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SUMMARY:Uncertainty Quantification with Multi-Level and Multi-Index method
 s - Raul Fidel Tempone (King Abdullah University of Science and Technology
  (KAUST))
DTSTART:20180208T143000Z
DTEND:20180208T153000Z
UID:TALK100222@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We start by recalling the Monte Carlo and Multi-level Monte Ca
 rlo (MLMC) methods for computing statistics of the solution of a Partial D
 ifferential Equation with random data. Then\, we present the Multi-Index M
 onte Carlo (MIMC) and Multi-Index Stochastic Collocation  (MISC) methods. 
 MIMC is both a stochastic version of the combination technique introduced 
 by Zenger\, Griebel and collaborators and an extension of the MLMC method 
 first described by Heinrich and Giles. Instead of using first-order differ
 ences as in MLMC\, MIMC uses mixed differences to reduce the variance of t
 he hierarchical differences dramatically\, thus yielding improved converge
 nce rates.  MISC is a deterministic combination technique that also uses m
 ixed differences to achieve better complexity than MIMC\, provided enough 
 regularity. During the presentation\, we will showcase the behavior of the
  numerical methods in applications\, some of them arising in the context o
 f Regression based Surrogates and Optimal Experimental Design.  Coauthors:
  J. Beck\, L. Espath (KAUST)\, A.-L. Haji-Ali (Oxford)\, Q. Long (UT)\, F.
  Nobile (EPFL)\,  M. Scavino (UdelaR)\, L. Tamellini (IMATI)\, S. Wolfers 
 (KAUST)   Webpages:  https://stochastic_numerics.kaust.edu.sa https://sri-
 uq.kaust.edu.sa
LOCATION:Seminar Room 1\, Newton Institute
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