- Class schedule: Tuesday, Feb. 4th, 2014, from 11:00 am to 12:00 pm
- Location: Building 9, Room 4222
- Refreshments: Pizza and Soft Drinks available @10:45 am
- Course material available at: link
Abstract
In this talk I will
explain what is uncertainty quantification and how to model uncertainties via
random variables/random fields. I will give several
examples of stochastic partial differential equations with uncertain
coefficients, uncertain computations domain, uncertain right-hand side or
boundary conditions. I will also give a short overview of the existing
numerical methods. You will learn how to
discretize such equations (via polynomial Chaos and Karhunen-Loeve expansions)
and how to solve it. I
will give link to the software package which can be used for uncertainty
quantification.
Biography
Alexander Litvinenko has
joined the Stochastic Numerics Group and SRI Uncertainty Quantification
Center
at KAUST in September 2013. Alexander is an Applied Mathematician and
Computational Scientist specializing in efficient numerical methods for
solving
stochastic PDEs, uncertainty quantification and multi-linear algebra.
He
is also involved in Bayesian update methods for solving inverse
problems.
During last 6 years he was actively participating in a large project
“Management and minimization of uncertainty in numerical aerodynamics”
between
German industry and eight German universities. Another interesting
project was
“Effective approaches and solution techniques for conditioning, robust
design
and control in the subsurface”. Results are published in numerous
publications
of Applied Math, Engineering, and Physics journals. He earned B.S.
(2000) and M.S. (2002) degrees in Mathematics at the Novosibirsk
State University in Novosibirsk, Russia. Alexander had honor to do his
PhD in a
very strong group of Prof. Hackbusch at Max-Planck-Institut fuer
Mathematik in
den Naturwissenschaften in Leipzig, Germany. His Ph.D. research
(2002-2006) focus was combination of domain decomposition methods and
hierarchical matrices for solving elliptic PDEs with jumping and
oscillatory
coefficients.From 2007-2013 he was a Postdoctoral Research Fellow at the
TU Braunschweig in
Germany where he became interested in his current research focus area of
low-rank/sparse methods for uncertainty quantification as well as
Bayesian
updating technique for multi-parametric problems. His interest spans
efficient numerical techniques, fast multi-linear algebra
algorithms, such as low-rank/sparse tensor approximations, and also
applications, such as numerical aerodynamics, multiscale problems,
subsurface
flow, optimal design and control under uncertainties and climate
prediction. His interest in methods of data analysis relates
particularly
to the building of optimal decision trees for various areas of
applications. The current area of interests is: adaptive goal-oriented Bayesian update
technique based on spectral representation. The aim is to reduce the
computational complexity both the stochastic forward problem as well as the
Bayesian update by a low-rank (sparse) tensor data approximation. The solution
of the inverse problem could be further used for optimal design of experiments
with the objective to maximize the information gain that can be obtained for a
given amount of experimental effort.