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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Multifidelity Monte Carlo estimation with adaptive
low-fidelity models - Benjamin Peherstorfer (Univ
ersity of Wisconsin-Madison)
DTSTART;TZID=Europe/London:20180309T110000
DTEND;TZID=Europe/London:20180309T114500
UID:TALK102127AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/102127
DESCRIPTION:Multifidelity Monte Carlo (MFMC) estimation combin
es low- and high-fidelity models to speedup the es
timation of statistics of the high-fidelity model
outputs. MFMC optimally samples the low- and high-
fidelity models such that the MFMC estimator has m
inimal mean-squared error for a given computationa
l budget. In the setup of MFMC\, the low-fidelity
models are static\, i.e.\, they are given and fixe
d and cannot be changed and adapted. We introduce
the adaptive MFMC (AMFMC) method that splits the c
omputational budget between adapting the low-fidel
ity models to improve their approximation quality
and sampling the low- and high-fidelity models to
reduce the mean-squared error of the estimator. Ou
r AMFMC approach derives the quasi-optimal balance
between adaptation and sampling in the sense that
our approach minimizes an upper bound of the mean
-squared error\, instead of the error directly. We
show that the quasi-optimal number of adaptations
of the low-fidelity models is bounded even in the
limit case that an infinite budget is available.
This shows that adapting low-fidelity models in MF
MC beyond a certain approximation accuracy is unne
cessary and can even be wasteful. Our AMFMC approa
ch trades-off adaptation and sampling and so avoid
s over-adaptation of the low-fidelity models. Besi
des the costs of adapting low-fidelity models\, ou
r AMFMC approach can also take into account the co
sts of the initial construction of the low-fidelit
y models (``offline costs'\;'\;)\, which is
critical if low-fidelity models are computationall
y expensive to build such as reduced models and da
ta-fit surrogate models. Numerical results demonst
rate that our adaptive approach can achieve orders
of magnitude speedups compared to MFMC estimators
with static low-fidelity models and compared to M
onte Carlo estimators that use the high-fidelity m
odel alone.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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