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Morozov, Dmitriy

Publications and source records attributed to Morozov, Dmitriy.

33 records · Page 2
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DOE OSTI2018

Measuring the Error in Approximating the Sub-Level Set Topology of Sampled Scalar Data

This paper studies here the influence of the definition of neighborhoods and methods used for creating point connectivity on topological analysis of scalar functions. It is assumed that a scalar function is known only at a finite set of points with associated function values. In order to utilize topological approaches to analyze the scalar-valued point set, it is necessary to choose point neighborhoods and, usually, point connectivity to meaningfully determine critical-point behavior for the point set. Two distances are used to measure the difference in topology when different point neighborhoods and means to define connectivity are used: (i) the bottleneck distance for persistence diagrams and (ii) the distance between merge trees. Usually, these distances define how different scalar functions are with respect to their topology. These measures, when properly adapted to point sets coupled with a definition of neighborhood and connectivity, make it possible to understand how topological characteristics depend on connectivity. Noise is another aspect considered. Five types of neighborhoods and connectivity are discussed: (i) the Delaunay triangulation; (ii) the relative neighborhood graph; (iii) the Gabriel graph; (iv) the k-nearest-neighbor (KNN) neighborhood; and (v) the Vietoris–Rips complex. It is discussed in detail how topological characterizations depend on the chosen connectivity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Programmable In Situ System for Iterative Workflows

We describe an in situ system for solving iterative problems. We specifically target inverse problems, where expensive simulations are approximated using a surrogate model. The model explores the parameter space of the simulation through iterative trials, each of which becomes a job managed by a parallel scheduler. Our work extends Henson [1], a cooperative multi-tasking system for in situ execution of loosely coupled codes.

Lohrmann, Erich↗
DOE OSTI2018

Communication-Avoiding Optimization Methods for Distributed Massive-Scale Sparse Inverse Covariance Estimation.

Across a variety of scientific disciplines, sparse inverse covariance estimation is a popular tool for capturing the underlying dependency relationships in multivariate data. Unfortunately, most estimators are not scalable enough to handle the sizes of modern high-dimensional data sets (often on the order of terabytes), and assume Gaussian samples. To address these deficiencies, we introduce HP-CONCORD, a highly scalable optimization method for estimating a sparse inverse covariance matrix based on a regularized pseudolikelihood framework, without assuming Gaussianity. Our parallel proximal gradient method uses a novel communication-avoiding linear algebra algorithm and runs across a multi-node cluster with up to 1k nodes (24k cores), achieving parallel scalability on problems with up to ~819 billion parameters (1.28 million dimensions); even on a single node, HP-CONCORD demonstrates scalability, outperforming a state-of-the-art method. We also use HP-CONCORD to estimate the underlying dependency structure of the brain from fMRI data, and use the result to identify functional regions automatically. The results show good agreement with a clustering from the neuroscience literature.

Koanantakool, Penporn↗
DOE OSTI2017

Block-Parallel Data Analysis with DIY2

DIY2 is a programming model and runtime for block-parallel analytics on distributed-memory machines. Its main abstraction is block-structured data parallelism: data are decomposed into blocks; blocks are assigned to processing elements (processes or threads); computation is described as iterations over these blocks, and communication between blocks is defined by reusable patterns. By expressing computation in this general form, the DIY2 runtime is free to optimize the movement of blocks between slow and fast memories (disk and flash vs. DRAM) and to concurrently execute blocks residing in memory with multiple threads. This enables the same program to execute in-core, out-of-core, serial, parallel, single-threaded, multithreaded, or combinations thereof. This paper describes the implementation of the main features of the DIY2 programming model and optimizations to improve performance. DIY2 is evaluated on benchmark test cases to establish baseline performance for several common patterns and on larger complete analysis codes running on large-scale HPC machines.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Efficient Delaunay Tessellation through K-D Tree Decomposition

Delaunay tessellations are fundamental data structures in computational geometry. They are important in data analysis, where they can represent the geometry of a point set or approximate its density. The algorithms for computing these tessellations at scale perform poorly when the input data is unbalanced. We investigate the use of k-d trees to evenly distribute points among processes and compare two strategies for picking split points between domain regions. Because resulting point distributions no longer satisfy the assumptions of existing parallel Delaunay algorithms, we develop a new parallel algorithm that adapts to its input and prove its correctness. We evaluate the new algorithm using two late-stage cosmology datasets. The new running times are up to 50 times faster using k-d tree compared with regular grid decomposition. Moreover, in the unbalanced data sets, decomposing the domain into a k-d tree is up to five times faster than decomposing it into a regular grid.

Morozov, Dmitriy↗
DOE OSTI2016

In situ and in-transit analysis of cosmological simulations

Abstract Modern cosmological simulations have reached the trillion-element scale, rendering data storage and subsequent analysis formidable tasks. To address this circumstance, we present a new MPI-parallel approach for analysis of simulation data while the simulation runs, as an alternative to the traditional workflow consisting of periodically saving large data sets to disk for subsequent ‘offline’ analysis. We demonstrate this approach in the compressible gasdynamics/ N -body code Nyx, a hybrid $\mbox{MPI}+\mbox{OpenMP}$ MPI + OpenMP code based on the BoxLib framework, used for large-scale cosmological simulations. We have enabled on-the-fly workflows in two different ways: one is a straightforward approach consisting of all MPI processes periodically halting the main simulation and analyzing each component of data that they own (‘ in situ ’). The other consists of partitioning processes into disjoint MPI groups, with one performing the simulation and periodically sending data to the other ‘sidecar’ group, which post-processes it while the simulation continues (‘in-transit’). The two groups execute their tasks asynchronously, stopping only to synchronize when a new set of simulation data needs to be analyzed. For both the in situ and in-transit approaches, we experiment with two different analysis suites with distinct performance behavior: one which finds dark matter halos in the simulation using merge trees to calculate the mass contained within iso-density contours, and another which calculates probability distribution functions and power spectra of various fields in the simulation. Both are common analysis tasks for cosmology, and both result in summary statistics significantly smaller than the original data set. We study the behavior of each type of analysis in each workflow in order to determine the optimal configuration for the different data analysis algorithms.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Communication-Avoiding Parallel Sparse-Dense Matrix-Matrix Multiplication

Multiplication of a sparse matrix with a dense matrix is a building block of an increasing number of applications in many areas such as machine learning and graph algorithms. However, most previous work on parallel matrix multiplication considered only both dense or both sparse matrix operands. This paper analyzes the communication lower bounds and compares the communication costs of various classic parallel algorithms in the context of sparse-dense matrix-matrix multiplication. We also present new communication-avoiding algorithms based on a 1D decomposition, called 1.5D, which - while suboptimal in dense-dense and sparse-sparse cases - outperform the 2D and 3D variants both theoretically and in practice for sparse-dense multiplication. Our analysis separates one-time costs from per iteration costs in an iterative machine learning context. Experiments demonstrate speedups up to 100x over a baseline 3D SUMMA implementation and show parallel scaling over 10 thousand cores.

Koanantakool, Penporn↗
DOE OSTI2016

Biological and Environmental Research Exascale Requirements Review. An Office of Science review sponsored jointly by Advanced Scientific Computing Research and Biological and Environmental Research, March 28-31, 2016, Rockville, Maryland

Understanding the fundamentals of genomic systems or the processes governing impactful weather patterns are examples of the types of simulation and modeling performed on the most advanced computing resources in America. High-performance computing and computational science together provide a necessary platform for the mission science conducted by the Biological and Environmental Research (BER) office at the U.S. Department of Energy (DOE). This report reviews BER’s computing needs and their importance for solving some of the toughest problems in BER’s portfolio. BER’s impact on science has been transformative. Mapping the human genome, including the U.S.-supported international Human Genome Project that DOE began in 1987, initiated the era of modern biotechnology and genomics-based systems biology. And since the 1950s, BER has been a core contributor to atmospheric, environmental, and climate science research, beginning with atmospheric circulation studies that were the forerunners of modern Earth system models (ESMs) and by pioneering the implementation of climate codes onto high-performance computers. See http://exascaleage.org/ber/ for more information.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Master of Puppets: Cooperative Multitasking for In Situ Processing

Modern scientific and engineering simulations track the time evolution of billions of elements. For such large runs, storing most time steps for later analysis is not a viable strategy. It is far more efficient to analyze the simulation data while it is still in memory. Here, we present a novel design for running multiple codes in situ: using coroutines and position-independent executables we enable cooperative multitasking between simulation and analysis, allowing the same executables to post-process simulation output, as well as to process it on the fly, both in situ and in transit. We present Henson, an implementation of our design, and illustrate its versatility by tackling analysis tasks with different computational requirements. This design differs significantly from the existing frameworks and offers an efficient and robust approach to integrating multiple codes on modern supercomputers. The techniques we present can also be integrated into other in situ frameworks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Geometry Helps to Compare Persistence Diagrams

Exploiting geometric structure to improve the asymptotic complexity of discrete assignment problems is a well-studied subject. In contrast, the practical advantages of using geometry for such problems have not been explored. We implement geometric variants of the Hopcroft--Karp algorithm for bottleneck matching (based on previous work by Efrat el al.), and of the auction algorithm by Bertsekas for Wasserstein distance computation. Both implementations use k-d trees to replace a linear scan with a geometric proximity query. Our interest in this problem stems from the desire to compute distances between persistence diagrams, a problem that comes up frequently in topological data analysis. We show that our geometric matching algorithms lead to a substantial performance gain, both in running time and in memory consumption, over their purely combinatorial counterparts. Moreover, our implementation significantly outperforms the only other implementation available for comparing persistence diagrams.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

DIY2

DIY2 is a data parallel out-of-core library, written in C++. It provides facilities for domain decomposition into blocks and abstracts both neighborhood and global communication patterns to the level of blocks. DIY2 supports automatic threading. It also provides a data serialization mechanism, using which it allows for automatic movement of blocks in and out of core.

Morozov, Dmitriy↗
DOE OSTI2015

Parallel Computation of Persistent Homology using the Blowup Complex

We describe a parallel algorithm that computes persistent homology, an algebraic descriptor of a filtered topological space. Our algorithm is distinguished by operating on a spatial decomposition of the domain, as opposed to a decomposition with respect to the filtration. We rely on a classical construction, called the Mayer--Vietoris blowup complex, to glue global topological information about a space from its disjoint subsets. We introduce an efficient algorithm to perform this gluing operation, which may be of independent interest, and describe how to process the domain hierarchically. We report on a set of experiments that help assess the strengths and identify the limitations of our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

High-Performance Computation of Distributed-Memory Parallel 3D Voronoi and Delaunay Tessellation

Computing a Voronoi or Delaunay tessellation from a set of points is a core part of the analysis of many simulated and measured datasets: N-body simulations, molecular dynamics codes, and LIDAR point clouds are just a few examples. Such computational geometry methods are common in data analysis and visualization; but as the scale of simulations and observations surpasses billions of particles, the existing serial and shared-memory algorithms no longer suffice. A distributed-memory scalable parallel algorithm is the only feasible approach. The primary contribution of this paper is a new parallel Delaunay and Voronoi tessellation algorithm that automatically determines which neighbor points need to be exchanged among the subdomains of a spatial decomposition. Other contributions include periodic and wall boundary conditions, comparison of our method using two popular serial libraries, and application to numerous science datasets.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Distributed Contour Trees

Topological techniques provide robust tools for data analysis. They are used, for example, for feature extraction, for data de-noising, and for comparison of data sets. This chapter concerns contour trees, a topological descriptor that records the connectivity of the isosurfaces of scalar functions. These trees are fundamental to analysis and visualization of physical phenomena modeled by real-valued measurements. We study the parallel analysis of contour trees. After describing a particular representation of a contour tree, called local{global representation, we illustrate how di erent problems that rely on contour trees can be solved in parallel with minimal communication.

97 MATHEMATICS AND COMPUTING↗