@inproceedings{6298beea1fde49cf9ce2c9ae02c8b663,

title = "Probabilistic error bounds for reduced order modeling",

abstract = "Reduced order modeling has proven to be an effective tool when repeated execution of reactor analysis codes is required. ROM operates on the assumption that the intrinsic dimensionality of the associated reactor physics models is sufficiently small when compared to the nominal dimensionality of the input and output data streams. By employing a truncation technique with roots in linear algebra matrix decomposition theory, ROM effectively discards all components of the input and output data that have negligible impact on reactor attributes of interest. This manuscript introduces a mathematical approach to quantify the errors resulting from the discarded ROM components. As supported by numerical experiments, the introduced analysis proves that the contribution of the discarded components could be upper-bounded with an overwhelmingly high probability. The reverse of this statement implies that the ROM algorithm can self-adapt to determine the level of the reduction needed such that the maximum resulting reduction error is below a given tolerance limit that is set by the user.",

keywords = "Error bounds, Reduced order modeling",

author = "Abdo, {Mohammad G.} and Congjian Wang and Abdel-Khalik, {Hany S.}",

year = "2015",

language = "English",

series = "Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015",

publisher = "American Nuclear Society",

pages = "1552--1560",

booktitle = "Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015",

note = "Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015 ; Conference date: 19-04-2015 Through 23-04-2015",

}