- Date & Time: Thursday, May 19th, 2016, 2:00 p.m.
- Location: Building 2 – Rm. 5220
Abstract:
Most problems in engineering
and natural sciences involve parametric equations in which the
parameters are
not known exactly due to measurement errors, lack of measurement data,
or even
intrinsic variability. In such problems, one objective is to compute
point or
aggregate values, called "quantities of interest". In such a setting,
the parametric equations must be accurately solved for
multiple values of the parameters to explore the dependence of the
quantities
of interest on these parameters, using various so-called "sampling
methods". In almost all cases, the parametric equations cannot be solved
exactly and suitable numerical discretization methods are required. The
high
computational complexity of these numerical methods coupled with the
fact that
the parametric equations must be solved for multiple values of the
parameters
make UQ problems computationally intensive, particularly when the
dimensionality of the underlying problem and/or the parameter space is
high. This thesis includes five published articles and one
soon-to-published one.
These articles are concerned with optimizing existing sampling methods,
namely
Multilevel Monte Carlo, and developing novel methods for high
dimensional
problems, namely Multi-index Monte Carlo and Multi-index Stochastic
Collocation. Assuming sufficient regularity of the underlying problem,
the
order of the computational complexity of these novel methods is, at
worst up to
a logarithmic factor, independent of the dimensionality of the problem.
The
articles also explore different applications, including an elliptic
partial
differential equation that models the flow of a fluid through a porous
medium
with random permeability and a stochastic particle system that models a
system
of coupled oscillators.
Biography: Abdul-Lateef Haji-Ali
was born in Damascus, Syria, in 1988. He received the B.E. degree in
Informatics Engineering at the Arab International University in Damascus in
2005. In 2010, he joined KAUST for a M.S. degree in applied mathematics under
the supervision of Prof. Raul Tempone. In 2012, after receiving the M.S.
degree, he then continued his academic career as a PhD student in KAUST under
the supervision of Prof. Temone. Haji-Ali's research interests are in the development and analysis of efficient
numerical methods for uncertainty quantification. More specifically, he is
interested in multilevel and sparse grid methods and their applications in high
or infinite dimensional problems. He is also interested in particle systems and
their applications in chemistry, physics and social sciences.
https://sri-uq.kaust.edu.sa/Pages/HajiAli.aspx