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Probabilistic collocation method for strongly nonlinear problems: 3. Transform by time
Author(s) -
Liao Qinzhuo,
Zhang Dongxiao
Publication year - 2016
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2015wr017724
Subject(s) - collocation (remote sensing) , probabilistic logic , nonlinear system , displacement (psychology) , computer science , mathematics , mathematical optimization , algorithm , series (stratigraphy) , artificial intelligence , machine learning , geology , psychology , paleontology , physics , quantum mechanics , psychotherapist
The probabilistic collocation method (PCM) has drawn wide attention for stochastic analysis recently. Its results may become inaccurate in case of a strongly nonlinear relation between random parameters and model responses. To tackle this problem, we proposed a location‐based transformed PCM (xTPCM) and a displacement‐based transformed PCM (dTPCM) in previous parts of this series. Making use of the transform between response and space, the above two methods, however, have certain limitations. In this study, we introduce a time‐based transformed PCM (tTPCM) employing the transform between response and time. We conduct numerical experiments to investigate its performance in uncertainty quantification. The results show that the tTPCM greatly improves the accuracy of the traditional PCM in a cost‐effective manner and is more general and convenient than the xTPCM/dTPCM.