Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression

TL;DR

This paper introduces a gradient-enhanced Gaussian process regression method for multi-fidelity data fusion, improving prediction accuracy of quantities of interest and their gradients by leveraging gradient information across different fidelity levels.

Contribution

It proposes a novel Gradient-enhanced Cokriging method that incorporates gradient data into multi-fidelity Gaussian process regression, outperforming traditional methods in accuracy and robustness.

Findings

GE-Cokriging outperforms conventional Cokriging in predicting QoI and gradients.

The method provides better generalization in cases with covariance matrix singularity.

Application examples include trajectory reconstruction and power system sensitivity analysis.

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. 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.