Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression
This work addresses the need for more accurate uncertainty-aware predictions in engineering and scientific domains, though it appears incremental as it builds on existing multi-fidelity frameworks by incorporating gradient information.
The authors tackled the problem of improving predictions in multi-fidelity data fusion by proposing a gradient-enhanced Gaussian process regression method, which showed better performance in predicting quantities of interest and their gradients compared to conventional methods, with demonstrated applications in practical cases like oscillator trajectories and power system sensitivity.
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. We also show that though GE-Cokriging method requires a little bit higher computational cost than Cokriging method, the result of accuracy comparison shows that this cost is usually worth it.