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SUMMARY:Dimensionality reduction and surrogate modelling for high-dimensio
 nal UQ problems - Bruno Sudret (ETH Zürich)
DTSTART:20180306T094500Z
DTEND:20180306T103000Z
UID:TALK101860@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In order to predict the behaviour of complex engineering syste
 ms (nuclear power plants\, aircraft\, infrastructure networks\, etc.)\, an
 alysts nowadays develop high-fidelity computational models that try and ca
 pture detailed physics. A single run of such simulators can take minutes t
 o hours even on the most advanced HPC architectures. In the context of unc
 ertainty quantification\, methods based on Monte Carlo simulation are simp
 ly not affordable. This has led to the rapid development of surrogate mode
 lling techniques in the last decade\, e.g. polynomial chaos expansions\, l
 ow-rank tensor representations\, Kriging (a.k.a Gaussian process models) a
 mong others. Surrogate models have proven remarkable efficiency in the cas
 e of moderate dimensionality (e.g. tens to a hundred of inputs). In the ca
 se of high-dimensional problems (hundreds to thousands of inputs)\, or whe
 n the input is cast as time series\, 2D maps\, etc.\, the classical set-up
  of surrogate modelling does not apply straightforwardly. Usually\, a pre-
 processing of the data is carried out to reduce this dimensionality\, befo
 re a surrogate is constructed. In this talk\, we show that the sequential 
 use of compression algorithms (for dimensionality reduction (DR)\, e.g. ke
 rnel principal component analysis) and surrogate modelling (SM) is subopti
 mal. Instead\, we propose a new general-purpose framework that cast the tw
 o sub-problems into a single DRSM optimization. In this set-up\, the param
 eters of the DR step are selected so that as to maximize the quality of th
 e subsequent surrogate model. The framework is versatile in the sense that
  the techniques used for DR and for SM can be freely selected and combined
 . Moreover\, the method is purely data-driven. The proposed approach is il
 lustrated on different engineering problems including 1D and 2D elliptical
  SPDEs and earthquake engineering applications.
LOCATION:Seminar Room 1\, Newton Institute
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