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DOE OSTI2024

Celeritas Midterm SciDAC Report

Celeritas is a new Monte Carlo (MC) code that helps satisfy the increasing demand for high energy physics (HEP) detector simulation, using Graphics Processing Unit (GPU) hardware on high performance computing (HPC) systems to model Large Hadron Collider (LHC) experiments and beyond. This report details the project’s progress midway through its SciDAC funding period, highlighting the first complete implementation of standard electromagnetic (EM) physics on GPUs, initial results for performance and scalability on Leadership Computing Facilities (LCFs), and preliminary integration into the CMS and ATLAS experiments. By integrating HEP domain knowledge with expertise in MC transport, Celeritas has catalyzed a shift in the HEP community’s perception of GPU platforms as the future for HPC simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

MARS-F/K modeling of plasma response and fast ion losses due to RMP in KSTAR

Abstract The toroidal single-fluid magnetohydrodynamic (MHD) code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) and the MHD-kinetic hybrid code MARS-K (Liu et al 2008 Phys. Plasmas 15 112503) are utilized to study the plasma response to the n = 1 ( n is the toroidal mode number) resonant magnetic perturbation (RMP), applied to suppress the type-I edge localized mode (ELM) in a KSTAR discharge. Both the resistive-rotating and ideal-static plasma models identify strong screening of the resonant radial field harmonics of the applied RMP due to the plasma response, and predict a strong edge-peeling response of the plasma which is consistent with the optimal ELM control coil current configuration adopted in experiment. The RMP-induced radial displacement of the plasma, computed by the resistive-rotating plasma model, agrees reasonably well with that reconstructed from the measured data in the plasma core. Taking into account the drift kinetic response of fast ions, MARS-K hybrid modeling also finds quantitative agreement of the plasma core fluid pressure perturbation with experiment. Based on the MARS-F computed plasma response, a guiding-center orbit-tracing simulation finds about 0.3% of fast ion losses due the n = 1 RMP in the KSTAR ELM control experiment considered. Most losses are associated with counter-current fast ions located near the plasma edge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2018

Computing resonant modes of accelerator cavities by solving nonlinear eigenvalue problems via rational approximation

Here, we present an efficient and reliable algorithm for solving a class of nonlinear eigenvalue problems arising from the modeling of particle accelerator cavities. The eigenvalue nonlinearity in these problems results from the use of waveguides to couple external power sources or to allow certain excited electromagnetic modes to exit the cavity. We use a rational approximation to reduce the nonlinear eigenvalue problem first to a rational eigenvalue problem. We then apply a special linearization procedure to turn the rational eigenvalue problem into a larger linear eigenvalue problem with the same eigenvalues, which can be solved by existing iterative methods. By using a compact scheme to represent both the linearized operator and the eigenvectors to be computed, we obtain a numerical method that only involves solving linear systems of equations of the same dimension as the original nonlinear eigenvalue problem. We refer to this method as a compact rational Krylov (CORK) method. We implemented the CORK method in the Omega3P module of the Advanced Computational Electromagnetic 3D Parallel (ACE3P) simulation suite and validated it by comparing the computed cavity resonant frequencies and damping Q factors of a small model problem to those obtained from a fitting procedure that uses frequency responses computed by another ACE3P module called S3P. We also used the CORK method to compute trapped modes damped in an ideal eight 9-cell SRF cavity cryomodule. This was the first time it was possible to compute these modes directly. The damping Q factors of the computed modes match well with those measured in experiments and the difference in resonant frequencies is within the range introduced by cavity imperfection. Therefore, the CORK method is an extremely valuable tool for computational cavity design.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Early experiences evaluating the HPE/Cray ecosystem for AMD GPUs

Summary The Oak Ridge Leadership Computing Facility (OLCF) has a long history of supporting and promoting GPU‐accelerated computing starting with the deployment of the Titan supercomputer in 2021 and continuing with the Summit supercomputer which has a theoretical peak performance of approximately 200 petaflops. Because the majority of Summit's computational power comes from its 27,972 GPUs, users must port their applications to one of the supported programming models in order to make efficient use of the system. To prepare the transition to Frontier, the OLCF's exascale supercomputer, users will need to adapt to an entirely new ecosystem which will include new hardware and software technologies. First, users will need to familiarize themselves with the AMD Radeon GPU architecture. Furthermore, users who have been previously relying on CUDA will need to transition to the Heterogeneous‐Computing Interface for Portability (HIP) or one of the other supported programming models (e.g., OpenMP, OpenACC). In this work, we describe our initial experiences and lessons learned in porting three applications or proxy apps currently running on Summit to the HPE/Cray ecosystem to leverage the compute power from AMD GPUs: minisweep, GenASiS, and Sparkler. Each one is representative of current production workloads utilized at the OLCF, different programming languages, and different programming models.

Melesse Vergara, Verónica G.↗

DOE OSTI2017

A New Look at Historic CRAC 'Divergence' Experiments - Implications for a CAAS Minimum Accident of Concern

This paper examines power history parameters and results based on historic fissile solution criticality 'divergence' experiments (referenced here as Divergence Experiments) from the 1960's-70's' Consequences Radiologiques d'un Accident de Criticite' (CRAC) campaign. The results from specific Divergence Experiments have implications for an ANSI/ANS-8.3 (1997) Criticality Accident Alarm System (CAAS) Minimum Accident of Concern (MAC). Specifically, this paper examines select CRAC Divergence Experiments in conjunction with 'qualifying reactivity additions' for a MAC defined by an absolute time constraint. A previous paper presented at the 2011 International Conference on Nuclear Criticality (ICNC 2011) illustrated the differences in 'qualifying reactivity additions' above delayed critical (and below prompt) for a variety of MAC constructs. That paper was the first to examine delayed critical kinetics in greater detail over a range of process and MAC considerations. The ICNC2011 work did not consider an absolute MAC time constraint from the excursion onset and assumed an initial excursion power. That study evaluated MAC constructs based on 'relative time differences' between reaching a specific fission rate and total fissions. The work presented here thus picks up where the ICNC2011 study left off. The primary focus of this work provides simulated power histories for specific Divergence Experiments that served as a basis for justifying a MAC noted in ANS-8.3 Appendix A. This paper documents computational modeling and dynamic multiphysics simulation with known Divergence Experiment parameters for reactivity additions at, below, and above the reported terminal reactivity. The initial step considers replicating what could be a reasonable power history for the terminal reactivity addition to the extent the same peak power and total fissions are obtained over the total time considered. Power histories for all other reactivity additions are simulated by varying the input reactivity and solution heights for the same model. A relationship is obtained between reactivity addition and the time to reach specific MAC power and fission levels within a given time constraint (e.g. 60 s). The 'qualifying reactivity addition' is determined for the total MAC fissions within that time. This value is then compared to the historic terminal value (e.g. $0.33) or any other values (e.g. 'excess reactivity of only a few cents') noted in ANS-8.3 Appendix A. In general, calculated MAC power levels have ranged from 1.8 kW to 173 kW depending on material type and form, H/U, enrichment, critical volume, and dose response function. A minimum accident consideration noted a SHEBA experiment with an excess reactivity 7 cents above delayed critical (TD ∼110 s). This excursion provided an additional 10{sup 15} fissions after an undetermined buildup time resulting in a 'few times 10{sup 15} fissions'. ICNC 2011 LEU solutions calculations show 0.2 Gy in air corresponds to 1.4 x10{sup 16} fissions. Thus, while historically, 0.2 Gy has been loosely associated with 'several times 10{sup 15} fissions', in reality, the actual total fissions could be an order of magnitude larger, and the power associated with 0.2 Gy/min (7.5 kW) larger as well. The reactivity addition required to obtain the actual 0.2 Gy total fissions over 60 s could be much larger than considered. Another reason the qualifying reactivity level could be larger than previously noted, involves temperature reactivity feedback. Compensated reactivity results in a departure from a pure exponential power rise, increasing the doubling time (TD) as the excursion approaches peak power. Uncompensated reactivity additions and constant TD have been traditionally assumed for a pure exponential power rise through the kW range to determine either total MAC fissions, power, or arrival time to these values.

42 ENGINEERING↗

DOE OSTI2021

Oxidation and pyrolysis of methyl propyl ether

The ignition, oxidation, and pyrolysis chemistry of methyl propyl ether (MPE) was probed experimentally at several different conditions, and a comprehensive chemical kinetic model was constructed to help understand the observations, with many of the key parameters computed using quantum chemistry and transition state theory. Experiments were carried out in a shock tube measuring time variation of CO concentrations, in a flow tube measuring product concentrations, and in a rapid compression machine (RCM) measuring ignition delay times. The detailed reaction mechanism was constructed using the Reaction Mechanism Generator software. Sensitivity and flux analyses were used to identify key rate and thermochemical parameters, which were then computed using quantum chemistry to improve the mechanism. Validation of the final model against the 1-20 bar 600-1500 K experimental data is presented with a discussion of the kinetics. The model is in excellent agreement with most of the shock tube and RCM data. Strong non-monotonic variation in conversion and product distribution is observed in the flow-tube experiments as the temperature is increased, and unusually strong pressure dependence and significant heat release during the compression stroke is observed in the RCM experiments. These observations are largely explained by a close competition between radical decomposition and addition to O2 at different sites in MPE; this causes small shifts in conditions to lead to big shifts in the dominant reaction pathways. The validated mechanism was used to study the chemistry occurring during ignition in a diesel engine, simulated using Ignition Quality Test (IQT) conditions. At the IQT conditions, where the MPE concentration is higher, bimolecular reactions of peroxy radicals are much more important than in the RCM.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Hydro-mechanical behavior of heated bentonite buffer for geologic disposal of high-level radioactive waste: A bench-scale X-ray computed tomography investigation

The behavior of heated bentonite buffer is critical for the security and long-term performance of a geological repository for high-level radioactive waste (HLW). While laboratory column experiments have been conducted to investigate compacted bentonite and coupled THMC (thermal-hydro-mechanical and chemical) processes for a moderate temperature range of up to 100 °C, data for a higher temperature range are limited. Understanding bentonite behavior and coupled THMC processes under higher temperatures (e.g., up to 200 °C) could allow for a more economic repository design and would expand the data and knowledge base for more reliable modeling. In this study, a bench-scale experiment was conducted in a compacted bentonite column experiencing both heating up to 200 °C in the center and hydration from a sand-clay boundary surrounding the column. During the experiment run for 1.5 years, frequent X-ray computed tomography (CT) scanning of bentonite provided insights into the spatiotemporal evolution of (1) hydration/dehydration, (2) clay swelling/shrinkage, (3) displacement, and (4) mineral precipitation. After the experiment, a comprehensive post-dismantling characterization of bentonite samples was conducted. Results showed that the bentonite hydration was axi-symmetrical despite the initial heterogeneity due to packing, confirming the ability of bentonite to seal fast flow/transport paths. Further, compared to a non-heated control experiment, the heated column showed greater CT density variations along the radial distance, indicating that homogenization of bentonite might be more difficult if a temperature gradient is maintained in the repository. Precipitation of an anhydrite layer occurred in the inner hot zone, pointing to potential concerns about salt precipitation causing canister corrosion. Ultimately, the experiments provided a high-resolution window into the strongly dynamic and coupled behavior of bentonite exposed to heating, hydration and swelling, which will be valuable for improving modeling of coupled processes, especially for the early state of a HLW repository.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2017

Virtual machine provisioning, code management, and data movement design for the Fermilab HEPCloud Facility

The Fermilab HEPCloud Facility Project has as its goal to extend the current Fermilab facility interface to provide transparent access to disparate resources including commercial and community clouds, grid federations, and HPC centers. This facility enables experiments to perform the full spectrum of computing tasks, including data-intensive simulation and reconstruction. We have evaluated the use of the commercial cloud to provide elasticity to respond to peaks of demand without overprovisioning local resources. Full scale data-intensive workflows have been successfully completed on Amazon Web Services for two High Energy Physics Experiments, CMS and NOνA, at the scale of 58000 simultaneous cores. This paper describes the significant improvements that were made to the virtual machine provisioning system, code caching system, and data movement system to accomplish this work. The virtual image provisioning and contextualization service was extended to multiple AWS regions, and to support experiment-specific data configurations. A prototype Decision Engine was written to determine the optimal availability zone and instance type to run on, minimizing cost and job interruptions. We have deployed a scalable on-demand caching service to deliver code and database information to jobs running on the commercial cloud. It uses the frontiersquid server and CERN VM File System (CVMFS) clients on EC2 instances and utilizes various services provided by AWS to build the infrastructure (stack). We discuss the architecture and load testing benchmarks on the squid servers. We also describe various approaches that were evaluated to transport experimental data to and from the cloud, and the optimal solutions that were used for the bulk of the data transport. Finally, we summarize lessons learned from this scale test, and our future plans to expand and improve the Fermilab HEP Cloud Facility.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

Efficient Discovery of Novel Multicomponent Mixtures for Hydrogen Storage: A Combined Computational/Experimental Approach

The objective of the proposed program is to discover novel mixed hydrides for hydrogen storage, which enable the DOE 2010 system-level goals. Our goal is to find a material that desorbs 8.5 wt.% H 2 or more at temperatures below 85°C. The research program will combine first-principles calculations of reaction thermodynamics and kinetics with material and catalyst synthesis, testing, and characterization. We will combine materials from distinct categories (e.g., chemical and complex hydrides) to form novel multicomponent reactions. Systems to be studied include mixtures of complex hydrides and chemical hydrides [e.g. LiNH 2+ NH 3 BH 3 ] and nitrogen-hydrogen based borohydrides [e.g. Al(BH 4 ) 3 (NH 3 ) 3 ]. The 2010 and 2015 FreedomCAR/DOE targets for hydrogen storage systems are very challenging, and cannot be met with existing materials. The vast majority of the work to date has delineated materials into various classes, e.g., complex and metal hydrides, chemical hydrides, and sorbents. However, very recent studies indicate that mixtures of storage materials, particularly mixtures between various classes, hold promise to achieve technological attributes that materials within an individual class cannot reach. Our project involves a systematic, rational approach to designing novel multicomponent mixtures of materials with fast hydrogenation/dehydrogenation kinetics and favorable thermodynamics using a combination of state-of-the-art scientific computing and experimentation. We will use the accurate predictive power of first-principles modeling to understand the thermodynamic and microscopic kinetic processes involved in hydrogen release and uptake and to design new material/catalyst systems with improved properties. Detailed characterization and atomic-scale catalysis experiments will elucidate the effect of dopants and nanoscale catalysts in achieving fast kinetics and reversibility. And, state-of-the-art storage experiments will give key storage attributes of the investigated reactions, validate computational predictions, and help guide and improve computational methods. In sum, our approach involves a powerful blend of: 1) H2 Storage measurements and characterization, 2) State-of-the-art computational modeling, 3) Detailed catalysis experiments, 4) In-depth automotive perspective.

08 HYDROGEN↗

DOE OSTI2026

The Road to Useful Quantum Computers

Building a useful quantum computer is a grand science and engineering challenge, currently pursued intensely by teams around the world. In the 1980s, Richard Feynman and Yuri Manin observed independently that computers based on quantum mechanics might enable better simulations of quantum phenomena. Their vision remained an intellectual curiosity until Peter Shor published his famous quantum algorithm for integer factoring, and shortly thereafter a proof that errors in quantum computations can be corrected. Since then, quantum computing R&D has progressed rapidly, from small-scale experiments in university physics laboratories to well-funded industrial efforts and prototypes. Hype notwithstanding, quantum computers have yet to solve scientifically or practically important problems -- a target often called quantum utility. In this article, we describe the capabilities of contemporary quantum computers, compare them to the requirements of quantum utility, and illustrate how to track progress from today to utility. We highlight key science and engineering challenges on the road to quantum utility, touching on relevant aspects of our own research.

Emerging Technologies (cs.ET)↗

DOE OSTI2021

Acoustic velocity and permeability of acidized and propped fractures in shale

We report that from geochemical reactions to proppant emplacement, hydraulic fracturing induces various chemomechanical fracture alterations in shale reservoirs. Hydraulic fracturing through the injection of a vast amount and variety of fluids and proppants has substantial impacts on fluid flow and hydrocarbon production. There is a strong need to improve our understanding on how fracture alterations affect flow pathways within the stimulated rock volume and develop monitoring tools. We have conducted time-lapse rock-physics experiments on clay-rich (carbonate-poor) Marcellus shales to characterize the acoustic velocity and permeability responses to fracture acidizing and propping. Acoustic P- and S-wave velocities and fracture permeability were measured before and after laboratory-induced fracture alterations along with microstructural imaging through X-ray computed tomography and scanning electron microscopy. Our experiments indicate that the S-wave velocity is an important geophysical observable, particularly the S-wave polarized perpendicular to fractures because it is sensitive to fracture stiffness. The acidizing and propping of a fracture decrease its elastic stiffness. This effect is stronger for acidizing, so it is possible that proppant monitoring will be masked by chemical alteration except when propping is highly efficient (i.e., most fractures are propped). However, fracture permeability is undermined by the softening of fracture surfaces due to acidizing, while being greatly enhanced by propping. These contrasting effects on fluid flow in combination with similar seismic attributes indicate the importance of experiments to improve existing rock-physics models, which must include changes to the rock frame. Such improvements are necessary for a correct interpretation of seismic velocity monitoring of flow pathways in stimulated shales.

58 GEOSCIENCES↗

DOE OSTI2019

Integrating in situ TEM experiments and atomistic simulations for defect mechanics

With recent advances in computational modeling and in situ transmission electron microscopy (TEM) technologies, there have been increased efforts to apply these approaches to understand defect-based mechanisms dictating deformation mechanics. In situ TEM experiments and atomistic simulations each have their own unique limitations, including observable length and time scales and accessibility of information, motivating approaches that combine the two approaches. In this paper, we review recent studies that combine atomistic simulations and in situ TEM experiments to understand defect mechanisms associated with deformation of metals and alloys. In addition, we discuss ongoing developments in characterization and simulation capabilities that are expected to significantly advance the field of defect mechanics and allow greater integration between atomistic simulations and in situ TEM experiments.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Using the automata processor for fast pattern recognition in high energy physics experiments. A proof of concept

Here, we explore the Micron Automata Processor (AP) as a suitable commodity technology that can address the growing computational needs of pattern recognition in High Energy Physics (HEP) experiments. A toy detector model is developed for which an electron track confirmation trigger based on the Micron AP serves as a test case. Although primarily meant for high speed text-based searches, we demonstrate a proof of concept for the use of the Micron AP in a HEP trigger application.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2020

JANA2 LDRD (Final Project Report)

The project sought to develop a second generation of the JANA reconstruction framework that leverages modern programming features (C++11 and C++14) while maintaining its basic user centric design. The goals included making the project easy to deploy to large HPC facilities such as NERSC and to include detailed documentation to allow scientists outside of Jefferson Lab to use it at such a facility. This would position JLab to play a key role in the larger Laboratory based computing ecosystem under the ASCR initiative. The experience gained will help inform the design of Exascale class applications for experimental nuclear physics. Developing a next generation JANA provides an advantage over older serial frameworks or ones retro-fitted to provide some multi-threading support. That technique requires significantly more memory than multi-threading which leads to compute jobs being limited by available RAM, and not fully utilizing the available CPU. The smaller memory footprint of multi-threaded programs also leads to increased efficiency due to fewer cache misses. It is for these and other reasons that multi-threading is the more accepted industry standard in the modern era.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Transforming Science Through Software: Improving While Delivering 100×

The U.S. Department of Energy (DOE) Exascale Computing Project (ECP) funded the development of new (and the transformation of important existing) applications, libraries, and tools that realized improvement in performance and capabilities of often 100 times or more on emerging exascale computers. This exceptional gain inspired the title of this special issue: Transforming Science through Software: Improving while delivering 100X. The term 100X refers to advancing capabilities in modeling, simulation, and analysis by a factor of 100 or more using some combination of new algorithms, optimization techniques, software libraries, and programming models, coupled with the next generation of hardware for high-performance computing (HPC). The papers in this issue share experiences with the practice and science of scientific software development, with an emphasis on developing a coherent, portable, and sustainable HPC software ecosystem for next-generation computational science. Finally, we hope to foster expanded community efforts related to the fundamental role of sustainable scientific software ecosystems in advancing the computing sciences.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

The LANL Common Modeling Framework (CMF) [Slides]

The Common Modeling Framework is a modern software repository built and maintained by the LANL Weapons Physics Directorate (ALDX). ALDX’s mission space is to develop and apply cutting-edge theory, computational models, and multi-physics simulation codes, and to design, execute, and analyze complex experiments

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

MFIX DEM Enhancement for Industry-Relevant Flows (Final Report)

The overall goal of this two-phase project is to implement performance improvements of the Multiphase Flow with Interphase Exchanges (MFIX) Discrete Element Model (DEM) code that enable a transformative shift for industrial use. Prior to this effort, the largest simulations performed using MFIX are O(10 7 ) particles. This falls short of the O(10 9 ) particle simulations that must be completed on a timescale of days or weeks (vs. months or years) to enable simulations with physically-relevant domain sizes to be incorporated into industrial design cycles within five years. This was accomplished by tailoring best-in-class practices to bear on the unique challenges posed by the MFIX-DEM algorithm and code base. Scientific simulations (e.g., in cosmology, turbulent combustion) routinely use massively parallel computing to update far more particles in short wall clock times. Results from Phase 1 (1.5 years in duration) indicated significant gains in speed were possible for a wide range of benchmark cases. Moreover, a survey sent to >35 companies indicates that the timing is ideal for such an enhanced tool, with >80% of the respondents indicating that DEM is already value-added or will be within the next 5 years, and >70% of the respondents indicating that improved speed is the top computational priority. In Phase 2 (3.5 years in duration), the two major barriers that hinder industry from effectively using multiphase Computational Fluid Dynamics (CFD) to cut costs and improve performance, namely computational overhead and confidence in predictions, continued to be addressed. Regarding the former, the results from Phase 1 to guide the effort, with enhancements focused on an improved time-stepping algorithm and particle sorting. Four target problems of 1 billion particles each and increasing complexity were identified: homogeneous cooling, tumbler with continuous particle size distribution, discharge from a rectangular hopper and a cylindrical riser. Each of these were successfully simulated for relevant time scales (on order of seconds) using less than 24 hours of wall clock time. These represent the first 1-billion particle DEM simulations performed with MFIX, namely using the MFIX-Exa code. This code is currently under development at NETL in collaboration with Lawrence Berkeley National Laboratory. Regarding the second barrier on predictive uncertainty, experiments from Phase 1 (interacting nozzles - hydrodynamics only) and Phase 2 (very small-scale segregation experiments) were used to demonstrate the ability of two simplified approaches to uncertainty quantification (UQ). By limiting the number of particles, UQ based on the simplified treatment was compared to standard UQ, which was shown to have much higher computational demands. Experiments were also performed on a pilot-scale stripper unit to provide validation data for future CFD-DEM simulations and UQ.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2017

Scaling Up Data-Parallel Analytics Platforms: Linear Algebraic Operation Cases

Linear algebraic operations such as matrix manipulations form the kernel of many machine learning and other crucial algorithms. Scaling up as well as scaling out such algorithms are key to supporting large scale data analysis that require efficient processing over millions of data samples. To this end, we present, ARION, a hardware acceleration based approach for scaling-up individual tasks of Spark, a popular data-parallel analytics platform. We support both linear algebraic operations of between two dense matrices, and between sparse and dense matrices in distributed environments. ARION provides a flexible control of acceleration according to matrix density, along with efficient scheduling based on runtime resource utilization. We demonstrate the benefit of our approach for general matrix multiplication operations over large matrices with up to four billion elements by using Gramian matrix computation that is commonly used in machine learning. Experiments show that our approach achieves more than 2× and 1.5× end-to-end performance speedups for dense and sparse matrices, respectively, and up to 57.04× faster computation compared to MLlib, a state of the art Spark-based implementation. This work is sponsored in part by the NSF under the grants: CNS-1565314, CNS-1405697, and CNS-1615411. The manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725.

Xu, Luna↗