Uncertainty Quantification and the Numerical Solution of Random Differential Equations

  • Oliver Ernst (TU Chemnitz)
A3 01 (Sophus-Lie room)


Uncertainty Quantification (UQ) is a rapidly developing field within applied mathematics and computational science concerned with identifying, modeling and quantifying the myriad uncertainties arising in computational models, specifically those involving differential equations. Besides discretization error and rounding error, which by now are well understood and can be managed, uncertainties in problem specifications such as coefficient functions, source and boundary data or domain geometry can often dominate the previously mentioned uncertainty and error sources.

In this talk we discuss the prevalent model problem in UQ, stationary diffusion with an uncertain diffusion coefficient which is modeled as a lognormal random field. We emphasize uncertainty modeling aspects in connection with a groundwater contamination problem leading to such a random diffusion equation and present numerical approaches for approximating its solution. In particular, the numerical representation of rough lognormal fields by Karhunen-Loève expansion raises interesting questions of stochastic homogenization. Continuing with the groundwater application, we also indicate how observational data can be incorporated to reduce uncertainty by large-scale Bayesian inference.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of This Seminar

  • Mar 12, 2024 tba with Theresa Simon
  • Mar 26, 2024 tba with Phan Thành Nam
  • Mar 26, 2024 tba with Dominik Schmid
  • May 7, 2024 tba with Manuel Gnann
  • May 14, 2024 tba with Barbara Verfürth
  • May 14, 2024 tba with Lisa Hartung
  • Jun 25, 2024 tba with Paul Dario
  • Jul 16, 2024 tba with Michael Loss