Attila Gyulassy

A Practical Approach to Morse-Smale Complex Computation: Scalability and Generality

The Morse-Smale (MS) complex has proven to be a useful tool in extracting and visualizing features from scalar-valued data. However, efficient computation of the MS complex for large scale data remains a challenging problem. We describe a new algorithm and easily extensible framework for computing MS complexes for large scale data of any dimension where scalar values are given at the vertices of a closure-finite and weak topology (CW) complex, therefore enabling computation on a wide variety of meshes such as regular grids, simplicial meshes, and adaptive multiresolution (AMR) meshes. A new divide-and-conquer strategy allows for memory-efficient computation of the MS complex and simplification on-the-fly to control the size of the output. In addition to being able to handle various data formats, the framework supports implementation-specific optimizations, for example, for regular data. We present the complete characterization of critical point cancellations in all dimensions. This technique enables the topology based analysis of large data on off-the-shelf computers. In particular we demonstrate the first full computation of the MS complex for a 1 billion/10243 node grid on a laptop computer with 2 Gb memory.

Topology-based simplification for feature extraction from 3D scalar fields

In this paper, we present a topological approach for simplifying continuous functions defined on volumetric domains. We introduce two atomic operations that remove pairs of critical points of the function and design a combinatorial algorithm that simplifies the Morse-Smale complex by repeated application of these operations. The Morse-Smale complex is a topological data structure that provides a compact representation of gradient flow between critical points of a function. Critical points paired by the Morse-Smale complex identify topological features and their importance. The simplification procedure leaves important critical points untouched, and is therefore useful for extracting desirable features. We also present a visualization of the simplified topology.

Combining in-situ and in-transit processing to enable extreme-scale scientific analysis

With the onset of extreme-scale computing, I/O constraints make it increasingly difficult for scientists to save a sufficient amount of raw simulation data to persistent storage. One potential solution is to change the data analysis pipeline from a post-process centric to a concurrent approach based on either in-situ or in-transit processing. In this context computations are considered in-situ if they utilize the primary compute resources, while in-transit processing refers to offloading computations to a set of secondary resources using asynchronous data transfers. In this paper we explore the design and implementation of three common analysis techniques typically performed on large-scale scientific simulations: topological analysis, descriptive statistics, and visualization. We summarize algorithmic developments, describe a resource scheduling system to coordinate the execution of various analysis workflows, and discuss our implementation using the DataSpaces and ADIOS frameworks that support efficient data movement between in-situ and in-transit computations. We demonstrate the efficiency of our lightweight, flexible framework by deploying it on the Jaguar XK6 to analyze data generated by S3D, a massively parallel turbulent combustion code. Our framework allows scientists dealing with the data deluge at extreme scale to perform analyses at increased temporal resolutions, mitigate I/O costs, and significantly improve the time to insight.

Efficient Computation of Morse-Smale Complexes for Three-dimensional Scalar Functions

The Morse-Smale complex is an efficient representation of the gradient behavior of a scalar function, and critical points paired by the complex identify topological features and their importance. We present an algorithm that constructs the Morse-Smale complex in a series of sweeps through the data, identifying various components of the complex in a consistent manner. All components of the complex, both geometric and topological, are computed, providing a complete decomposition of the domain. Efficiency is maintained by representing the geometry of the complex in terms of point sets.

A topological approach to simplification of three-dimensional scalar functions

This paper describes an efficient combinatorial method for simplification of topological features in a 3D scalar function. The Morse-Smale complex, which provides a succinct representation of a functions associated gradient flow field, is used to identify topological features and their significance. The simplification process, guided by the Morse-Smale complex, proceeds by repeatedly applying two atomic operations that each remove a pair of critical points from the complex. Efficient storage of the complex results in execution of these atomic operations at interactive rates. Visualization of the simplified complex shows that the simplification preserves significant topological features while removing small features and noise.

Analysis of large-scale scalar data using hixels

One of the greatest challenges for todays visualization and analysis communities is the massive amounts of data generated from state of the art simulations. Traditionally, the increase in spatial resolution has driven most of the data explosion, but more recently ensembles of simulations with multiple results per data point and stochastic simulations storing individual probability distributions are increasingly common. This paper introduces a new data representation for scalar data, called hixels, that stores a histogram of values for each sample point of a domain. The histograms may be created by spatial down-sampling, binning ensemble values, or polling values from a given distribution. In this manner, hixels form a compact yet information rich approximation of large scale data. In essence, hixels trade off data size and complexity for scalar-value “uncertainty”. Based on this new representation we propose new feature detection algorithms using a combination of topological and statistical methods. In particular, we show how to approximate topological structures from hixel data, extract structures from multi-modal distributions, and render uncertain isosurfaces. In all three cases we demonstrate how using hixels compares to traditional techniques and provide new capabilities to recover prominent features that would otherwise be either infeasible to compute or ambiguous to infer. We use a collection of computer tomography data and large scale combustion simulations to illustrate our techniques.

Scalable parallel building blocks for custom data analysis

We present a set of building blocks that provide scalable data movement capability to computational scientists and visualization researchers for writing their own parallel analysis. The set includes scalable tools for domain decomposition, process assignment, parallel I/O, global reduction, and local neighborhood communicationtasks that are common across many analysis applications. The global reduction is performed with a new algorithm, described in this paper, that efficiently merges blocks of analysis results into a smaller number of larger blocks. The merging is configurable in the number of blocks that are reduced in each round, the number of rounds, and the total number of resulting blocks. We highlight the use of our library in two analysis applications: parallel streamline generation and parallel Morse-Smale topological analysis. The first case uses an existing local neighborhood communication algorithm, whereas the latter uses the new merge algorithm.

In-situ feature extraction of large scale combustion simulations using segmented merge trees

The ever increasing amount of data generated by scientific simulations coupled with system I/O constraints are fueling a need for in-situ analysis techniques. Of particular interest are approaches that produce reduced data representations while maintaining the ability to redefine, extract, and study features in a post-process to obtain scientific insights. This paper presents two variants of in-situ feature extraction techniques using segmented merge trees, which encode a wide range of threshold based features. The first approach is a fast, low communication cost technique that generates an exact solution but has limited scalability. The second is a scalable, local approximation that nevertheless is guaranteed to correctly extract all features up to a predefined size. We demonstrate both variants using some of the largest combustion simulations available on leadership class supercomputers. Our approach allows state-of-the-art, feature-based analysis to be performed in-situ at significantly higher frequency than currently possible and with negligible impact on the overall simulation runtime.

Exploring power behaviors and trade-offs of in-situ data analytics

As scientific applications target exascale, challenges related to data and energy are becoming dominating concerns. For example, coupled simulation workflows are increasingly adopting in-situ data processing and analysis techniques to address costs and overheads due to data movement and I/O. However it is also critical to understand these overheads and associated trade-offs from an energy perspective. The goal of this paper is exploring data-related energy/performance trade-offs for end-to-end simulation workflows running at scale on current high-end computing systems. Specifically, this paper presents: (1) an analysis of the data-related behaviors of a combustion simulation workflow with an insitu data analytics pipeline, running on the Titan system at ORNL; (2) a power model based on system power and data exchange patterns, which is empirically validated; and (3) the use of the model to characterize the energy behavior of the workflow and to explore energy/performance tradeoffs on current as well as emerging systems.

Topological feature extraction and tracking

Scientific datasets obtained by measurement or produced by computational simulations must be analyzed to understand the phenomenon under study. The analysis typically requires a mathematically sound definition of the features of interest and robust algorithms to identify these features, compute statistics about them, and often track them over time. Because scientific datasets often capture phenomena with multi-scale behaviour, and almost always contain noise the definitions and algorithms must be designed with sufficient flexibility and care to allow multi-scale analysis and noise-removal. In this paper, we present some recent work on topological feature extraction and tracking with applications in molecular analysis, combustion simulation, and structural analysis of porous materials.