This document presents current technical progress and dissemination of results for the Mathematics for Analysis of Petascale Data (MAPD) project titled 'Topology for Statistical Modeling of Petascale Data', funded by the Office of Science Advanced Scientific Computing Research (ASCR) Applied Math program. Many commonly used algorithms for mathematical analysis do not scale well enough to accommodate the size or complexity of petascale data produced by computational simulations. The primary goal of this project is thus to develop new mathematical tools that address both the petascale size and uncertain nature of current data. At a high level, our approach is based on the complementary techniques of combinatorial topology and statistical modeling. In particular, we use combinatorial topology to filter out spurious data that would otherwise skew statistical modeling techniques, and we employ advanced algorithms from algebraic statistics to efficiently find globally optimal fits to statistical models. This document summarizes the technical advances we have made to date that were made possible in whole or in part by MAPD funding. These technical contributions can be divided loosely into three categories: (1) advances in the field of combinatorial topology, (2) advances in statistical modeling, and (3) new integrated topological and statistical methods.
This report describes the limitations to parallel scalability which we have encountered when applying our otherwise optimally scalable parallel statistical analysis tool kit to large data sets distributed across the parallel file system of the current premier DOE computational facility. This report describes our study to evaluate the effect of parallel I/O on the overall scalability of a parallel data analysis pipeline using our scalable parallel statistics tool kit [PTBM11]. In this goal, we tested it using the Jaguar-pf DOE/ORNL peta-scale platform on a large combustion simulation data under a variety of process counts and domain decompositions scenarios. In this report we have recalled the foundations of the parallel statistical analysis tool kit which we have designed and implemented, with the specific double intent of reproducing typical data analysis workflows, and achieving optimal design for scalable parallel implementations. We have briefly reviewed those earlier results and publications which allow us to conclude that we have achieved both goals. However, in this report we have further established that, when used in conjuction with a state-of-the-art parallel I/O system, as can be found on the premier DOE peta-scale platform, the scaling properties of the overall analysis pipeline comprising parallel data access routines degrade rapidly. This finding is problematic and must be addressed if peta-scale data analysis is to be made scalable, or even possible. In order to attempt to address these parallel I/O limitations, we will investigate the use the Adaptable IO System (ADIOS) [LZL+10] to improve I/O performance, while maintaining flexibility for a variety of IO options, such MPI IO, POSIX IO. This system is developed at ORNL and other collaborating institutions, and is being tested extensively on Jaguar-pf. Simulation code being developed on these systems will also use ADIOS to output the data thereby making it easier for other systems, such as ours, to process that data.