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CATEGORIES:ps583's list
SUMMARY:Active Subspace Methods in Theory and Practice - D
r. Paul Constantine\, Colorado School of Mines
DTSTART;TZID=Europe/London:20140522T130000
DTEND;TZID=Europe/London:20140522T140000
UID:TALK52645AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/52645
DESCRIPTION:*Abstract:*\nScience and engineering models typica
lly contain multiple parameters representing input
data---e.g.\, boundary conditions or material pro
perties. The map from model inputs to model output
s can be viewed as a multivariate function. One ma
y naturally be interested in how the function chan
ges as inputs are varied. However\, if computing t
he model output is expensive given a set of inputs
\, then exploring the high-dimensional input space
is infeasible. Such issues arise in the study of
uncertainty quantification\, where uncertainty in
the inputs begets uncertainty in model predictions
.\n\nFortunately\, many practical models with high
-dimensional inputs vary primarily along only a fe
w directions in the space of inputs. I will descri
be a method for detecting and exploiting these dir
ections of variability to construct a response sur
face on a low-dimensional linear subspace of the f
ull input space\; detection is accomplished throug
h analysis of the gradient of the model output wit
h respect to the inputs\, and the subspace is defi
ned by a projection. I will show error bounds for
the low-dimensional approximation that motivate co
mputational heuristics for building a kriging resp
onse surface on the subspace. As a demonstration\,
I will apply the method to a nonlinear heat trans
fer model on a turbine blade\, where a 250-paramet
er model for the heat flux represents uncertain tr
ansition to turbulence of the flow field. I will a
lso discuss the range of existing applications of
the method---including the motivating application
from Stanford's DOE PSAAP center---and the future
research challenges.\n\n*Bio:*\nPaul Constantine i
s the Ben L. Fryrear Assistant Professor of Applie
d Mathematics and Statistics at Colorado School of
Mines. He received his Ph.D. in 2009 from Stanfor
d's Institute for Computational and Mathematical E
ngineering and was awarded the John von Neumann Re
search Fellowship at Sandia National Labs. Paul's
interests include methods for dimension reduction
and reduced order modeling in the context of uncer
tainty quantification. (inside.mines.edu/~pconstan
)
LOCATION:Lecture Theatres - LT1\, Cambridge University Depa
rtment of Engineering\, Inglis Building
CONTACT:Pranay Seshadri
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