Event Information:

• Tue

  08

  Jul

  2025

  SC Seminar: Emil Løvbak

  14:30 Hybrid (Room 32-349 and via Zoom)

  Dr. Emil Løvbak, Computational Science and Mathematical Methods Group at SCC, Karlsruhe Institute of Technology (KIT)

  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