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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Fast sampling from parameterised Gaussian random f
ields - Jonas Latz (Technische Universität München
)
DTSTART;TZID=Europe/London:20180216T110000
DTEND;TZID=Europe/London:20180216T130000
UID:TALK100930AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/100930
DESCRIPTION:Gaussian random fields are popular models for spat
ially varying uncertainties\, arising for instance
in geotechnical engineering\, hydrology or image
processing. A Gaussian random field is fully chara
cterised by its mean function and covariance opera
tor. In more complex models these can also be part
ially unknown. Then we need to handle a family of
Gaussian random fields indexed with hyperparameter
s. Sampling for a fixed configuration of hyperpara
meters is already very expensive\, as it requires
a Cholesky or spectral decomposition of the discre
tised covariance operator\, which is in general a
large dense matrix. Sampling from multiple configu
rations increases the total computational cost sev
erely.  \;  \; In this report we constr
uct a reduced basis surrogate for parameterised Ka
rhunen-Loè\;ve expansions - upon which our s
ampling procedure relies. The reduced basis is bui
lt using snapshots of Karhunen-Loè\;ve eigen
vectors. In particular\, we consider Matern type c
ovariance operators with unknown correlation lengt
h and standard deviation. We suggest a linearisati
on of the covariance function and describe the ass
ociated online-offline decomposition. In numerical
experiments\, we investigate the approximation er
ror of the reduced eigenpairs. As an application\,
we consider forward uncertainty propagation and B
ayesian inversion in an elliptic PDE\, where the l
og of the diffusion coefficient is a parameterised
Gaussian random field. We discretise PDE operator
s and covariance operators with finite elements. I
n the Bayesian inverse problem we employ a Markov
Chain Monte Carlo method on the reduced space to g
enerate samples from the posterior measure. All nu
merical experiments are done in 2D space with non-
separable covariance operators on finite element g
rids with tens of thousands of degrees of freedom.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:INI IT
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