RMFGP：高维不确定性量化的旋转多保真度高斯过程降维
RMFGP: Rotated Multi-fidelity Gaussian process with Dimension Reduction for High-dimensional Uncertainty Quantification
摘要：
在计算科学和工程领域中，多保真度建模出现在许多场合。即使只有一小部分准确数据可用，它也可以实现准确的推断。这些数据通常来自高保真模型，这在计算上是昂贵的。通过将高保真度模型的实现与一个或多个低保真度模型相结合，多保真度方法可以对感兴趣的量进行准确的预测。本文提出了一种新的基于旋转多保真度高斯过程回归的降维框架和一种贝叶斯主动学习方案。通过从训练好的旋转多保真度模型中抽取样本，可以按照切片平均方差估计（SAVE）方法结合高斯过程回归降维技术的思想解决所谓的监督降维问题。这个通用的框架，我们开发可以有效地解决高维问题，而数据不足，适用于传统的降维方法。此外，基于我们的训练模型，可以得到一个更准确的代理高斯过程模型的原始问题。四个数值算例证明了所提出的旋转多保真度高斯过程（RMFGP）模型的有效性。结果表明，我们的方法具有更好的性能在所有情况下，最后两个案例涉及随机偏微分方程的不确定性传播分析。
英文摘要：
Multi-fidelity modelling arises in many situations in computational science and engineering world. It enables accurate inference even when only a small set of accurate data is available. Those data often come from a high-fidelity model, which is computationally expensive. By combining the realizations of the high-fidelity model with one or more low-fidelity models, the multi-fidelity method can make accurate predictions of quantities of interest. This paper proposes a new dimension reduction framework based on rotated multi-fidelity Gaussian process regression and a Bayesian active learning scheme when the available precise observations are insufficient. By drawing samples from the trained rotated multi-fidelity model, the so-called supervised dimension reduction problems can be solved following the idea of the sliced average variance estimation (SAVE) method combined with a Gaussian process regression dimension reduction technique. This general framework we develop can effectively solve high-dimensional problems while the data are insufficient for applying traditional dimension reduction methods. Moreover, a more accurate surrogate Gaussian process model of the original problem can be obtained based on our trained model. The effectiveness of the proposed rotated multi-fidelity Gaussian process(RMFGP) model is demonstrated in four numerical examples. The results show that our method has better performance in all cases and uncertainty propagation analysis is performed for last two cases involving stochastic partial differential equations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
