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Validation by Monte Carlo sampling of experimental observation functionals
Author(s) -
Taddei Tommaso,
Penn James D,
Patera Anthony T
Publication year - 2017
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5599
Subject(s) - monte carlo method , variance reduction , sampling (signal processing) , confidence interval , algorithm , variance (accounting) , mathematics , set (abstract data type) , computer science , mathematical optimization , statistical physics , statistics , physics , accounting , filter (signal processing) , business , computer vision , programming language
Summary We present and analyze a validation procedure for a given state estimate u ⋆ of the true field u true based on Monte Carlo sampling of experimental observation functionals. Our method provides, given a set of N possibly noisy local experimental observation functionals over the spatial domain Ω, confidence intervals for the L 2 (Ω) error in state and the error in L 2 (Ω) outputs. For L 2 (Ω) outputs, our approach also provides a confidence interval for the output itself, which can be used to improve the initial output estimate based on u ⋆ . Our approach implicitly takes advantage of variance reduction, through the proximity of u ⋆ to u true , to provide tight confidence intervals even for modest values of N . We present results for a synthetic model problem to illustrate the elements of the methodology and confirm the numerical properties suggested by the theory. Finally, we consider an experimental thermal patch configuration to demonstrate the applicability of our approach to real physical systems.