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DOE OSTI2025

Dispatch Manager for NEML2 Constitutive Model Calculations Embedded in MOOSE

This report describes the extended capabilities of the NEML2 constitutive modeling library, including a flexible and efficient work dispatching system designed to leverage both CPU and GPU resources. This enhancement addresses one of the primary computational challenges in large-scale simulations: the ability to distribute and execute batches of material model evaluations across heterogeneous computing devices. The new dispatch system introduces a modular set of dispatcher and scheduler classes that coordinate the flow of data and execution between devices. The dispatcher is responsible for efficiently packaging work, managing device-specific memory operations, and synchronizing results. This modularity allows for extensibility, making it straightforward to integrate additional computing backends in the future. From an implementation standpoint, the dispatcher system interfaces seamlessly with NEML2's existing models. They handle device-aware tensor operations, optimize memory transfers, and support asynchronous execution when applicable. This design ensures that batches of material points can be evaluated concurrently, substantially improving throughput compared to previous single-device or serial implementations. These improvements not only enhance the raw performance of NEML2 but also improve its usability in multiscale and high-fidelity simulations, where the simultaneous evaluation of large material point batches is critical. Benchmarks included in the report demonstrate the system’s scalability, highlighting its effectiveness when leveraging modern GPU architectures.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS2016

Retrieval of Macro- and Micro-Physical Properties of Oceanic Hydrosols from Polarimetric Observations

Remote sensing has mainly relied on measurements of scalar radiance and its spectral and angular features to retrieve micro- and macro-physical properties of aerosols/hydrosols. However, it is recognized that measurements that include the polarimetric characteristics of light provide more intrinsic information about particulate scattering. To take advantage of this, we used vector radiative transfer (VRT) simulations and developed an analytical relationship to retrieve the macro and micro-physical properties of the oceanic hydrosols. Specifically, we investigated the relationship between the observed degree of linear polarization (DoLP) and the ratio of attenuation-to- absorption coefficients (c/a) in water, from which the scattering coefficient can be readily computed (b equals c minus a), after retrieving a. This relationship was parameterized for various scattering geometries, including sensor zenith/azimuth angles relative to the Sun's principal plane, and for varying Sun zenith angles. An inversion method was also developed for the retrieval of the microphysical properties of hydrosols, such as the bulk refractive index and the particle size distribution. The DoLP vs c/a relationship was tested and validated against in-situ measurements of underwater light polarization obtained by a custom-built polarimeter and measurements of the coefficients a and c, obtained using an in-water WET (Western Environmental Technologies) Labs ac-s (attenuation coefficients In-Situ Spectrophotometer) instrument package. These measurements confirmed the validity of the approach, with retrievals of attenuation coefficients showing a high coefficient of determination depending on the wavelength. We also performed a sensitivity analysis of the DoLP at the Top of Atmosphere (TOA) over coastal waters showing the possibility of polarimetric remote sensing application for ocean color.

PACE↗

NASA NTRS2011

Space Radiation Effects on Human Cells: Modeling DNA Breakage, DNA Damage Foci Distribution, Chromosomal Aberrations and Tissue Effects

Future long-tem space travel will face challenges from radiation concerns as the space environment poses health risk to humans in space from radiations with high biological efficiency and adverse post-flight long-term effects. Solar particles events may dramatically affect the crew performance, while Galactic Cosmic Rays will induce a chronic exposure to high-linear-energy-transfer (LET) particles. These types of radiation, not present on the ground level, can increase the probability of a fatal cancer later in astronaut life. No feasible shielding is possible from radiation in space, especially for the heavy ion component, as suggested solutions will require a dramatic increase in the mass of the mission. Our research group focuses on fundamental research and strategic analysis leading to better shielding design and to better understanding of the biological mechanisms of radiation damage. We present our recent effort to model DNA damage and tissue damage using computational models based on the physics of heavy ion radiation, DNA structure and DNA damage and repair in human cells. Our particular area of expertise include the clustered DNA damage from high-LET radiation, the visualization of DSBs (DNA double strand breaks) via DNA damage foci, image analysis and the statistics of the foci for different experimental situations, chromosomal aberration formation through DSB misrepair, the kinetics of DSB repair leading to a model-derived spectrum of chromosomal aberrations, and, finally, the simulation of human tissue and the pattern of apoptotic cell damage. This compendium of theoretical and experimental data sheds light on the complex nature of radiation interacting with human DNA, cells and tissues, which can lead to mutagenesis and carcinogenesis later in human life after the space mission.

Ponomarev, A. L.↗

NASA NTRS2004

Simple Models of the Spatial Distribution of Cloud Radiative Properties for Remote Sensing Studies

This project aimed to assess the degree to which estimates of three-dimensional cloud structure can be inferred from a time series of profiles obtained at a point. The work was motivated by the desire to understand the extent to which high-frequency profiles of the atmosphere (e.g. ARM data streams) can be used to assess the magnitude of non-plane parallel transfer of radiation in thc atmosphere. We accomplished this by performing an observing system simulation using a large-eddy simulation and a Monte Carlo radiative transfer model. We define the 3D effect as the part of the radiative transfer that isn't captured by one-dimensional radiative transfer calculations. We assess the magnitude of the 3D effect in small cumulus clouds by using a fine-scale cloud model to simulate many hours of cloudiness over a continental site. We then use a Monte Carlo radiative transfer model to compute the broadband shortwave fluxes at the surface twice, once using the complete three-dimensional radiative transfer F(sup 3D), and once using the ICA F (sup ICA); the difference between them is the 3D effect given.

Source record↗

DOE OSTI2020

Two-phase flow measurements and observations in a cooling panel of the reactor cavity cooling system

The analysis of the flow behavior within a cooling panel of a scaled water-cooled reactor cavity cooling system has been performed supported by high-resolution measurements of the void fraction at the risers’ outlet. The results have shown a stable, symmetric distribution of the flow through the risers during subcooled boiling conditions, characterized by small, slow bubbles with average void fraction lower than 0.3 for all risers. As the temperature increased to saturation, flow distribution appeared strongly asymmetrical and unstable, with peaks of void fraction as high as 0.9. Large, faster bubbles were observed during these peaks, immediately followed by flow of subcooled liquid water. Flow stagnation and inversion has also been observed. The high resolution void fraction results, complemented by the measurements of the coolant flow rate and temperatures, not only have further described the behavior of the system under hypothetical accident conditions, but represent a unique set of data to support the validation of system-level codes, and more advanced computational tools.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

A comparison of probabilistic generative frameworks for molecular simulations

Generative artificial intelligence is now a widely used tool in molecular science. Despite the popularity of probabilistic generative models, numerical experiments benchmarking their performance on molecular data are lacking. Here, in this work, we introduce and explain several classes of generative models, broadly sorted into two categories: flow-based models and diffusion models. We select three representative models: neural spline flows, conditional flow matching, and denoising diffusion probabilistic models, and examine their accuracy, computational cost, and generation speed across datasets with tunable dimensionality, complexity, and modal asymmetry. Our findings are varied, with no one framework being the best for all purposes. In a nutshell, (i) neural spline flows do best at capturing mode asymmetry present in low-dimensional data, (ii) conditional flow matching outperforms other models for high-dimensional data with low complexity, and (iii) denoising diffusion probabilistic models appear the best for low-dimensional data with high complexity. Our datasets include a Gaussian mixture model and the dihedral torsion angle distribution of the Aib9 peptide, generated via a molecular dynamics simulation. We hope our taxonomy of probabilistic generative frameworks and numerical results may guide model selection for a wide range of molecular tasks.

Artificial intelligence↗

DOE OSTI2025

Suppressing the sample variance of DESI-like galaxy clustering with fast simulations

Ongoing and upcoming galaxy redshift surveys, such as the Dark Energy Spectroscopic Instrument (DESI) survey, will observe vast regions of sky and a wide range of redshifts. In order to model the observations and address various systematic uncertainties, N-body simulations are routinely adopted, however, the number of large simulations with sufficiently high mass resolution is usually limited by available computing time. Therefore, achieving a simulation volume with the effective statistical errors significantly smaller than those of the observations becomes prohibitively expensive. In this study, we apply the Convergence Acceleration by Regression and Pooling (CARPool) method to mitigate the sample variance of the DESI-like galaxy clustering in the AbacusSummit simulations, with the assistance of the quasi-N-body simulations FastPM. Based on the halo occupation distribution (HOD) models, we construct different FastPM galaxy catalogs, including the luminous red galaxies (LRGs), emission line galaxies (ELGs), and quasars, with their number densities and two-point clustering statistics well matched to those of AbacusSummit. We also employ the same initial conditions between AbacusSummit and FastPM to achieve high cross-correlation, as it is useful in effectively suppressing the variance. Our method of reducing noise in clustering is equivalent to performing a simulation with volume larger by a factor of 5 and 4 for LRGs and ELGs, respectively. We also mitigate the standard deviation of the LRG bispectrum with the triangular configurations k 2 = 2k 1 = 0.2 h Mpc -1 by a factor of 1.6. With smaller sample variance on galaxy clustering, we are able to constrain the baryon acoustic oscillations (BAO) scale parameters to higher precision. The CARPool method will be beneficial to better constrain the theoretical systematics of BAO, redshift space distortions (RSD) and primordial non-Gaussianity (NG).

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

SU-F-T-279: Impact of Beam Energy Drifts On IMRT Delivery Accuracy

Purpose: According to TG-40 percent-depth-dose (PDD) tolerance is ±2% but TG-142 is ±1%. Now the question is, which one is relevant in IMRT era? The primary objective of this study is to evaluate dosimetric impact of beam-energy-drifts on IMRT-delivery. Methods: Beam-energy drifts were simulated by adjusting Linac’s bending-magnet-current (BMC) followed by tuning the pulse-forming network and adjusting gun-current. PDD change of −0.6% and +1.2% were tested. Planar-dosimetry measurements were performed using an ionization-chamber-array in solid-water phantoms. Study includes 10-head-and-neck and 3-breast cancer patients. en-face beam-deliveries were also tested at 1.3cm and 5.3cm depths. Composite and single-field dose-distributions were compared against the plans to determine %Gamma pass-rates (%GPRs). For plan dose comparisons, changes in %Gamma pass-rates (cPGPRs) were computed/reported to exclude the differences between dose-computation and delivery. Dose distributions of the drifted-energies were compared against their baseline measurements to determine the% GPRs. A Gamma criteria of 3%/3mm was considered for plan-dose comparisons while 3%/1mm used for measured dose intercomparisons. Results: For composite-dose delivery, average cPGPRs were 0.41%±2.48% and −2.54%±3.65% for low-energy (LE) and high-energy (HE) drifts, respectively. For measured dose inter-comparisons, the average%GPRs were 98.4%±2.2% (LE-drift) and 95.8%±4.0 (HE-drift). The average %GPR of 92.6%±4.3% was noted for the worst-case scenario comparing LE-drift to HE-drift. All en-face beams at 5.3 cm depth have cPGPRs within ±4% of the baseline-energy measurements. However, greater variations were noted for 1.3cm depth. Average %GPRs for drifted energies were >99% at 5.3cm and >97% at 1.3cm depths. However, for the worst-case scenario (LE-drift to HE-drift) these numbers dropped to 95.2% at 5.3cm and 93.1% at 1.3cm depths. Conclusion: The dosimetric impact of beam-energy drifts was found to be within clinically acceptable tolerance. However, this study includes a single energy with limited range of PDD change. Further studies are on going and the results will be presented. Received funding from Varian Medical Systems, Palo Alto, CA.

60 APPLIED LIFE SCIENCES↗

NASA NTRS2001

Probabilistic Structural Analysis and Reliability Using NESSUS With Implemented Material Strength Degradation Model

This project included both research and education objectives. The goal of this project was to advance innovative research and education objectives in theoretical and computational probabilistic structural analysis, reliability, and life prediction for improved reliability and safety of structural components of aerospace and aircraft propulsion systems. Research and education partners included Glenn Research Center (GRC) and Southwest Research Institute (SwRI) along with the University of Texas at San Antonio (UTSA). SwRI enhanced the NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) code and provided consulting support for NESSUS-related activities at UTSA. NASA funding supported three undergraduate students, two graduate students, a summer course instructor and the Principal Investigator. Matching funds from UTSA provided for the purchase of additional equipment for the enhancement of the Advanced Interactive Computational SGI Lab established during the first year of this Partnership Award to conduct the probabilistic finite element summer courses. The research portion of this report presents the cumulation of work performed through the use of the probabilistic finite element program, NESSUS, Numerical Evaluation and Structures Under Stress, and an embedded Material Strength Degradation (MSD) model. Probabilistic structural analysis provided for quantification of uncertainties associated with the design, thus enabling increased system performance and reliability. The structure examined was a Space Shuttle Main Engine (SSME) fuel turbopump blade. The blade material analyzed was Inconel 718, since the MSD model was previously calibrated for this material. Reliability analysis encompassing the effects of high temperature and high cycle fatigue, yielded a reliability value of 0.99978 using a fully correlated random field for the blade thickness. The reliability did not change significantly for a change in distribution type except for a change in distribution from Gaussian to Weibull for the centrifugal load. The sensitivity factors determined to be most dominant were the centrifugal loading and the initial strength of the material. These two sensitivity factors were influenced most by a change in distribution type from Gaussian to Weibull. The education portion of this report describes short-term and long-term educational objectives. Such objectives serve to integrate research and education components of this project resulting in opportunities for ethnic minority students, principally Hispanic. The primary vehicle to facilitate such integration was the teaching of two probabilistic finite element method courses to undergraduate engineering students in the summers of 1998 and 1999.

Bast, Callie C.↗

DOE OSTI2016

Comparison of Surrogate Models with Physical Models for Dynamic Probabilistic Risk Analysis Using the RAVEN Code

Dynamic probabilistic risk analysis (DPRA) has emerged in the nuclear industry as an effective tool to identify points of weakness in nuclear reactors and create a comprehensive approach to quantifying risk. While DPRA allows for detailed analysis, it usually requires thousands of runs due to the necessity of exploring low probability, high consequence events, which can be computationally prohibitively difficult to assess. Risk Analysis Virtual Environment (RAVEN) is a software package being developed under the Nuclear Energy Advanced Modeling and Simulation program at the Idaho National Laboratory. It is able to manage complex control logic to drive a RELAP-7 simulation and to handle sampling strategies including Monte Carlo, Latin Hypercube, Grid and Adaptive samplers. By performing a thorough investigation of the possibility space of an accident scenario with RELAP-7, RAVEN is able to identify consequences of accident scenarios that have not been encountered. The most computational resource intensive step of a RAVEN analysis is running the RELAP-7 code modeling the physical system behavior. Using surrogate models to represent the outcomes of more complex simulations rather than the full model can greatly reduce the computation effort required. In situations where the uncertainty distributions of a model are unknown, or when there are multiple sets of uncertainty distributions, DPRA generally requires rerunning the physical model for each set of uncertainty distributions used. By taking an unbiased sample of the physical model and creating a surrogate model from the results, the surrogate model can be sampled under a different set of uncertainty distributions to provide equivalent results. This paper presents an example of this approach. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

NASA NTRS2002

Effects of Ordering Strategies and Programming Paradigms on Sparse Matrix Computations

The Conjugate Gradient (CG) algorithm is perhaps the best-known iterative technique to solve sparse linear systems that are symmetric and positive definite. For systems that are ill-conditioned, it is often necessary to use a preconditioning technique. In this paper, we investigate the effects of various ordering and partitioning strategies on the performance of parallel CG and ILU(O) preconditioned CG (PCG) using different programming paradigms and architectures. Results show that for this class of applications: ordering significantly improves overall performance on both distributed and distributed shared-memory systems, that cache reuse may be more important than reducing communication, that it is possible to achieve message-passing performance using shared-memory constructs through careful data ordering and distribution, and that a hybrid MPI+OpenMP paradigm increases programming complexity with little performance gains. A implementation of CG on the Cray MTA does not require special ordering or partitioning to obtain high efficiency and scalability, giving it a distinct advantage for adaptive applications; however, it shows limited scalability for PCG due to a lack of thread level parallelism.

Oliker, Leonid↗

DOE OSTI2025

Real-Time Lifetime Prediction of Semiconductor Devices Using Hardware-in-the-Loop

This paper presents a unique approach to enable real-time lifespan prediction of semiconductor power modules using a Hardware-in-the-Loop (HIL) system. By integrating the module's overall loss characteristics-specifically switching and conduction losses-with a thermoelectric model of the thermal management system, this research demonstrates that the model can dynamically estimates the junction temperature profile of the semiconductor devices in response to a changing torque demand profile for the motor drive system. This capability enables continuous monitoring of the module's operational time and cumulative stress induced on the devices to compute accumulated remaining lifetime or time-to-failure (TTF). This study provides an architectural framework for the HIL system with high-fidelity component models of multiple physical domains, allowing simulation of dynamic behaviors of a closely-coupled motor drive system. The advanced real-time computation and measurement functionalities of the HIL system allow for both dynamic lifetime calculations based on simulated data and aggregate lifetime predictions utilizing historical data. Moreover, this paper details an algorithm that not only computes cumulative damage but also synthesizes these data into a comprehensive aggregated lifetime metric. This methodology can enhance the maintenance scheduling strategies and operational reliability of semiconductor devices in critical applications, ultimately extending their service life while optimizing performance.

hardware-in-the-loop (HIL)↗

DOE OSTI2021

A New Class of AMG Interpolation Methods Based on Matrix-Matrix Multiplications

A new class of distance-two interpolation methods for algebraic multigrid (AMG) that can be formulated in terms of sparse matrix-matrix multiplications is presented and analyzed. Compared with similar distance-two prolongation operators, the proposed algorithms exhibit improved efficiency and portability to various computing platforms, since they allow one to easily exploit existing high-performance sparse matrix kernels. The new interpolation methods have been implemented in hypre, a widely used parallel multigrid solver library. With the proposed interpolations, the overall time of hypre's BoomerAMG setup can be considerably reduced, while sustaining equivalent, sometimes improved, convergence rates. Numerical results for a variety of test problems on parallel machines are presented that support the superiority of the proposed interpolation operators over the existing ones in hypre.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2003

GSRP/David Marshall: Fully Automated Cartesian Grid CFD Application for MDO in High Speed Flows

With the renewed interest in Cartesian gridding methodologies for the ease and speed of gridding complex geometries in addition to the simplicity of the control volumes used in the computations, it has become important to investigate ways of extending the existing Cartesian grid solver functionalities. This includes developing methods of modeling the viscous effects in order to utilize Cartesian grids solvers for accurate drag predictions and addressing the issues related to the distributed memory parallelization of Cartesian solvers. This research presents advances in two areas of interest in Cartesian grid solvers, viscous effects modeling and MPI parallelization. The development of viscous effects modeling using solely Cartesian grids has been hampered by the widely varying control volume sizes associated with the mesh refinement and the cut cells associated with the solid surface. This problem is being addressed by using physically based modeling techniques to update the state vectors of the cut cells and removing them from the finite volume integration scheme. This work is performed on a new Cartesian grid solver, NASCART-GT, with modifications to its cut cell functionality. The development of MPI parallelization addresses issues associated with utilizing Cartesian solvers on distributed memory parallel environments. This work is performed on an existing Cartesian grid solver, CART3D, with modifications to its parallelization methodology.

Source record↗

DOE OSTI2016

TH-AB-207A-06: The Use of Realistic Phantoms to Predict CT Dose to Pediatric Patients

Purpose: To predict pediatric patient dose from diagnostic CT scans using Monte Carlo simulation of realistic reference phantoms of various ages, weights, and heights. Methods: A series of deformable pediatric reference phantoms using Non-Uniform Rational B-Splines (NURBS) was developed for a large range of ages, percentiles, and reference anatomy. Individual bones were modeled using age-dependent factors, and red marrow was modeled as functions of age and spatial distribution based on Cristy1. Organ and effective doses for the phantom series were calculated using Monte Carlo simulation of chest, abdominopelvic, and chest-abdomen-pelvis CT exams. Non-linear regression was performed to determine the relationship between dose-length-product (DLP)-normalized organ and effective doses and phantom diameter. Patient-specific voxel computational phantoms were also created by manual segmentation of previously acquired CT images for 40 pediatric patients (0.7 to 17 years). Organ and effective doses were determined by Monte Carlo simulation of these patient-specific phantoms. Each patient was matched to the closest pediatric reference phantom based primarily on age and diameter for all major organs within the torso. Results: A total of 80 NURBS phantoms were created ranging from newborn to 15 years with height/weight percentiles from 10 to 90%. Organ and effective dose normalized by DLP correlated strongly with exponentially decreasing average phantom diameter (R{sup 2} > 0.95 for most organs). A similar relationship was determined for the patient-specific voxel phantoms. Differences between patient-phantom matched organ-dose values ranged from 0.37 to 2.39 mGy (2.87% to 22.1%). Conclusion: Dose estimation using NURBS-based pediatric reference phantoms offers the ability to predict patient dose before and after CT examinations, and physicians and scientists can use this information in their analysis of dose prescriptions for particular subjects and study types. This may lead to practices that minimize radiation dose while still achieving high quality images and, ultimately, improved patient care. NIH/NCI 1 R01 CA155400-01A1.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2024

Forecasting high-dimensional spatio-temporal systems from sparse measurements

This paper introduces a new neural network architecture designed to forecast high-dimensional spatio-temporal data using only sparse measurements. The architecture uses a two-stage end-to-end framework that combines neural ordinary differential equations (NODEs) with vision transformers. Initially, our approach models the underlying dynamics of complex systems within a low-dimensional space; and then it reconstructs the corresponding high-dimensional spatial fields. Many traditional methods involve decoding high-dimensional spatial fields before modeling the dynamics, while some other methods use an encoder to transition from high-dimensional observations to a latent space for dynamic modeling. In contrast, our approach directly uses sparse measurements to model the dynamics, bypassing the need for an encoder. This direct approach simplifies the modeling process, reduces computational complexity, and enhances the efficiency and scalability of the method for large datasets. We demonstrate the effectiveness of our framework through applications to various spatio-temporal systems, including fluid flows and global weather patterns. Although sparse measurements have limitations, our experiments reveal that they are sufficient to forecast system dynamics accurately over long time horizons. Our results also indicate that the performance of our proposed method remains robust across different sensor placement strategies, with further improvements as the number of sensors increases. This robustness underscores the flexibility of our architecture, particularly in real-world scenarios where sensor data is often sparse and unevenly distributed.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1990

Probabilistic analysis of a materially nonlinear structure

A probabilistic finite element program is used to perform probabilistic analysis of a materially nonlinear structure. The program used in this study is NESSUS (Numerical Evaluation of Stochastic Structure Under Stress), under development at Southwest Research Institute. The cumulative distribution function (CDF) of the radial stress of a thick-walled cylinder under internal pressure is computed and compared with the analytical solution. In addition, sensitivity factors showing the relative importance of the input random variables are calculated. Significant plasticity is present in this problem and has a pronounced effect on the probabilistic results. The random input variables are the material yield stress and internal pressure with Weibull and normal distributions, respectively. The results verify the ability of NESSUS to compute the CDF and sensitivity factors of a materially nonlinear structure. In addition, the ability of the Advanced Mean Value (AMV) procedure to assess the probabilistic behavior of structures which exhibit a highly nonlinear response is shown. Thus, the AMV procedure can be applied with confidence to other structures which exhibit nonlinear behavior.

Millwater, H. R.↗

DOE OSTI2017

Frog: Asynchronous Graph Processing on GPU with Hybrid Coloring Model

GPUs have been increasingly used to accelerate graph processing for complicated computational problems regarding graph theory. Many parallel graph algorithms adopt the asynchronous computing model to accelerate the iterative convergence. Unfortunately, the consistent asynchronous computing requires locking or atomic operations, leading to significant penalties/overheads when implemented on GPUs. As such, coloring algorithm is adopted to separate the vertices with potential updating conflicts, guaranteeing the consistency/correctness of the parallel processing. Common coloring algorithms, however, may suffer from low parallelism because of a large number of colors generally required for processing a large-scale graph with billions of vertices. We propose a light-weight asynchronous processing framework called Frog with a preprocessing/hybrid coloring model. The fundamental idea is based on Pareto principle (or 80-20 rule) about coloring algorithms as we observed through masses of realworld graph coloring cases. We find that a majority of vertices (about 80%) are colored with only a few colors, such that they can be read and updated in a very high degree of parallelism without violating the sequential consistency. Accordingly, our solution separates the processing of the vertices based on the distribution of colors. In this work, we mainly answer three questions: (1) how to partition the vertices in a sparse graph with maximized parallelism, (2) how to process large-scale graphs that cannot fit into GPU memory, and (3) how to reduce the overhead of data transfers on PCIe while processing each partition. Here, we conduct experiments on real-world data (Amazon, DBLP, YouTube, RoadNet-CA, WikiTalk and Twitter) to evaluate our approach and make comparisons with well-known non-preprocessed (such as Totem, Medusa, MapGraph and Gunrock) and preprocessed (Cusha) approaches, by testing four classical algorithms (BFS, PageRank, SSSP and CC). On all the tested applications and datasets, Frog is able to significantly outperform existing GPU-based graph processing systems except Gunrock and MapGraph. MapGraph gets better performance than Frog when running BFS on RoadNet-CA. The comparison between Gunrock and Frog is inconclusive. Frog can outperform Gunrock more than 1.04X when running PageRank and SSSP, while the advantage of Frog is not obvious when running BFS and CC on some datasets especially for RoadNet-CA.

97 MATHEMATICS AND COMPUTING↗