Abstract Ordinary Kriging (OK) is a popular geostatistical algorithm for spatial interpolation and estimation. The computational complexity of OK changes quadratically and cubically for memory and speed, respectively, given the number of data. Therefore, it is computationally intensive and also challenging to process a large set of data, especially in three-dimensional (3D) cases. This paper develops a geostatistics-informed machine learning (GIML) model to improve the efficiency of OK by reducing the number of points required to be estimated using OK. Specifically, only a very few of the unknown points are estimated by OK to get the weights and estimations, which are used as the training dataset. Moreover, the governing equations of OK are used to guide our proposed machine learning to better reproduce the spatial distributions. Our results show that the proposed GIML can reduce the computational time of OK by at least one order of magnitude. The effectiveness of the GIML is evaluated and compared using a 2D case. Furthermore, we demonstrate its efficiency and robustness by considering a different number of training samples on various 3D simulation grids.

中文翻译：

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使用地统计信息机器学习加速地统计建模

摘要 普通克里金法 (OK) 是一种流行的用于空间插值和估计的地统计算法。给定数据数量，OK 的计算复杂度分别随内存和速度呈二次方和三次方变化。因此，处理大量数据是计算密集型的，也具有挑战性，尤其是在三维 (3D) 情况下。本文开发了一种地统计信息机器学习 (GIML) 模型，通过减少使用 OK 估计所需的点数来提高 OK 的效率。具体来说，只有极少数未知点被OK估计得到权重和估计值，作为训练数据集。此外，OK 的控制方程用于指导我们提出的机器学习以更好地再现空间分布。我们的结果表明，所提出的 GIML 可以将 OK 的计算时间减少至少一个数量级。使用 2D 案例评估和比较 GIML 的有效性。此外，我们通过在各种 3D 模拟网格上考虑不同数量的训练样本来证明其效率和稳健性。