论文标题
通过梯度增强的高斯过程回归的多重数据融合
Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression
论文作者
论文摘要
我们提出了一种基于多保真高斯过程回归（GPR）框架的数据融合方法。该方法结合了利息量（QOI）及其梯度的可用数据，即具有不同的保真度水平，即，它是一种梯度增强的cokriging方法（GE-Cokriging）。它同时提供了QOI及其梯度的近似值，并提供不确定性估计。我们将这种方法与不使用梯度信息的常规多性cokriging方法进行了比较，结果表明，GE-Cokriging在预测QOI及其梯度方面具有更好的性能。此外，在某些情况下，由于协方差矩阵的奇异性，GE-Cokriging甚至显示出更好的概括会导致概括。我们证明了在几种实际情况下使用GE-Cokriging的应用，包括重建不受欢迎的振荡器相对于时间的轨迹和速度，并研究负载总线对大规模电力系统中发电机总线的动力输入的功率因子的敏感性。我们还表明，尽管GE-Cokriging方法比Cokriging方法需要更高的计算成本，但准确性比较的结果表明，这种成本通常值得。
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.
