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Adaptive POD–DEIM basis construction and its application to a nonlinear population balance system
Author(s) -
Feng Lihong,
Mangold Michael,
Benner Peter
Publication year - 2017
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.15749
Subject(s) - interpolation (computer graphics) , basis (linear algebra) , nonlinear system , population , mathematical optimization , computer science , point of delivery , extension (predicate logic) , mathematics , process (computing) , decomposition , algorithm , artificial intelligence , ecology , physics , geometry , demography , quantum mechanics , sociology , agronomy , biology , programming language , operating system , motion (physics)
We propose an adaptive algorithm for constructing reduced‐order models (ROMs) of nonlinear systems based on proper orthogonal decomposition (POD) combined with the discrete empirical interpolation method (DEIM). Using an efficient output error estimation, the reduced basis and the DEIM interpolation basis are adaptively adjusted to derive a small, yet accurate ROM. The adaptive algorithm is further explored for a population balance system of a crystallization process. Simulation results show that much smaller and reliable ROMs can be adaptively obtained using the algorithm with ignorable extra computational load as compared with the standard POD–DEIM method. © 2017 American Institute of Chemical Engineers AIChE J , 63: 3832–3844, 2017