期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 309, 期 -, 页码 52-68出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2015.12.035
关键词
Gaussian functional regression; Multi-fidelity models; Reduced basis method; Model reduction; Experimental design
资金
- Air Force Office of Scientific Research under AFOSR [FA9550-12-1-0357, FA9550-11-1-0141]
In this paper, we introduce a Gaussian functional regression (GFR) technique that integrates multi-fidelity models with model reduction to efficiently predict the input-output relationship of a high-fidelity model. The GFR method combines the high-fidelity model with a low-fidelity model to provide an estimate of the output of the high-fidelity model in the form of a posterior distribution that can characterize uncertainty in the prediction. A reduced basis approximation is constructed upon the low-fidelity model and incorporated into the GFR method to yield an inexpensive posterior distribution of the output estimate. As this posterior distribution depends crucially on a set of training inputs at which the high-fidelity modelsare simulated, we develop a greedy sampling algorithm to select the training inputs. Our approach results in an output prediction model that inherits the fidelity of the high-fidelity model and has the computational complexity of the reduced basis approximation. Numerical results are presented to demonstrate the proposed approach. (C) 2015 Elsevier Inc. All rights reserved.
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