Statistical modeling of large-scale simulation data

Abstract

With the advent of fast computer systems, scientists are now able to generate terabytes of simulation data. Unfortunately, the sheer size of these data sets has made efficient exploration of them impossible. To aid scientists in gleaning insight from their simulation data, we have developed an ad-hoc query infrastructure. Our system, called AQSim (short for Ad-hoc Queries for Simulation) reduces the data storage requirements and query access times in two stages. First, it creates and stores mathematical and statistical models of the data at multiple resolutions. Second, it evaluates queries on the models of the data instead of on the entire data set. In this paper, we present two simple but effective statistical modeling techniques for simulation data. Our first modeling technique computes the true (unbiased) mean of systematic partitions of the data. It makes no assumptions about the distribution of the data and uses a variant of the root mean square error to evaluate a model. Our second statistical modeling technique uses the Andersen-Darling goodness-of-fit method on systematic partitions of the data. This method evaluates a model by how well it passes the normality test on the data. Both of our statistical models effectively answer range queries. At each resolution of the data, we compute the precision of our answer to the user's query by scaling the one-sided Chebyshev Inequalities with the original mesh's topology. We combine precisions at different resolutions by calculating their weighted average. Our experimental evaluations on two scientific simulation data sets illustrate the value of using these statistical modeling techniques on multiple resolutions of large simulation data sets.