeiten sie eigenständig an Projekten, um das neu erworbene Wissen anzuwenden.
Die Praktikumsinhalte werden vom KOMMS sowie den Arbeitsgruppen des Fachbereichs Mathematik gestaltet.
Informationen zum Praktikum am Fachbereich Mathematik können hier nachgelesen werden.
Reference
Emil Løvbak, Monte Carlo Adjoints with Reversible Random Number Generators
Title: Monte Carlo Adjoints with Reversible Random Number Generators
Abstract:
Kinetic equations, modeling particles in a position-velocity phase space, have many high-impact application areas, including nuclear fusion research and radiation therapy. In these applications, particle-based Monte Carlo methods are often used to simulate the kinetic models. These methods solve the PDE by tracing sample particle trajectories through physical space in such a way that their ensemble distribution in phase space corresponds to the solution of the PDE. One then uses these trajectories as samples to compute quantities such as the particles’ mass density, momentum, and energy as a function of space and time. These methods have the advantage of not constructing grids in the high-dimensional phase space; however, they produce results subject to a stochastic sampling error.
In this talk, I consider PDE-constrained optimization problems, where the PDE is solved with a Monte Carlo solver. Here, gradients are computed through a discrete adjoint approach. To ensure convergence, it is imperative that the same stochastic paths are used when solving the original PDE to evaluate the objective functional and the adjoint PDE to compute gradients. I present an approach that leverages reversible random number generators to ensure path consistency, despite the adjoint PDE running backward in time. I first present this strategy with a didactic example using a 1D diffusion equation and then present some results from a fusion plasma-edge simulation case.
How to join online
You can join online via Zoom, using the following link:
https://uni-kl-de.zoom-x.de/j/69269239534?pwd=Z9UOzMpkhMjrxVhll3d49sNHFe9Fd1.1
Referent: Dr. Emil Løvbak, Computational Science and Mathematical Methods Group at SCC, Karlsruhe Institute of Technology (KIT)
Zeit: 14:30 Uhr
Ort: Hybrid (Room 32-349 and via Zoom)