Oberseminar Wissenschaftliches Rechnen (Prof. Georg Stadler, Courant Institute of Mathematical Sciences New York University)

Abstract:

We study optimal control of PDEs under uncertainty, where the state variable is subject to joint
chance constraints.
While we seek deterministic controls, the corresponding states are probabilistic due to uncertainty
in the governing equation. Joint chance constraints require that realizations of the state satisfy
pointwise bounds with a given probability.
We consider linear and bilinear PDEs with in nite-dimensional uncertain parameters. We show
that properties of the governing equations reduce the e ective random space dimension and show
how this can be used to approximate the chance probabilities. We use a spherical-radial decom-
position of Gaussian random variables, which allows not only computation of the joint chance
probabilities, but also their derivatives.
In numerical examples we compare Monte Carlo and quasi Monte Carlo sampling methods and
study the convergence as we increase the number of samples, and the sensitivity of these proba-
bilities to the discretization of the physical space and to the truncation of expansions in random
space.
This is joint work with Florian Wechsung (NYU) and Rene Henrion (WIAS Berlin).

via Zoom video conference (request the Zoom link from frank.werner@mathematik.uni-wuerzburg.de)
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