# Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression

arXiv: https://arxiv.org/abs/2008.01066 · HTML: https://mlsanity.com/paper/2008.01066/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Aug 2020.

## Built on by (most cited first, 3 of 3)

- [Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems](https://mlsanity.com/paper/2111.02801/) (2021)
- [Uncertainty Quantification in Machine Learning for Engineering Design and Health Prognostics: A Tutorial](https://mlsanity.com/paper/2305.04933/) (2023)
- [Gradient-enhanced multifidelity neural networks for high-dimensional function approximation](https://mlsanity.com/paper/2103.12247/) (2021)

## Abstract (arXiv)

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.