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Volume 28, Issue 5
Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression

Yixiang Deng, Guang Lin & Xiu Yang

Commun. Comput. Phys., 28 (2020), pp. 1812-1837.

Published online: 2020-11

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  • Abstract

We propose a data fusion method based on multi-fidelity Gaussian process regression (GPR) framework. This method combines available data of the quantity of interest (QoI) and its gradients with different fidelity levels, namely, it is a Gradient-enhanced Cokriging method (GE-Cokriging). It provides the approximations of both the QoI and its gradients simultaneously with uncertainty estimates. We compare this method with the conventional multi-fidelity Cokriging method that does not use gradients information, and the result suggests that GE-Cokriging has a better performance in predicting both QoI and its gradients. Moreover, GE-Cokriging even shows better generalization result in some cases where Cokriging performs poorly due to the singularity of the covariance matrix. We demonstrate the application of GE-Cokriging in several practical cases including reconstructing the trajectories and velocity of an underdamped oscillator with respect to time simultaneously, and investigating the sensitivity of power factor of a load bus with respect to varying power inputs of a generator bus in a large scale power system. Although GE-Cokriging requires slightly higher computational cost than Cokriging in some cases, the comparison of the accuracy shows that this cost is worthwhile.

  • Keywords

Gaussian process regression, multifidelity Cokriging, gradient-enhanced, integral-enhanced.

  • AMS Subject Headings

60G15, 65D10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-28-1812, author = {Yixiang and Deng and and 9581 and and Yixiang Deng and Guang and Lin and and 9582 and and Guang Lin and Xiu and Yang and and 9583 and and Xiu Yang}, title = {Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression}, journal = {Communications in Computational Physics}, year = {2020}, volume = {28}, number = {5}, pages = {1812--1837}, abstract = {

We propose a data fusion method based on multi-fidelity Gaussian process regression (GPR) framework. This method combines available data of the quantity of interest (QoI) and its gradients with different fidelity levels, namely, it is a Gradient-enhanced Cokriging method (GE-Cokriging). It provides the approximations of both the QoI and its gradients simultaneously with uncertainty estimates. We compare this method with the conventional multi-fidelity Cokriging method that does not use gradients information, and the result suggests that GE-Cokriging has a better performance in predicting both QoI and its gradients. Moreover, GE-Cokriging even shows better generalization result in some cases where Cokriging performs poorly due to the singularity of the covariance matrix. We demonstrate the application of GE-Cokriging in several practical cases including reconstructing the trajectories and velocity of an underdamped oscillator with respect to time simultaneously, and investigating the sensitivity of power factor of a load bus with respect to varying power inputs of a generator bus in a large scale power system. Although GE-Cokriging requires slightly higher computational cost than Cokriging in some cases, the comparison of the accuracy shows that this cost is worthwhile.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0151}, url = {http://global-sci.org/intro/article_detail/cicp/18397.html} }
TY - JOUR T1 - Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression AU - Deng , Yixiang AU - Lin , Guang AU - Yang , Xiu JO - Communications in Computational Physics VL - 5 SP - 1812 EP - 1837 PY - 2020 DA - 2020/11 SN - 28 DO - http://doi.org/10.4208/cicp.OA-2020-0151 UR - https://global-sci.org/intro/article_detail/cicp/18397.html KW - Gaussian process regression, multifidelity Cokriging, gradient-enhanced, integral-enhanced. AB -

We propose a data fusion method based on multi-fidelity Gaussian process regression (GPR) framework. This method combines available data of the quantity of interest (QoI) and its gradients with different fidelity levels, namely, it is a Gradient-enhanced Cokriging method (GE-Cokriging). It provides the approximations of both the QoI and its gradients simultaneously with uncertainty estimates. We compare this method with the conventional multi-fidelity Cokriging method that does not use gradients information, and the result suggests that GE-Cokriging has a better performance in predicting both QoI and its gradients. Moreover, GE-Cokriging even shows better generalization result in some cases where Cokriging performs poorly due to the singularity of the covariance matrix. We demonstrate the application of GE-Cokriging in several practical cases including reconstructing the trajectories and velocity of an underdamped oscillator with respect to time simultaneously, and investigating the sensitivity of power factor of a load bus with respect to varying power inputs of a generator bus in a large scale power system. Although GE-Cokriging requires slightly higher computational cost than Cokriging in some cases, the comparison of the accuracy shows that this cost is worthwhile.

Yixiang Deng, Guang Lin & Xiu Yang. (2020). Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression. Communications in Computational Physics. 28 (5). 1812-1837. doi:10.4208/cicp.OA-2020-0151
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