Dimension Reduction for Gaussian Process Emulation: An Application to the Influence of Bathymetry on Tsunami Heights
Dimension Reduction for Gaussian Process Emulation: An Application to the Influence of Bathymetry on Tsunami Heights
复制标题
DOI：
10.1137/16m1090648
复制
发表时间：
2016-03
期刊：
影响因子：
--
通讯作者：
Xiaoyu Liu;S. Guillas
中科院分区：
文献类型：
--
作者：
Xiaoyu Liu;S. Guillas
高精度复杂的计算机模型或模拟器需要大量的时间和内存资源来产生逼真的结果。统计模拟器是此类模拟器的计算廉价近似值。它们可以用来代替模拟器用于各种目的，例如从输入到输出的不确定性传播或根据观测校准某些内部参数。然而，当输入空间是高维时，仿真器的构造可能会变得非常昂贵。为了克服这一障碍，本文引入了一种将仿真与降维相结合的联合框架。选择基于梯度的核降维技术是因为它能够在信息损失很小的情况下大幅降低维数。将高斯过程仿真技术与该降维方法相结合。我们提出的方法为仿真中的降维问题提供了一个答案，这些问题是现有方法无法解决的。从理论上证明了该框架的有效性和准确性，并与其他方法进行了椭圆型偏微分方程问题的比较。最后给出了海啸模拟的一个实际应用。水深测量（海底高程）的不确定性采用地质统计学方法建模为空间过程的高维实现。我们的降维模拟使我们能够计算这些不确定性对近海和岸上可能产生的海啸波高的影响。我们观察到，由于测深不确定性的贡献，海啸高度不确定性的传播显著增加。这些结果突出表明，需要在海啸早期预警和风险评估中纳入测深不确定性的影响。
High accuracy complex computer models, or simulators, require large resources in time and memory to produce realistic results. Statistical emulators are computationally cheap approximations of such simulators. They can be built to replace simulators for various purposes, such as the propagation of uncertainties from inputs to outputs or the calibration of some internal parameters against observations. However, when the input space is of high dimension, the construction of an emulator can become prohibitively expensive. In this paper, we introduce a joint framework merging emulation with dimension reduction in order to overcome this hurdle. The gradient-based kernel dimension reduction technique is chosen due to its ability to drastically decrease dimensionality with little loss in information. The Gaussian process emulation technique is combined with this dimension reduction approach. Our proposed approach provides an answer to the dimension reduction issue in emulation for a wide range of simulation problems that cannot be tackled using existing methods. The efficiency and accuracy of the proposed framework is demonstrated theoretically, and compared with other methods on an elliptic partial differential equation (PDE) problem. We finally present a realistic application to tsunami modeling. The uncertainties in the bathymetry (seafloor elevation) are modeled as high-dimensional realizations of a spatial process using a geostatistical approach. Our dimension-reduced emulation enables us to compute the impact of these uncertainties on resulting possible tsunami wave heights near-shore and on-shore. We observe a significant increase in the spread of uncertainties in the tsunami heights due to the contribution of the bathymetry uncertainties. These results highlight the need to include the effect of uncertainties in the bathymetry in tsunami early warnings and risk assessments.