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

Yixiang Deng, Guang LinXiu 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 = {Deng , Yixiang and Lin , Guang and Yang , Xiu}, 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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