Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression (Communications in Computational Physics, 2020)
We propose a data fusion method based on multi-fidelity Gaussian processregression (GPR) framework. This method combines available data of the quantity ofinterest (QoI) and its gradients with different fidelity levels, namely, it is a Gradient-enhanced Cokriging method (GE-Cokriging). It provides the approximations of boththe QoI and its gradients simultaneously with uncertainty estimates. We compare thismethod with the conventional multi-fidelity Cokriging method that does not use gradients information, and the result suggests that GE-Cokriging has a better performancein predicting both QoI and its gradients. Moreover, GE-Cokriging even shows bettergeneralization result in some cases where Cokriging performs poorly due to the singularity of the covariance matrix. We demonstrate the application of GE-Cokrigingin several practical cases including reconstructing the trajectories and velocity of anunderdamped oscillator with respect to time simultaneously, and investigating thesensitivity of power factor of a load bus with respect to varying power inputs of agenerator bus in a large scale power system. Although GE-Cokriging requires slightlyhigher 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.