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SUMMARY:Multifidelity Monte Carlo estimation with adaptive low-fidelity mo
 dels - Benjamin Peherstorfer (University of Wisconsin-Madison)
DTSTART:20180309T110000Z
DTEND:20180309T114500Z
UID:TALK102256@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Multifidelity Monte Carlo (MFMC) estimation combines low- and 
 high-fidelity models to speedup the estimation of statistics of the high-f
 idelity model outputs. MFMC optimally samples the low- and high-fidelity m
 odels such that the MFMC estimator has minimal mean-squared error for a gi
 ven computational budget. In the setup of MFMC\, the low-fidelity models a
 re static\, i.e.\, they are given and fixed and cannot be changed and adap
 ted. We introduce the adaptive MFMC (AMFMC) method that splits the computa
 tional budget between adapting the low-fidelity models to improve their ap
 proximation quality and sampling the low- and high-fidelity models to redu
 ce the mean-squared error of the estimator. Our AMFMC approach derives the
  quasi-optimal balance between adaptation and sampling in the sense that o
 ur approach minimizes an upper bound of the mean-squared error\, instead o
 f 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 infi
 nite budget is available. This shows that adapting low-fidelity models in 
 MFMC beyond a certain approximation accuracy is unnecessary and can even b
 e wasteful. Our AMFMC approach trades-off adaptation and sampling and so a
 voids over-adaptation of the low-fidelity models. Besides the costs of ada
 pting low-fidelity models\, our AMFMC approach can also take into account 
 the costs of the initial construction of the low-fidelity models (``offlin
 e costs&#39\;&#39\;)\, which is critical if low-fidelity models are comput
 ationally expensive to build such as reduced models and data-fit surrogate
  models. Numerical results demonstrate that our adaptive approach can achi
 eve orders of magnitude speedups compared to MFMC estimators with static l
 ow-fidelity models and compared to Monte Carlo estimators that use the hig
 h-fidelity model alone.
LOCATION:Seminar Room 1\, Newton Institute
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