At this colloquium, we are happy to welcome:

Upanshu Sharma

Soft constraints in Langevin dynamics

Sampling probability measures on submanifolds is an important task in molecular dynamics. This is typically achieved by adding soft constraints to a diffusion process (which corresponds to a drift-diffusion PDE). In this talk, I will discuss two constraints for the so-called Langevin dynamics (which corresponds to the kinetic Fokker-Planck equation) and derive the soft-constrained limits. This is joint work with Lara Neureither and Carsten Hartmann.

Philipp Guth

Quasi-Monte Carlo integration for feedback control under uncertainty

A control in feedback form is derived for linear quadratic, time-invariant optimal control problems subject to parabolic partial differential equations with coefficients depending on a countably infinite number of uncertain parameters. It is shown that the Riccati-based feedback operator depends analytically on the parameters provided that the system operator depends analytically on the parameters, as is the case, for instance, in diffusion problems when the diffusion coefficient is parameterized by a Karhunen--Loève expansion. These novel parametric regularity results allow the application of quasi-Monte Carlo (QMC) methods to efficiently compute an a-priori chosen feedback law based on the expected value. Moreover, under moderate assumptions on the input random field, QMC methods achieve superior error rates compared to ordinary Monte Carlo methods, independently of the stochastic dimension of the problem.