Building an accurate surrogate model for the spatio-temporal outputs of a computer simulation is a challenging task. A simple approach to improve the accuracy of the surrogate is to cluster the outputs based on similarity and build a separate surrogate model for each cluster. This clustering is relatively straightforward when the output at each time step is of moderate size. However, when the spatial domain is represented by a large number of grid points, numbering in the millions, the clustering of the data becomes more challenging. In this report, we consider output data from simulations of a jet interacting with high explosives. These data are available on spatial domains of different sizes, at grid points that vary in their spatial coordinates, and in a format that distributes the output across multiple files at each time step of the simulation. We first describe how we bring these data into a consistent format prior to clustering. Borrowing the idea of random projections from data mining, we reduce the dimension of our data by a factor of thousand, making it possible to use the iterative k-means method for clustering. We show how we can use the randomness of both the random projections, and the choice of initial centroids in k-means clustering, to determine the number of clusters in our data set. Our approach makes clustering of extremely high dimensional data tractable, generating meaningful cluster assignments for our problem, despite the approximation introduced in the random projections.

翻译：构建计算机模拟时空输出的精确替代模型是一项具有挑战性的任务。提升替代模型精度的简便方法之一是依据输出相似性进行聚类，并为每个聚类单独构建替代模型。当每个时间步的输出规模适中时，此类聚类操作相对直接。然而，当空间域由数百万个网格点表示时，数据聚类变得更具挑战性。本报告研究射流与高能炸药相互作用模拟的输出数据：这些数据存在于不同规模的空间域中，网格点坐标动态变化，且每个模拟时间步的输出以多文件分布式格式存储。我们首先阐述如何在聚类前将数据统一为一致格式。借鉴数据挖掘中随机投影的思想，我们将数据维度降低千倍，从而能够采用迭代k-means方法进行聚类。我们展示了如何利用随机投影的随机性以及k-means聚类中初始质心选择的随机性，来确定数据集中的聚类数量。尽管随机投影引入了一定近似，但我们的方法使得极高维数据的聚类变得可行，并为研究问题生成了有意义的聚类分配结果。