Data from: Surrogate modelling for the prediction of spatial fields based on simultaneous dimensionality reduction of high-dimensional input/output spaces

Time-consuming numerical simulators for solving groundwater flow and dissolution models of physico-chemical processes in deep aquifers normally require some of the model inputs to be defined in high-dimensional spaces in order to return realistic results. Sometimes, the outputs of interest are spatial fields leading also to high-dimensional output spaces. Although Gaussian process emulation has been satisfactorily used for computing faithful and inexpensive approximations of complex simulators, these have been mostly applied to problems defined in low-dimensional input spaces. In this paper, we propose a method for simultaneously reducing the dimensionality of very high-dimensional input and output spaces in Gaussian process emulators for stochastic partial differential equation models while retaining the qualitative features of the original models. This allows us to build a surrogate model for the prediction of spatial fields in such time-consuming simulators. We apply the methodology to a model of convection and dissolution processes occurring during carbon capture and storage.

用于求解深部含水层中物理化学过程的地下水流与溶解模型的耗时数值模拟器，通常需要将部分模型输入定义于高维空间，以获得符合实际的模拟结果。有时，关注的输出为空间场（spatial fields），这同样会导致输出空间维度较高。尽管高斯过程仿真（Gaussian process emulation）已被成功用于构建复杂模拟器的保真且低开销近似模型，但此类方法大多仅适用于低维输入空间定义的问题。本文提出一种方法，可在保留原模型定性特征的前提下，同时降低随机偏微分方程（stochastic partial differential equation）模型所用高斯过程仿真器的超高维输入与输出空间维度。该方法可帮助我们为这类耗时模拟器中的空间场预测构建代理模型。我们将所提方法应用于碳捕获与封存（carbon capture and storage）过程中发生的对流与溶解过程模型。