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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Facilitating Staging-based Unstructured Mesh Processing to Support Hybrid In-Situ Workflows

In-situ and in-transit processing alleviate the gap between the computing and I/O capabilities by scheduling data analytics close to the data source. Hybrid in-situ processing splits data analytics into two stages: the data processing that runs in-situ aims to extract regions of interest, which are then transferred to staging services for further in-transit analytics. To facilitate this type of hybrid in-situ processing, the data staging service needs to support complex intermediate data representations generated/consumed by the in-situ tasks. Unstructured (or irregular) mesh is one such derived data representation that is typically used and bridges simulation data and analytics. However, how staging services efficiently support unstructured mesh transfer and processing remains to be explored. This paper investigates design options for transferring and processing unstructured mesh data using staging services. Using polygonal mesh data as an example, we show that hybrid in-situ workflows with staging-based unstructured mesh processing can effectively support hybrid in-situ workflows, and can significantly decrease data movement overheads.

data-driven↗
DOE OSTI2019

A Picture Speaks 360,000 Words - Virtual Reality as a Decommissioning Planning Tool - 19364

Whiteshell Laboratories, located in Manitoba, Canada, provided research facilities for the Canadian nuclear industry since the early 1960's. Decommissioning of Whiteshell Laboratories has been ongoing since 2002 under Atomic Energy of Canada (AECL) and, more currently, since 2015 under the WL Closure Project managed by Canadian Nuclear Laboratories (CNL). One of the key steps to ensuring safe decommissioning operations is effective planning, including pre-job briefings, and post-job verification and review. Effective planning involves clear and concise communication of the field conditions, system configurations, hazards, and task goals or achievements to front line employees, and task approvers and verifiers. In many instances, employees can enter, view, inspect, verify or otherwise familiarize themselves with the task and task location. However, in several cases, hazardous conditions in the task location make it difficult for employees to easily access the location themselves, due to hazardous conditions, PPE requirements, training qualification gaps or space limitations. Since 2016, 360 deg. cameras have been used to create a virtual 'tour' of the hazardous task locations at Whiteshell Laboratories, which can be viewed by one or all of the employees involved in a task, from a position of safety. This allows a task to be discussed with all employees involved without the need for added risk of exposure to dose or industrial hazards or costly PPE, and supports ALARA control techniques of removing the hazard by moving work planning walk downs away from hazardous locations and guarding the worker by limiting the time a worker is exposed to the hazard. This paper provides an overview of the technologies used to capture and present the 360 virtual tours, the benefits from a safety, schedule and cost perspective, and the limitations of the current implementation that could be improved upon in a future iteration. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

Illinois Express Quantum Network (IEQNET): metropolitan-scale experimental quantum networking over deployed optical fiber

The Illinois Express Quantum Network (IEQNET) is a program to realize metro-scale quantum networking over deployed optical fiber using currently available technology. IEQNET consists of multiple sites that are geographically dispersed in the Chicago metropolitan area. Each site has one or more quantum nodes (Qnodes) representing the communication parties in a quantum network. Q-nodes generate or measure quantum signals such as entangled photons and communicate the results via standard, classical, means. The entangled photons in IEQNET nodes are generated at multiple wavelengths, and are selectively distributed to the desired users via optical switches. Here we describe the network architecture of IEQNET, including the Internet-inspired layered hierarchy that leverages software-defined-networking (SDN) technology to perform traditional wavelength routing and assignment between the Q-nodes. Specifically, SDN decouples the control and data planes, with the control plane being entirely classical. Issues associated with synchronization, calibration, network monitoring, and scheduling will be discussed. An important goal of IEQNET is demonstrating the extent to which the control plane can coexist with the data plane using the same fiber lines. This goal is furthered by the use of tunable narrow-band optical filtering at the receivers and, at least in some cases, a wide wavelength separation between the quantum and classical channels. We envision IEQNET to aid in developing robust and practical quantum networks by demonstrating metro-scale quantum communication tasks such as entanglement distribution and quantum-state teleportation.

Chung, Joaquin↗
DOE OSTI2021

Accelerating Transformer-based Deep Learning Models on FPGAs using Column Balanced Block Pruning

Although Transformer-based language representations achieve state-of-the-art accuracy on various natural language processing (NLP) tasks, the large model size has been challenging the resource constrained computing platforms. Weight pruning, as a popular and effective technique in reducing the number of weight parameters and accelerating the Transformer, has been investigated on GPUs. However, the Transformer acceleration using weight pruning on field-programmable gate array (FPGAs) remains unexplored. This paper investigates the column balanced block-wise pruning on Transformer and designs an FPGA acceleration engine to customize the balanced blockwise matrix multiplication. We implement the Transformer model with proper hardware scheduling, and the experiments show that the Transformer inference on FPGA achieves 10.35 ms latency with the batch size of 32, which is 10.96 × speed up comparing to CPU platform and 2.08 × speed up comparing to GPU platform.

Peng, Hongwu↗
DOE OSTI2019

Resilient Disaster Recovery Logistics of Distribution Systems: Co-Optimize Service Restoration With Repair Crew and Mobile Power Source Dispatch

Repair crews (RCs) and mobile power sources (MPSs) are critical resources for distribution system (DS) outage management after a natural disaster. However, their logistics have not been well investigated. We propose a resilient scheme for disaster recovery logistics to co-optimize DS restoration with the dispatch of RCs and MPSs. A novel co-optimization model is formulated to route RCs and MPSs in the transportation network, schedule them in the DS, and reconfigure the DS for microgrid formation coordinately, etc. The model incorporates different timescales of DS restoration and RC/MPS dispatch, the coupling of transportation and power networks, etc. To ensure radiality of the DS with variable physical structure and MPS allocation, we also model topology constraints based on the concept of spanning forest. The model is convexified equivalently and linearized into a mixed-integer linear programming. To reduce its computation time, preprocessing methods are proposed to preassign a minimal set of repair tasks to depots and reduce the number of candidate nodes for MPS connection. Resilient recovery strategies thus are generated to enhance service restoration, especially by dynamic formation of microgrids that are powered by MPSs and topologized by repair actions of RCs and network reconfiguration of the DS. Case studies demonstrate the proposed methodology.

Disaster recovery logistics↗
DOE OSTI2024

Enabling groundbreaking experiments that advance our understanding of the universe through accurate target specifications

The Target Fabrication (TFAB) team at the National Ignition Facility (NIF) is tasked with assembling and qualifying targets for physics experiments. These targets are critical components used in experiments that advance research in areas such as fusion energy, high-energy-density physics, and astrophysics. Target Fabrication Engineers (TFEs) are responsible for producing and validating target specifications, which are compiled into detailed specification packages. TFAB produces hundreds of targets annually, with each target requiring several specification datasheets that culminate in a comprehensive specification package. TFAB needs an efficient and accurate means to generate these specification datasheets to maintain the rigorous NIF shot schedule.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

CalTestBed - Parthian Energy: Electromagnetic Sensing of Pre-mature Cell Failure (CRADA Final Report)

We had lengthy discussions with Parthian on the interpretation of the original SOW as laid out in the original proposal and on whether or not these tasks were allowable under the rules set by Cal Test Bed. There were also discussions on program limitations on purchasing equipment. We were engaged with vendors identified by Parthian as companies from which we could lease equipment, and in most cases, came to find, that these products were only available for purchase. As a result, we configured translational stages into an x-y plotter arrangement and established computer control over the setup as a step toward building our own system for acquiring data to meet Parthian's requirements. The project reached its scheduled end prior to the start of testing and was allowed to elapse uncompleted.

25 ENERGY STORAGE↗
DOE OSTI2024

Transportation and Systems Analysis Collaborations in Support of a Federal Consolidated Interim Storage Facility

The U.S. Department of Energy’s Integrated Waste Management (IWM) program under the Office of Nuclear Energy is planning for the future transportation, storage, and eventual disposal of spent nuclear fuel (SNF) and high-level radioactive waste (HLW) from nuclear power plant sites across the United States. To better enable informed decision-making regarding the back end of the nuclear fuel cycle, the IWM program has been sponsoring the development and application of system analysis tools capable of analyzing various options for managing SNF and HLW. With these tools, integrated waste management system (IWMS) architecture analyses are being conducted to support the future deployment of a comprehensive nuclear waste management system that considers all major back-end aspects of the nuclear fuel cycle (i.e., transportation, storage, and disposal). System analyses and assessments typically use these modeling and simulation tools to investigate implications of changes in various assumptions and parameters such as acceptance rates, receipt logic, facility capacities and capabilities, use of standardized canisters, start and stop dates of facilities, etc. The Next Generation System Analysis Model (NGSAM) is an agent-based simulation toolkit that is used for a system-level simulation and analysis focused on SNF management in the United States. An analyst using NGSAM has the ability to define several factors like the number of storage facilities, capacity at each facility, transportation schedules, shipment rates, and other conditions. NGSAM’s primary purpose is to provide a system analyst with capabilities to model the IWMS and gain insights into SNF and HLW management alternatives including the impact of system choices, associated cost estimates, and development of integrated yet flexible approaches. IWM is also developing the Stakeholder Tool for Assessing Radioactive Transportation (START). START is a web-based geospatial tool developed to provide visualization and initial evaluation of transportation options associated with future SNF and HLW shipment planning and operations. This includes characterizing safety, economic, and environmental conditions on and in proximity to shipment origins as well as along prospective transportation routes. Information from the START tool can be presented/shared as maps, graphics, geospatial files, and tabular form to enable easy data representation and export functionality. The system analysis, NGSAM, and START teams had been working closely for several years before formalizing this collaboration. START provides the SNF routing information for use in NGSAM. System analysts use the NGSAM tool to generate results (schedule, costs, infrastructure acquisitions, shipment rates, etc.). Subject-matter experts and system analysts work together to inform how NGSAM should model the waste management system. Specifically, this paper discusses the collaborations between the system analysis, NGSAM, and START teams and their accomplishments over the past year. Some examples of these efforts include calibrating and adding data to the START output files to meet NGSAM needs, gaining a better understanding of START data used in NGSAM, as well as how updates in START data could result in an improved NGSAM analysis. Detailed examples of various tasks that have been performed by the team will be discussed in the full paper. Continued efforts in this direction are expected in the coming years.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Transportation and System Analysis Collaborations in Support of a Federal Consolidated Interim Storage Facility

The U.S. Department of Energy’s Integrated Waste Management (IWM) program under the Office of Nuclear Energy is planning for the future transportation, storage, and eventual disposal of spent nuclear fuel (SNF) and high-level radioactive waste (HLW) from nuclear power plant and waste custodian sites across the United States. To better enable informed decision-making regarding the back end of the nuclear fuel cycle, the IWM program has been sponsoring the development and application of system analysis tools capable of analyzing various options for managing SNF and HLW. With these tools, integrated waste management system (IWMS) architecture analyses are being conducted to support the future deployment of a comprehensive nuclear waste management system that considers all major back-end aspects of the nuclear fuel cycle (i.e., transportation, storage, and disposal). System analyses and assessments typically use these modeling and simulation tools to investigate implications of changes in various assumptions and parameters such as acceptance rates, receipt logic, facility capacities and capabilities, use of standardized canisters, start and stop dates of facilities, etc. The Next Generation System Analysis Model (NGSAM) is an agent-based simulation toolkit that is used for a system-level simulation and analysis focused on SNF management in the United States. NGSAM’s primary purpose is to provide a system analyst with capabilities to model the IWMS and gain insights into SNF and HLW management alternatives including the impact of system choices, associated cost estimates, and development of integrated yet flexible approaches. An analyst using NGSAM can define several factors like the number of storage facilities, capacity at each facility, transportation schedules, shipment rates, and other conditions. IWM is also developing the Stakeholder Tool for Assessing Radioactive Transportation (START). START is a web-based geospatial tool developed to provide the visualization and initial evaluation of transportation options associated with future SNF and HLW shipment planning and operations. This includes characterizing safety, economic, and environmental conditions at and in proximity to shipment origins as well as along prospective transportation routes. Information from the START tool can be presented/shared as maps, graphics, geospatial files, and tabular form to enable easy data representation and export functionality. The system analysis, NGSAM, and START teams have been working closely for several years before formalizing this collaboration. START provides the SNF transportation routing information for use in NGSAM. System analysts use the NGSAM tool to generate results (schedule, costs, infrastructure acquisitions, shipment rates, etc.). Subject-matter experts and system analysts work together to inform how NGSAM should model the waste management system. Specifically, this paper discusses the collaborations between the system analysis, NGSAM, and START teams and their accomplishments over the past year. Some examples of these efforts include calibrating and adding data to the START output files to meet NGSAM needs, gaining a better understanding of START data used in NGSAM as well as how updates in START data could result in an improved NGSAM analysis. Detailed examples of various tasks that have been performed by the team will be discussed in the full paper. Continued efforts in this direction are expected in the coming years.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Verification and validation of developed short-term forecasting models

Recent advancements in machine learning (ML) and artificial intelligence (AI) technologies provide an opportunity for leveraging data-driven algorithms to predict future nuclear power plant (NPP) operating conditions by using recorded plant process data. Successfully implementing these models can lead to cost-reducing, conditioned-based predictive maintenance through optimized maintenance schedules and a reduction of unnecessary maintenance activities. This report discusses the verification and validation of short-term forecasting processes (i.e., data cleaning, feature selection, model optimization, and forecasting) developed in previous reports. The verification and validation (V&V) process demonstrates the expected precision and accuracy when the ML model encounters new datasets from different systems. Shapley additive explanations were used as the primary means of feature selection across these different data set. Individual models were trained for each data set, then validated through a cross-validation procedure. In this report, two different ML models were tasked to predict variables from three different plant process data sets with varying prediction horizons. The results indicate that support vector regression (SVR) outperformed long short-term memory (LSTM) neural networks in regard to each data set and each prediction horizon in this study, but further tuning and optimization could improve long short-term memory results. However, each forecasting model showed reduced performance as the prediction horizon was extended from 1 hour to 1 day ahead. Research is ongoing to evaluate the optimal input variable space, which is based on a given set of process parameters, to further improve forecasting accuracy.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Dynamic Charging Rendezvous and Motion Planning for a Multi-AGV Team Including a Mobile Charging Host

Teams of automated battery-powered electric vehicles have the potential to execute complex mission tasks in off-road environments for agriculture, military, and other applications. Limited onboard energy reserves hinder their adoption in large-scale resource-constrained environments, where recharging is a necessity. It may be infeasible to install a network of static charging stations in off-road environments. For this reason, dedicated mobile host vehicles with charging capabilities are proposed as a means to increase range and capabilities of the multivehicle team. Here, in this study, we consider an ad hoc planning framework, where results from a high-confidence trajectory planner are leveraged to plan charging rendezvous between a host and other worker vehicles in a receding horizon fashion to provide high confidence that energy reserves will not be prematurely exhausted. The core problem is posed so as to minimize the impact of recharging on the mission in terms of task delays, overall energy utilization, and costs of fast charging. Through extensive Monte Carlo simulations of an off-road mission, we show a decrease in task delays without substantial increases in energy needs by updating the charging rendezvous plan during the mission. However, if updates are made too often, model mismatch may cause unnecessary cycling and mission failure.

Energy constraints↗
DOE OSTI2022

Enabling machine learning-ready HPC ensembles with Merlin

With the growing complexity of computational and experimental facilities, many scientific researchers are turning to machine learning (ML) techniques to analyze large scale ensemble data. With complexities such as multi-component workflows, heterogeneous machine architectures, parallel file systems, and batch scheduling, care must be taken to facilitate this analysis in a high performance computing (HPC) environment. Here, we present Merlin, a workflow framework to enable large ML-friendly ensembles of scientific HPC simulations. By augmenting traditional HPC with distributed compute technologies, Merlin aims to lower the barrier for scientific subject matter experts to incorporate ML into their analysis. As a producer–consumer workflow model, Merlin enables multi-machine, cross-batch job, dynamically allocated yet persistent workflows capable of utilizing surge-compute resources. Key features of Merlin are a flexible HPC-centric interface, low per-task overhead, multi-tiered fault recovery, and a hierarchical sampling algorithm that allows for $\mathscr{O}$(N) task execution and $\mathscr{O}$(N ln N) task queuing to ensembles of millions of tasks. In addition to Merlin’s design, we test the algorithm’s performance in an HPC center and demonstrate the ability to enqueue 40 million simulations in 100 s, with a 30 millisecond per-task overhead that is independent of ensemble size. Finally, we describe some example applications that Merlin has enabled on leadership-class HPC resources, such as the ML-augmented optimization of nuclear fusion experiments and the calibration of infectious disease models to study the progression of and possible mitigation strategies for COVID-19.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Reaching new peaks for the future of the CMS HTCondor Global Pool

The CMS experiment at CERN employs a distributed computing infrastructure to satisfy its data processing and simulation needs. The CMS Submission Infrastructure team manages a dynamic HTCondor pool, aggregating mainly Grid clusters worldwide, but also HPC, Cloud and opportunistic resources. This CMS Global Pool, which currently involves over 70 computing sites worldwide and peaks at 350k CPU cores, is employed to successfully manage the simultaneous execution of up to 150k tasks. While the present infrastructure is sufficient to harness the current computing power scales, CMS latest estimates predict a noticeable expansion in the amount of CPU that will be required in order to cope with the massive data increase of the High-Luminosity LHC (HL-LHC) era, planned to start in 2027. This contribution presents the latest results of the CMS Submission Infrastructure team in exploring and expanding the scalability reach of our Global Pool, in order to preventively detect and overcome any barriers in relation to the HL-LHC goals, while maintaining high effciency in our workload scheduling and resource utilization.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Development and Application of a Risk Analysis Toolkit for Plant Resources Optimization

This report summarizes the R&D activities of the Risk Informed Asset Management (RIAM) project during fiscal year 2020 (FY20). This project focuses on the development of methods designed to optimize plant operations (e.g., maintenance/replacement schedule, optimal maintenance posture) provided system/component health/cost data. This project development lives in cooperation with the Plant Health Management (PHM) project which focuses on the development of methods that integrate component health data and propagate such information at the system level to evaluate most relevant sources of risk. This year’s activities for the RIAM project focused on the continuation of schedule optimization algorithms developed in FY19. While in FY19 we focused on both deterministic and stochastic capital budgeting methods, in FY20 we moved forward by implementing two versions of schedule optimization methods. The first one reformulates the capital budgeting problem in a distributionally robust form which allows the user to rely on data directly rather than proposing a distribution from the data itself. The second version reformulates the capital budgeting explicitly using risk measures as variables to maximize/minimize. Lastly, we focused on the development of methods designed to identify the optimal maintenance posture based on the Pareto Frontier analysis. Rather than performing a tradeoff analysis (i.e., identify the absolute best posture), the Pareto Frontier analysis performs a trade space exploration approach (i.e., identify value and costs of several postures and have the analyst perform the task of imposing desired value and cost constraints). This is performed by identifying maintenance postures that maximize value (e.g., system availability) and minimize operational costs, i.e., the Pareto frontier in a value-cost trade space.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Assessment of the Electrical Substation-Grid Testbed with Inside/Outside Devices and Distributed Ledger Technology

The electrical substation-grid testbed was created to integrate the GOOSE and/or DNP (Distributed Network Protocol) messages with time synchronized sources and Distributed Ledger Technology (DLT). The objective was to study the impact of faults and cyber-events at an electrical substation with inside (protective relays) and outside (power meters) substation devices. The electrical substation-grid testbed was based on the design of a 34.5/ 12.47 kV electrical substation (sectionalized bus configuration) with two power transformers, connected to radial power lines and load feeders. The electrical substation-grid testbed was installed at 252 lab space (Advanced Power System Protection), Grid Research Integration and Deployment Center (GRID-C), Oak Ridge National Laboratory. This testbed was created for Task 5, DarkNet project. The electrical substation-grid testbed was created to simulate fault and/or cyber events that could potentially result in damage to the electrical infrastructure. In addition, tests were run that are usually not allowed to be performed in an operational electrical power grid, because these test scenarios could trip breakers and/or generate fault situations that could potentially damage equipment. The number of tests performed in the electrical substation-grid testbed were executed in a better way than in a real electrical substation and/or power grid, because multiple tests could be run in a short period of time, and complex permits, and safety/ schedule restrictions like in a real electrical substation environment were not needed. The electrical substation-grid testbed was created using real measurement, communication, and protection devices that are used by electrical utilities, to have same conditions that we could observe in a real power grid or electrical substation. The electrical substation-grid testbed was based on using a real time simulator and expansion box with amplifiers that were wired to electrical substation-grid devices. This hardware-in-the-loop (HIL) was provided by protective relays, power meters, ethernet switches, remote terminal units, synchronized timing network clock, DLT devices, workstations, and servers. This report includes the design, installation, and assessment of the electrical substation-grid testbed that was similar to an operational electrical substation, integrating the power system protection, communication, and control systems. The results for the electrical substation-grid testbed were based on:• verifying the analog signals for protective relays and power meters, • observing the synchronized time source frame at devices, • authenticating the GOOSE (IEC 61850) and DNP messages from power meters and protective relays, and • verifying the trip conditions of protective relays at fault tests with the power system fault event detection, using DLT devices. For future work, the electrical substation-grid testbed with protective relays and power meters, using DLT and synchronized time source from DarkNet, will be used to study the impact of cyber-events at inside and outside substation devices. Advanced algorithms for detecting cyber-events produced by non-desired protective relay settings will be studied, to improve the detection and reliability of protection, control, and communication systems at power grids.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Ad Hoc File Systems for High-Performance Computing

Storage backends of parallel compute clusters are still based mostly on magnetic disks, while newer and faster storage technologies such as flash-based SSDs or non-volatile random access memory (NVRAM) are deployed within compute nodes. Including these new storage technologies into scientific workflows is unfortunately today a mostly manual task, and most scientists therefore do not take advantage of the faster storage media. One approach to systematically include nodelocal SSDs or NVRAMs into scientific workflows is to deploy ad hoc file systems over a set of compute nodes, which serve as temporary storage systems for single applications or longer-running campaigns. This paper presents results from the Dagstuhl Seminar 17202 “Challenges and Opportunities of User-Level File Systems for HPC” and discusses application scenarios as well as design strategies for ad hoc file systems using node-local storage media. The discussion includes open research questions, such as how to couple ad hoc file systems with the batch scheduling environment and how to schedule stage-in and stage-out processes of data between the storage backend and the ad hoc file systems. Also presented are strategies to build ad hoc file systems by using reusable components for networking and how to improve storage device compatibility. Various interfaces and semantics are presented, for example those used by the three ad hoc file systems BeeOND, GekkoFS, and BurstFS. Their presentation covers a range from file systems running in production to cutting-edge research focusing on reaching the performance limits of the underlying devices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

C-SAW: a framework for graph sampling and random walk on GPUs

Many applications require to learn, mine, analyze and visualize large-scale graphs. These graphs are often too large to be addressed efficiently using conventional graph processing technologies. Fortunately, recent research efforts find out graph sampling and random walk, which significantly reduce the size of original graphs, can benefit the tasks of learning, mining, analyzing and visualizing large graphs by capturing the desirable graph properties. This paper introduces C-SAW, the first framework that accelerates Sampling and Random Walk framework on GPUs. Particularly, C-SAW makes three contributions: First, our framework provides a generic API which allows users to implement a wide range of sampling and random walk algorithms with ease. Second, offloading this framework on GPU, we introduce warp-centric parallel selection, and two novel optimizations for collision migration. Third, towards supporting graphs that exceed the GPU memory capacity, we introduce efficient data transfer optimizations for out-of-memory and multi-GPU sampling, such as workload-aware scheduling and batched multi-instance sampling. Taken together, our framework constantly outperforms the state of the art projects in addition to the capability of supporting a wide range of sampling and random walk algorithms.

97 MATHEMATICS AND COMPUTING↗