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SUMMARY:Active Subspace Methods in Theory and Practice - Dr. Paul Constant
 ine\, Colorado School of Mines
DTSTART:20140522T120000Z
DTEND:20140522T130000Z
UID:TALK52645@talks.cam.ac.uk
CONTACT:Pranay Seshadri
DESCRIPTION:*Abstract:*\nScience and engineering models typically contain 
 multiple parameters representing input data---e.g.\, boundary conditions o
 r material properties. The map from model inputs to model outputs can be v
 iewed as a multivariate function. One may naturally be interested in how t
 he function changes as inputs are varied. However\, if computing the model
  output is expensive given a set of inputs\, then exploring the high-dimen
 sional input space is infeasible. Such issues arise in the study of uncert
 ainty quantification\, where uncertainty in the inputs begets uncertainty 
 in model predictions.\n\nFortunately\, many practical models with high-dim
 ensional inputs vary primarily along only a few directions in the space of
  inputs. I will describe a method for detecting and exploiting these direc
 tions of variability to construct a response surface on a low-dimensional 
 linear subspace of the full input space\; detection is accomplished throug
 h analysis of the gradient of the model output with respect to the inputs\
 , and the subspace is defined by a projection. I will show error bounds fo
 r the low-dimensional approximation that motivate computational heuristics
  for building a kriging response surface on the subspace. As a demonstrati
 on\, I will apply the method to a nonlinear heat transfer model on a turbi
 ne blade\, where a 250-parameter model for the heat flux represents uncert
 ain transition to turbulence of the flow field. I will also discuss the ra
 nge of existing applications of the method---including the motivating appl
 ication from Stanford's DOE PSAAP center---and the future research challen
 ges.\n\n*Bio:*\nPaul Constantine is the Ben L. Fryrear Assistant Professor
  of Applied Mathematics and Statistics at Colorado School of Mines. He rec
 eived his Ph.D. in 2009 from Stanford's Institute for Computational and Ma
 thematical Engineering and was awarded the John von Neumann Research Fello
 wship at Sandia National Labs. Paul's interests include methods for dimens
 ion reduction and reduced order modeling in the context of uncertainty qua
 ntification. (inside.mines.edu/~pconstan)
LOCATION:Lecture Theatres - LT1\, Cambridge University Department of Engin
 eering\, Inglis Building
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