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All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

The fusion code XGC: Enabling kinetic study of multi-scale edge turbulent transport in ITER [Book Chapter]

The XGC fusion gyrokinetic code combines state-of-the-art, portable computational and algorithmic technologies to enable complicated multiscale simulations of turbulence and transport dynamics in ITER edge plasma on the largest US open-science computer, the CRAY XK7 Titan, at its maximal heterogeneous capability, which have not been possible before due to a factor of over 10 shortage in the time-to-solution for less than 5 days of wall-clock time for one physics case. Frontier techniques such as nested OpenMP parallelism, adaptive parallel I/O, staging I/O and data reduction using dynamic and asynchronous applications interactions, dynamic repartitioning for balancing computational work in pushing particles and in grid related work, scalable and accurate discretization algorithms for non-linear Coulomb collisions, and communication-avoiding subcycling technology for pushing particles on both CPUs and GPUs are also utilized to dramatically improve the scalability and time-to-solution, hence enabling the difficult kinetic ITER edge simulation on a present-day leadership class computer.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Streaming data analytics via message passing with application to graph algorithms

The need to process streaming data, which arrives continuously at high-volume in real-time, arises in a variety of contexts including data produced by experiments, collections of environmental or network sensors, and running simulations. Streaming data can also be formulated as queries or transactions which operate on a large dynamic data store, e.g. a distributed database. We describe a lightweight, portable framework named PHISH which enables a set of independent processes to compute on a stream of data in a distributed-memory parallel manner. Datums are routed between processes in patterns defined by the application. PHISH can run on top of either message-passing via MPI or sockets via ZMQ. The former means streaming computations can be run on any parallel machine which supports MPI; the latter allows them to run on a heterogeneous, geographically dispersed network of machines. We illustrate how PHISH can support streaming MapReduce operations, and describe streaming versions of three algorithms for large, sparse graph analytics: triangle enumeration, subgraph isomorphism matching, and connected component finding. Lastly, we also provide benchmark timings for MPI versus socket performance of several kernel operations useful in streaming algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Solving Unit Commitment Problems with Demand Responsive Loads: Preprint

This paper focuses on using variations of the Frank-Wolfe algorithm for solving unit commitment problems with high volumes of demand responsive loads on the power grid. We present a formulation of the unit commitment problem with demand responsive loads. We then show through reformulation and relaxations of the problem that variations of the Frank-Wolfe algorithm can be used to determine the time series decisions for the demand responsive loads. We show through computational experiments on the RTS-GMLC test system that the time series of demand responsive load decisions obtained through our approach are near optimal and provide details regarding how large scale parallel implementations of our approach can be highly computationally efficient.

demand response↗
DOE OSTI2014

Dynamic load balance scheme for the DSMC algorithm

The direct simulation Monte Carlo (DSMC) algorithm, devised by Bird, has been used over a wide range of various rarified flow problems in the past 40 years. While the DSMC is suitable for the parallel implementation on powerful multi-processor architecture, it also introduces a large load imbalance across the processor array, even for small examples. The load imposed on a processor by a DSMC calculation is determined to a large extent by the total of simulator particles upon it. Since most flows are impulsively started with initial distribution of particles which is surely quite different from the steady state, the total of simulator particles will change dramatically. The load balance based upon an initial distribution of particles will break down as the steady state of flow is reached. The load imbalance and huge computational cost of DSMC has limited its application to rarefied or simple transitional flows. In this paper, by taking advantage of METIS, a software for partitioning unstructured graphs, and taking the total of simulator particles in each cell as a weight information, the repartitioning based upon the principle that each processor handles approximately the equal total of simulator particles has been achieved. The computation must pause several times to renew the total of simulator particles in each processor and repartition the whole domain again. Thus the load balance across the processors array holds in the duration of computation. The parallel efficiency can be improved effectively. The benchmark solution of a cylinder submerged in hypersonic flow has been simulated numerically. Besides, hypersonic flow past around a complex wing-body configuration has also been simulated. The results have displayed that, for both of cases, the computational time can be reduced by about 50%.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A Feynman-Kac based numerical method for the exit time probability of a class of transport problems

The exit time probability, which gives the likelihood that an initial condition leaves a prescribed region of the phase space of a dynamical system at, or before, a given time, is arguably one of the most natural and important transport problems. In this work, we present an accurate and efficient numerical method for computing this probability for systems described by non-autonomous (time-dependent) stochastic differential equations (SDEs) or their equivalent Fokker-Planck partial differential equations. The method is based on the direct approximation of the Feynman-Kac formula that establishes a link between the adjoint Fokker-Planck equation and the forward SDE. The Feynman-Kac formula is approximated using the Gauss-Hermite quadrature rules and piecewise cubic Hermite interpolating polynomials, and a GPU accelerated matrix representation is used to compute the entire time evolution of the exit time probability using a single pass of the algorithm. The method is unconditionally stable, exhibits second order convergence in space, first order convergence in time, and it is straightforward to parallelize. Applications are presented to the advection diffusion of a passive tracer in a fluid flow exhibiting chaotic advection, and to the runaway acceleration of electrons in a plasma in the presence of an electric field, collisions, and radiation damping. Benchmarks against analytical solutions as well as comparisons with explicit and implicit finite difference standard methods for the adjoint Fokker-Planck equation are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Non-intrusive, high-resolution, real-time, two-dimensional imaging of multiphase materials using acoustic array sensors

Two parallel multi-element ultrasonic acoustic arrays combined with sets of focal laws for acoustic signal generation and a classical tomographic inversion algorithm are used to generate real-time two-dimensional micro seismic acoustic images of multiphase materials. Proof of concept and calibration measurements were performed for single phase and two phase liquids, uniform polyvinyl chloride (PVC) plates, and aluminum cylinders imbedded in PVC plates. Measurement artefacts, arising from the limited range of viewing angles, and the compromise between data acquisition rate and image quality are discussed. The angle range of scanning and the image resolution were varied, and the effects on the quality of the reproduction of the speed of sound profiles of model solids and liquids with known geometries and compositions were analysed in detail. The best image quality results were obtained for a scanning angle range of [−35°, 35°] at a step size of 2.5° post processed to generate images on a 40 μm square grid. The data acquisition time for high quality images with a 30 mm × 40 mm view field is 10 min. Representation of two-phase solids with large differences in speed of sound between phases and where one phase is dispersed in the form of macroscopic objects (greater than 1 mm in diameter) proved to be the most difficult to image accurately. Liquid-liquid and liquid-vapor phase boundaries, in micro porous solids by contrast, were more readily defined. Displacement of air by water and water by heptane in natural porous limestone provides illustrative kinetic examples. Measurement results with these realistic cases demonstrate the feasibility of the technique to monitor in real time and on the micrometer length scale local composition and flow of organic liquids in inorganic porous media, one of many envisioned engineering applications. Improvement of data acquisition rate is an area for future collaborative study.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2017

CMS readiness for multi-core workload scheduling

In the present run of the LHC, CMS data reconstruction and simulation algorithms benefit greatly from being executed as multiple threads running on several processor cores. The complexity of the Run 2 events requires parallelization of the code to reduce the memory-per- core footprint constraining serial execution programs, thus optimizing the exploitation of present multi-core processor architectures. The allocation of computing resources for multi-core tasks, however, becomes a complex problem in itself. The CMS workload submission infrastructure employs multi-slot partitionable pilots, built on HTCondor and GlideinWMS native features, to enable scheduling of single and multi-core jobs simultaneously. This provides a solution for the scheduling problem in a uniform way across grid sites running a diversity of gateways to compute resources and batch system technologies. This paper presents this strategy and the tools on which it has been implemented. The experience of managing multi-core resources at the Tier-0 and Tier-1 sites during 2015, along with the deployment phase to Tier-2 sites during early 2016 is reported. The process of performance monitoring and optimization to achieve efficient and flexible use of the resources is also described.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Research and Education in Computational Science and Engineering

Over the past two decades the field of computational science and engineering (CSE) has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and educate the scientific and engineering workforce. Informed by centuries of theory and experiment, CSE performs computational experiments to answer questions that neither theory nor experiment alone is equipped to answer. CSE provides scientists and engineers of all persuasions with algorithmic inventions and software systems that transcend disciplines and scales. Carried on a wave of digital technology, CSE brings the power of parallelism to bear on troves of data. Mathematics-based advanced computing has become a prevalent means of discovery and innovation in essentially all areas of science, engineering, technology, and society; and the CSE community is at the core of this transformation. However, a combination of disruptive developments— including the architectural complexity of extreme-scale computing, the data revolution that engulfs the planet, and the specialization required to follow the applications to new frontiers—is redefining the scope and reach of the CSE endeavor. This report describes the rapid expansion of CSE and the challenges to sustaining its bold advances. The report also presents strategies and directions for CSE research and education for the next decade.

computational science and engineering↗
DOE OSTI2024

HydraGNN_Predictive_GFM_2024 - Ensemble of predictive graph foundation models for ground state atomistic materials modeling

We provide the ensemble of fifteen pre-trained graph foundation models (GFMs) for atomistic materials modeling applications. Each one of the fifteen GFMs has been trained on five open-source datasets that (once aggregated) amount to over 154 million atomistic structures, which cover over two-thirds of the natural elements of the periodic table and that comprises a broad set of organic and inorganic compounds. This vast set of atomistic structures comprises ground state configurations that are dynamically stable (i.e., equilibrated structures with atomic forces approximately close to zero values) as well as dynamically unstable structures (i.e., non-equilibrium structures with non-negligible non-zero values of atomic forces). The ensemble of datasets aggregated does NOT include excited states. The datasets have been curated to remove atomistic structures with spectral norm of the force tensor above 100 eV/angstrom. Moreover, a linear term of the energy was computed for each dataset using a linear regression model that uses the chemical concentration of each natural element as regressor. The linear term predicted by the linear regression model has been subtracted from each original energy value to perform a re-alignment of the energy values across different electronic structures approximation theories performed to generate the diverse multi-source, multi-fidelity datasets. The folder "ADIOS_files" contains the set of pre-processed datasets in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used for the development and training of GFMs in this work. The "ADIOS_files" directory contains 6 sub-directories named as follows: - ANI1x-v3.bp - MPTrj-v3.bp - OC2020-20M-v3.bp - OC2020-v3.bp - OC2022-v3.bp - qm7x-v3.bp Each sub-directory contains the pre-processed datasets converted in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used to the development, training, and performance testing of the ensemble go predictive graph foundation models. Each GFM was developed using HydraGNN (https://github.com/ORNL/HydraGNN) as underlying graph neural network (GNN) architecture. The multi-task learning (MTL) capability of HydraGNN was used to simultaneously train the GFMs on labeled values for direct predictions of energy (a total system property of an atomistic structure that measures the chemical stability) and atomic forces (an atomic level property of an atomistic structure that measures the dynamical stability). The hyper parameters of the GFM have been tuned using scalable hyperparameter optimization (HPO) algorithms implemented in the software DeepHyper (https://github.com/deephyper/deephyper). The pre-training of each HPO trial was performed using distributed data parallelism (DDP) to scale the training across 128 compute nodes of the exascale OLCF supercomputer Frontier. Each HPO trial was trained only for 10 epochs and an early stopping was performed to avoid wasting significant computational resources on GNN architectures that were clearly underperforming. For each HPO trial, the 'omnistat' tool developed by (AMD Research - Advanced Micro Device) was used to measure the total energy consumption in kWh. The ensemble of GFMs was obtained by selecting the fifteen best performing HPO trials. Four models have been selected for their clear advantage in accuracy, and these are the GFMs with IDs 229, 156, 147, 260. Additional eleven models have been selected based on judicious balance between accuracy and energy consumption needed for training, and these are the GFMs with IDs 165, 78, 137, 1, 175, 171, 181, 67, 179, 167, 351. Each selected GFM of the ensemble was continued to cumulate a total of at most 30 epochs. In some cases, the total number of epochs actually performed was les than 30 due to two combined factors: (1) the size of the GFM (i.e., the number of model parameters to train) and (2) the total wall-clock time for which the computational resources could be allocated on OLCF-Frontier. The "Ensemble_of_models" directory contains 15 sub-directories named as follows: - gfm_0.229 - gfm_0.156 - gfm_0.147 - gfm_0.260 - gfm_0.165 - gfm_0.78 - gfm_0.137 - gfm_0.1 - gfm_0.175 - gfm_0.171 - gfm_0.181 - gfm_0.67 - gfm_0.179 - gfm_0.167 - gfm_0.351 Each one of these sub-directories refers to one of the fifteen HPO trials that have been selected to continue the pre-training with at most 30 epochs. With each sub-directory associated with a specific HPO trial, the following files can be found: - config.json: file for argument parsing to develop and train an HydraGNN architecture - gfm_0.ID_epoch_N.pk: file with model parameters for HPO ID trial after N epochs of training The ensemble of fifteen GFM architectures was used for (1) ensemble averaging to stabilize the predictions of energy and atomic forces after pre-training for post-processing analysis and (2) ensemble uncertainty quantification (UQ). The code used to develop, pre-train, and load the pre-trained models for post-processing analysis is available on the ORNL-GitHub at the following link: https://github.com/ORNL/HydraGNN/tree/Predictive_GFM_2024

36 MATERIALS SCIENCE↗
DOE OSTI2025

GSplit: Scaling Graph Neural Network Training on Large Graphs via Split-Parallelism

Graph neural networks (GNNs), an emerging class of machine learning models for graphs, have gained popularity for their superior performance in various graph analytical tasks. Mini-batch training is commonly used to train GNNs on large graphs, and data parallelism is the standard approach to scale mini-batch training across multiple GPUs. Data parallel approaches contain redundant work as subgraphs sampled by different GPUs contain significant overlap. To address this issue, we introduce a hybrid parallel mini-batch training paradigm called Split parallelism. Split parallelism avoids redundant work by splitting the sampling, loading, and training of each mini-batch across multiple GPUs. Split parallelism, however, introduces communication overheads that can be more than the savings from removing redundant work. We further present a lightweight partitioning algorithm that probabilistically minimizes these overheads. We implement spllit parllelism in GSplit and show that it outperforms state-of-the-art mini-batch training systems like DGL, Quiver, and P3.

Lim, Seung-Hwan [ORNL] (ORCID:0000000194616866)↗
DOE OSTI2017

An efficient MPI/OpenMP parallelization of the Hartree–Fock–Roothaan method for the first generation of Intel® Xeon Phi™ processor architecture

The Hartree-Fock (HF) method in the quantum chemistry package GAMESS represents one of the most irregular algorithms in computation today. Major steps in the calculation are the irregular computation of electron repulsion integrals (ERIs) and the building of the Fock matrix. These are the central components of the main Self Consistent Field (SCF) loop, the key hotspot in Electronic Structure (ES) codes. By threading the MPI ranks in the official release of the GAMESS code, we not only speed up the main SCF loop (4x to 6x for large systems), but also achieve a significant (>2x) reduction in the overall memory footprint. These improvements are a direct consequence of memory access optimizations within the MPI ranks. We benchmark our implementation against the official release of the GAMESS code on the Intel R Xeon PhiTM supercomputer. Here, scaling numbers are reported on up to 7,680 cores on Intel Xeon Phi coprocessors.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Computer Science Research Needs for Parallel Discrete Event Simulation (PDES)

Historically, scientific computing efforts have demonstrated the clear need for, and effective use of, supercomputing with traditional time-stepped simulations. Nevertheless, there are several areas in the mission spaces of the U.S. Department of Energy and other agencies waiting to tap advanced computing research using a different, discrete event style of modeling, simulation, and analysis. These span a wide spectrum of applications including energy grid resilience, urban planning and policy, transportation science, building technologies, emergency response and planning, environmental impact analysis, computational epidemiology, Internet communications, cyber security, and cyber-physical systems, to name only a few. Even within traditional scientific applications, the role of discrete event modes of execution is increasing in the form of new event-based mathematical solvers such as quantized state integration methods and discrete-continuous hybrid system solvers. Co-design of advanced supercomputing hardware systems is another area that exploits discrete event simulation at its core for effective analyses. Complex systems, entity behaviors and interconnections play a significant role in all these applications, which are mapped to large-scale models with discrete event formulations. To make advancements in all the aforementioned scientific areas, many technical aspects need to be more thoroughly studied and deeply understood in parallel discrete event simulation (PDES). The unique dynamics inherent in a discrete event modeling approach, by their very nature, intersect and influence the entire stack of the computing system, including (a) the unique nature of the instruction sets exercised in PDES workloads without a predominance of high-precision floating point operations, (b) virtual time-constrained multi-threaded execution of many logical processes per processor, (c) extremely variable and difficult to predict network traffic characteristics, (d) interfaces and inter-dependencies with machine learning and artificial intelligence codes at higher software layers, and (e) highly challenging load balancing needs, especially in effectively accounting for accelerated/extremely heterogeneous computing in current and future high-performance computing systems. Efficient and accurate parallel execution of PDES workloads is also dominated by challenges in dealing with their asynchronous concurrency fundamentally present at the model level. Conservative synchronization, optimistic/speculative synchronization, and their hybrid schemes open new questions in fundamental computer science with respect to reversibility of computation and prediction (lookahead) of behaviors inherent within model codes. On the implementation front, there are relatively few scalable, general-purpose parallel discrete event simulators in the world, and even fewer have been studied on emerging hardware platforms. To enable scientific advances using PDES, the research needs in computer science must also be pursued and met in the intersection of the algorithmic and hardware-aware aspects of scalable PDES engines. This report is aimed at capturing a computer science-oriented view of this important area of research in PDES, presenting a sample of important applications with their inherent discrete event technology elements. Needs are outlined in core areas of parallel discrete event research as well as cross-cutting directions in computer science research that positively impact scientific advancements across several important application areas. A selection of priority research opportunities in advanced computing for PDES is identified to serve as reference for key research topics and their order of importance for scientific advancements.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

SU-E-T-499: Initial Developments of An OpenCL-Based Cross-Platform Monte Carlo Dose Engine for Carbon Ion Therapy

Purpose Dose calculation is of critical importance for carbon ion therapy. Monte Carlo (MC) simulation is considered to be the most accurate method for calculation of absorbed dose and of all the more fundamental physical quantities related to biological effects. The long computation time, however, limits its routine clinical applications. We have recently started developing a fast MC package, gCMC for carbon therapy on a parallel processing platform, e.g. GPU, aiming at achieving sufficient efficiency to enable MC in clinically important tasks. This abstract reports our progress. Methods gCMC was developed in OpenCL environment. Our initial developments focused on water material. gCMC supported carbon ion transport in the energy range of 1–450 MeV/u. A Class II condensed history algorithm was implemented for charged particle transport simulations with stopping power computed via Bethe-Bloch equation. Energy straggling and multiple scattering were modeled. Total cross section of nuclear interaction was extracted from Geant4. At present, nuclear interaction events were sampled but transports of secondary particles were not included. Results We tested cases with a homogeneous water phantom and a pencil carbon ion beam with energy of 200–400 MeV/u. When only electro-magnetic channel was included, dose/fluence difference between gCMC and Geant4 results averaged within 10% isodose line was <0.5% of the maximum dose/fluence. After enabling nuclear interactions without transporting secondary particles, dose and fluence agreed with the corresponding results computed by Geant4 with <1% difference. Due to the support for multiple platforms of OpenCL, gCMC was executable on NVidia and AMD GPUs, and Intel CPUs. It took ∼50 sec to transport 107 200MeV/u source carbon ions on an NVidia Titan GPU card. Conclusion Preliminary studies have demonstrated the accuracy and efficiency of gCMC. With further developments in near future, gCMC will potentially achieve clinically acceptable fast and accurate MC simulations for carbon ion therapy.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-C-BRC-06: OpenCL-Based Cross-Platform Monte Carlo Simulation Package for Carbon Ion Therapy

Purpose: Monte Carlo (MC) simulation is considered to be the most accurate method for calculation of absorbed dose and fundamental physical quantities related to biological effects in carbon ion therapy. Its long computation time impedes clinical and research applications. We have developed an MC package, goCMC, on parallel processing platforms, aiming at achieving accurate and efficient simulations for carbon therapy. Methods: goCMC was developed under OpenCL framework. It supported transport simulation in voxelized geometry with kinetic energy up to 450 MeV/u. Class II condensed history algorithm was employed for charged particle transport with stopping power computed via Bethe-Bloch equation. Secondary electrons were not transported with their energy locally deposited. Energy straggling and multiple scattering were modeled. Production of secondary charged particles from nuclear interactions was implemented based on cross section and yield data from Geant4. They were transported via the condensed history scheme. goCMC supported scoring various quantities of interest e.g. physical dose, particle fluence, spectrum, linear energy transfer, and positron emitting nuclei. Results: goCMC has been benchmarked against Geant4 with different phantoms and beam energies. For 100 MeV/u, 250 MeV/u and 400 MeV/u beams impinging to a water phantom, range difference was 0.03 mm, 0.20 mm and 0.53 mm, and mean dose difference was 0.47%, 0.72% and 0.79%, respectively. goCMC can run on various computing devices. Depending on the beam energy and voxel size, it took 20∼100 seconds to simulate 10{sup 7} carbons on an AMD Radeon GPU card. The corresponding CPU time for Geant4 with the same setup was 60∼100 hours. Conclusion: We have developed an OpenCL-based cross-platform carbon MC simulation package, goCMC. Its accuracy, efficiency and portability make goCMC attractive for research and clinical applications in carbon therapy.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Ordering Traces Logically to Identify Lateness in Message Passing Programs

Event traces are valuable for understanding the behavior of parallel programs. However, automatically analyzing a large parallel trace is difficult, especially without a specific objective. We aid this endeavor by extracting a trace's logical structure, an ordering of trace events derived from happened-before relationships, while taking into account developer intent. Using this structure, we can calculate an operation's delay relative to its peers on other processes. The logical structure also serves as a platform for comparing and clustering processes as well as highlighting communication patterns in a trace visualization. We present an algorithm for determining this idealized logical structure from traces of message passing programs, and we develop metrics to quantify delays and differences among processes. We implement our techniques in Ravel, a parallel trace visualization tool that displays both logical and physical timelines. Rather than showing the duration of each operation, we display where delays begin and end, and how they propagate. As a result, we apply our approach to the traces of several message passing applications, demonstrating the accuracy of our extracted structure and its utility in analyzing these codes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

The parallelism motifs of genomic data analysis

Genomic datasets are growing dramatically as the cost of sequencing continues to decline and small sequencing devices become available. Enormous community databases store and share these data with the research community, but some of these genomic data analysis problems require large-scale computational platforms to meet both the memory and computational requirements. These applications differ from scientific simulations that dominate the workload on high-end parallel systems today and place different requirements on programming support, software libraries and parallel architectural design. For example, they involve irregular communication patterns such as asynchronous updates to shared data structures. We consider several problems in high-performance genomics analysis, including alignment, profiling, clustering and assembly for both single genomes and metagenomes. We identify some of the common computational patterns or ‘motifs’ that help inform parallelization strategies and compare our motifs to some of the established lists, arguing that at least two key patterns, sorting and hashing, are missing. This article is part of a discussion meeting issue ‘Numerical algorithms for high-performance computational science’.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

FunM2C: A Filter for Uncertainty Visualization of Multivariate Data on Multi-Core Devices

Uncertainty visualization is an emerging research topic in data visualization because neglecting uncertainty in visualization can lead to inaccurate assessments. In this paper, we study the propagation of multivariate data uncertainty in visualization. Although there have been a few advancements in probabilistic uncertainty visualization of multivariate data, three critical challenges remain to be addressed. First, the state-of-the-art probabilistic uncertainty visualization framework is limited to bivariate data (two variables). Second, existing uncertainty visualization algorithms use computationally intensive techniques and lack support for cross-platform portability. Third, as a consequence of the computational expense, integration into production visualization tools is impractical. In this work, we address all three issues and make a threefold contribution. First, we take a step to generalize the state-of-the-art probabilistic framework for bivariate data to multivariate data with an arbitrary number of variables. Second, through utilization of VTK-m’s shared-memory parallelism and cross-platform compatibility features, we demonstrate acceleration of multivariate uncertainty visualization on different many-core architectures, including OpenMP and AMD GPUs. Third, we demonstrate the integration of our algorithms with the ParaView software. We demonstrate the utility of our algorithms through experiments on multivariate simulation data with three and four variables.

Hari, Gautam↗