Post-graduate seminar SS 18 Graduate Seminar on Numerical Analysis
High-Dimensional Approximation and Uncertainty Quantification
First meeting: January 29, 2018, at 16:00 (c.t.) in We6 5.002
If you are interested in participating in the seminar, please register via email to Prof. Bachmayr before the first meeting.
Topics for seminar talks are in the area of high-dimensional approximation with applications to stochastic problems in uncertainty quantification. Our focus is especially on tensor product polynomial approximations and on sampling methods.
In addition to the talk of approximately 60 minutes (projector or blackboard), a written summary needs to be prepared and provided to the audience.
The precise schedule will be fixed at the beginning of the semester.
Talks can be based on one or parts of several research articles and survey papers or book chapters. The topics are not limited to the following list of suggestions and can be adjusted according to the interests of participants. Please inform Prof. Bachmayr at the first meeting, or ideally via email before the first meeting, about your preferred topics.
- Basic convergence analysis of sparse polynomial approximations in high dimensions [CDS11], [CD15]
- Frame representations of Gaussian random fields [LP09]
- Stochastic collocation methods [BNT07], [BNT10], [EST16], [TJWG15]
- Optimal weighted least squares methods [CDL13], [NJZ16], [JNZ17], [CM16], [GNZY17]
- Compressive sensing approximations [RS17], [A17], [CDTW17]
- Quasi-Monte Carlo methods: basics [N92], [DKS13]; applications to parameter-dependent PDEs [KN16], [KN16]
- Markov chain Monte Carlo: basics [L04], [MNR12]; application on Hilbert spaces [CRSW13], [RS16] (arXiv), [BGLFS17]
- Multilevel Markov chain Monte Carlo [DKST15]
- Importance sampling [APSM17]