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At least 235 records · Page 13

Cognitive simulation models for inertial confinement fusion: Combining simulation and experimental data

The design space for inertial confinement fusion (ICF) experiments is vast, and experiments are extremely expensive. Researchers rely heavily on computer simulations to explore the design space in search of high-performing implosions. However, ICF multiphysics codes must make simplifying assumptions, and thus deviate from experimental measurements for complex implosions. For more effective design and investigation, simulations require input from past experimental data to better predict future performance. In this work, we describe a cognitive simulation method for combining simulation and experimental data into a common, predictive model. This method leverages a machine learning technique called “transfer learning,” the process of taking a model trained to solve one task, and partially retraining it on a sparse dataset to solve a different, but related task. In the context of ICF design, neural network models are trained on large simulation databases and partially retrained on experimental data, producing models that are far more accurate than simulations alone. Here, we demonstrate improved model performance for a range of ICF experiments at the National Ignition Facility and predict the outcome of recent experiments with less than 10% error for several key observables. We discuss how the methods might be used to carry out a data-driven experimental campaign to optimize performance, illustrating the key product—models that become increasingly accurate as data are acquired.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Uncertainty and Sensitivity Analysis of TREAT Transient Test no. 15

The U.S. Department of Energy (DOE) is preparing for the resumption of transient testing using the Transient Reactor Test Facility (TREAT) located at the Idaho National Laboratory (INL). In order to support the analysis of TREAT operation and experiment planning, the MAMMOTH reactor physics team has recently begun development of uncertainty and sensitivity analysis for the TREAT core simulated via MAMMOTH. MAMMOTH is a high-fidelity three-dimensional transient multi-physics code developed at INL under the DOE-NE Advanced Modeling and Simulation program (NEAMS). This research is part of the development presenting some initial uncertainty and sensitivity analysis of TREAT Transient Test no. 15. In this summary, we employ the Sobol sampling strategy implemented in RAVEN to efficiently perform the sensitivity and uncertainty analysis. The idea is using Sobol functional decomposition with generalized polynomial chaos (gPC) expansions to estimate the responses of interest. The gPC coefficients are then computed via the sparse grid spectral projection method. In addition, this strategy includes evaluation of the second or higher order sensitivity indices, allowing the study of interactions between several input variables. The principal focus of this analysis is to quantify the uncertainties in the total power and maximum fuel temperatures with respect to uncertainties in the initial transient conditions, such as rated power, fuel temperature, graphite fuel density and control rod boron concentration. In addition, both the first order and second order time-dependent sensitivity indices are computed and analyzed. The results show that the interactions between initial control rod boron concentration and the rated power will contribute at most 1% to the total uncertainty of the power peak.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

The Kokkos OpenMPTarget Backend: Implementation and Lessons Learned

As the supercomputing landscape diversifies, solutions such as Kokkos to write vendor agnostic applications and libraries have risen in popularity. Kokkos provides a programming model designed for performance portability, which allows developers to write a single source implementation that can run efficiently on various architectures. At its heart, Kokkos maps parallel algorithms to architecture and vendor specific backends written in lower level programming models such as CUDA and HIP. Another approach to writing vendor agnostic parallel code is using OpenMP’s directives based approach, which lets developers annotate code to express parallelism. It is implemented at the compiler level and is supported by all major high performance computing vendors, as well as the primary Open Source toolchains GNU and LLVM. Since its inception, Kokkos has used OpenMP to parallelize on CPU architectures. In this paper, we explore leveraging OpenMP for a GPU backend and discuss the challenges we encountered when mapping the Kokkos APIs and semantics to OpenMP target constructs. As an exemplar workload we chose a simple conjugate gradient solver for sparse matrices. We find that performance on NVIDIA and AMD GPUs varies widely based on details of the implementation strategy and the chosen compiler. Furthermore, the performance of the OpenMP implementations decreases with increasing complexity of the investigated algorithms.

Gayatri, Rahulkumar↗

Dissecting Tensor Cores via Microbenchmarks: Latency, Throughput and Numeric Behaviors

Tensor Cores have been an important unit to accelerate Fused Matrix Multiplication Accumulation (MMA) in all NVIDIA GPUs since Volta Architecture. To program Tensor Cores, users have to use either legacy wmma APIs or current mma APIs. Legacy wmma APIs are more easy-to-use but can only exploit limited features and power of Tensor Cores. Specifically, wmma APIs support fewer operand shapes and can not leverage the new sparse matrix multiplication feature of the newest Ampere Tensor Cores. However, the performance of current programming interface has not been well explored. Furthermore, the computation numeric behaviors of low-precision floating points (TF32, BF16, and FP16) supported by the newest Ampere Tensor Cores are also mysterious. In this paper, we explore the throughput and latency of current programming APIs. Further, we intuitively study the numeric behaviors of Tensor Cores MMA and profile the intermediate operations including multiplication, addition of inner product, and accumulation. All codes used in this work can be found in https://github.com/sunlex0717/DissectingTensorCores.

97 MATHEMATICS AND COMPUTING↗

Uncertainty and Sensitivity Analysis of TREAT Transient Test #15

The U.S. Department of Energy (DOE) is preparing for the resumption of transient testing using the Transient Reactor Test Facility (TREAT) located at the Idaho National Laboratory (INL). In order to support the analysis of TREAT operation and experiment planning, the MAMMOTH reactor physics team has recently begun development of uncertainty and sensitivity analysis for the TREAT core simulated via MAMMOTH. MAMMOTH is a high-fidelity three-dimensional transient multi-physics code developed at INL under the DOE-NE Advanced Modeling and Simulation program (NEAMS) [1]. This research is part of the development presenting some initial uncertainty and sensitivity analysis of TREAT Transient Test #15 [2]. In this summary, we employ the Sobol sampling strategy implemented in RAVEN [3] to efficiently perform the sensitivity and uncertainty analysis. The idea is using Sobol functional decomposition with generalized polynomial chaos (gPC) expansions to estimate the responses of interest [4]. The gPC coefficients are then computed via the spectral projection method with sparse grid approach. In addition, this strategy includes evaluation of the second or higher order sensitivity indices, allowing the study of interactions between several input variables. The principal focus of this analysis is to quantify the uncertainties in the total power and maximum fuel temperatures with respect to uncertainties in the initial transient conditions, such as rated power, fuel temperature, graphite fuel density and control rod boron concentration. In addition, both the first order and second order time-dependent sensitivity indices are computed and analyzed. The results show that the interactions between initial control rod boron concentration and the rated power will contribute at most 1% to the total uncertainty of the power peak.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Sparse, iterative simulation methods for one-dimensional laminar flames

Sparse, iterative simulation methods for one-dimensional laminar flames are proposed. The resulting steady and unsteady flame solvers exploit approximate Jacobians to greatly reduce the computational cost associated with matrix operations. The constant, non-unity Lewis number assumption is introduced to further reduce the computational cost. The solvers are also parallelized to reduce time-to-solution on distributed memory computer systems. Computed laminar flame speeds and species profiles for a range of chemical mechanisms (from 10 to 2878 species) are compared against a well-validated commercial code and are found to be consistent within solver tolerances. The computation times of both the unsteady and steady solutions increase only linearly with the number of species, which is a significant improvement over the quadratic or cubic scaling of existing steady-state flame solvers. For the largest mechanism tested, the steady-state flame solver is two orders of magnitude faster than commonly-used codes. The use of an approximate Jacobian is shown to reduce the rate of convergence for the steady-state solver, but does not significantly affect the domain of convergence. The steady-state solver with approximate Jacobian is thus well suited for computationally efficient laminar flame speed sweeps with large kinetic mechanisms.

42 ENGINEERING↗

Analysing the effects of heating and gas puffing in Proto-MPEX helicon and auxiliary heated plasmas

The Material Plasma Exposure Experiment (MPEX) is being constructed at Oak Ridge National Laboratory to investigate critical fusion reactor issues, such as plasma–material interactions (PMIs) under reactor-relevant conditions and time scales. The linear device Proto-MPEX was used as a test bed to address anticipated research and development issues associated with heating scenarios and establish the physics basis for MPEX. The SOLPS-ITER code suite has been applied to understand plasma and neutral transport in Proto-MPEX and to increase confidence in predictive simulations for MPEX. Coupling between COMSOL and SOLPS is performed to implement a 2D electron heating profile of the helicon source. The simulations show reasonable agreement with the experimental data for plasma with helicon and auxiliary electron cyclotron heating (ECH). Both Bohm and constant diffusion (D$_\perp$: 0.5 m 2 s –1 and $\chi_\perp$: 1 m 2 s –1 ) simulations show similar levels of agreement with respect to the sparse experimental data available, assuming a few per cent impurity concentration. ECH significantly increases the target electron temperature, however, the target electron density is reduced compared to helicon-only heated plasmas due to an increase in flow velocity and radial losses. The simulations show that further increasing the ECH power results in an increase in the target electron density due to increased recycling flux and ionization. The results indicate that ECH significantly enhances the target heat flux, with ECH power of 50 kW increasing the target heat flux from 0.4 to 17 MW m –2 . It is found that a small amount of gas puffing (GP) near the target plate can further increase the target heat fluxes at the higher ECH power cases, but the target heat flux is reduced at higher GP conditions due to a significant reduction in electron temperature via radiation. ECH and GP scenarios can generate a higher target flux, facilitating improved PMI studies with more reactor-relevant plasma conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Porting AMG2013 to Heterogeneous CPU+GPU Nodes

LLNL's future advanced technology system SIERRA will feature heterogeneous compute nodes that consist of IBM PowerV9 CPUs and NVIDIA Volta GPUs. Conceptually, the motivation for such an architecture is quite straightforward: While GPUs are optimized for throughput on massively parallel workloads, CPUs strive to minimize latency for rather sequential operations. Yet, making optimal use of heterogeneous architectures raises new challenges for the development of scalable parallel software, e.g., with respect to work distribution. Porting LLNL's parallel numerical libraries to upcoming heterogeneous CPU+GPU architectures is therefore a critical factor for ensuring LLNL's future success in ful lling its national mission. One of these libraries, called HYPRE, provides parallel solvers and precondi- tioners for large, sparse linear systems of equations. In the context of this intern- ship project, I consider AMG2013 which is a proxy application for major parts of HYPRE that implements a benchmark for setting up and solving di erent systems of linear equations. In the following, I describe in detail how I ported multiple parts of AMG2013 to the GPU (Section 2) and present results for di erent experiments that demonstrate a successful parallel implementation on the heterogeneous ma- chines surface and ray (Section 3). In Section 4, I give guidelines on how my code should be used. Finally, I conclude and give an outlook for future work (Section 5).

97 MATHEMATICS AND COMPUTING↗

Small Genomes and Sparse Metabolisms of Sediment-Associated Bacteria from Four Candidate Phyla

Cultivation-independent surveys of microbial diversity have revealed many bacterial phyla that lack cultured representatives. These lineages, referred to as candidate phyla, have been detected across many environments. Here, we deeply sequenced microbial communities from acetate-stimulated aquifer sediment to recover the complete and essentially complete genomes of single representatives of the candidate phyla SR1, WWE3, TM7, and OD1. All four of these genomes are very small, 0.7 to 1.2 Mbp, and have large inventories of novel proteins. Additionally, all lack identifiable biosynthetic pathways for several key metabolites. The SR1 genome uses the UGA codon to encode glycine, and the same codon is very rare in the OD1 genome, suggesting that the OD1 organism could also transition to alternate coding. Interestingly, the relative abundance of the members of SR1 increased with the appearance of sulfide in groundwater, a pattern mirrored by a member of the phylum Tenericutes . All four genomes encode type IV pili, which may be involved in interorganism interaction. On the basis of these results and other recently published research, metabolic dependence on other organisms may be widely distributed across multiple bacterial candidate phyla. Few or no genomic sequences exist for members of the numerous bacterial phyla lacking cultivated representatives, making it difficult to assess their roles in the environment. This paper presents three complete and one essentially complete genomes of members of four candidate phyla, documents consistently small genome size, and predicts metabolic capabilities on the basis of gene content. These metagenomic analyses expand our view of a lifestyle apparently common across these candidate phyla.

59 BASIC BIOLOGICAL SCIENCES↗

Sparse triangular solves for ILU revisited: data layout crucial to better performance.; .

A key to good processor utilization for sparse matrix computations is storing the data in the format that is most conducive to fast access by the memory system. In particular, for sparse matrix triangular solves the traditional compressed sparse matrix format is poor, and minor adjustments to the data structure can increase the processor utilization dramatically. Such adjustments involve storing the L and U factors separately and storing the U rows 'backwards' so that they are accessed in a simple streaming fashion during the triangular solves. Changes to the PETSc libraries to use this modified storage format resulted in over twice the floating-point rate for some matrices. This improvement can be accounted for by a decrease in the cache misses and TLB (transaction lookaside buffer) misses in the modified code.

99 GENERAL AND MISCELLANEOUS↗

Application of adaptive hierarchical sparse grid collocation to the uncertainty quantification of nuclear reactor simulators

Recent efforts in the application of uncertainty quantification to nuclear systems have utilized methods based on generalized perturbation theory and stochastic sampling. While these methods have proven to be effective they both have major drawbacks that may impede further progress. A relatively new approach based on spectral elements for uncertainty quantification is applied in this paper to several problems in reactor simulation. Spectral methods based on collocation attempt to couple the approximation free nature of stochastic sampling methods with the determinism of generalized perturbation theory. The specific spectral method used in this paper employs both the Smolyak algorithm and adaptivity by using Newton-Cotes collocation points along with linear hat basis functions. Using this approach, a surrogate model for the outputs of a computer code is constructed hierarchically by adaptively refining the collocation grid until the interpolant is converged to a user-defined threshold. The method inherently fits into the framework of parallel computing and allows for the extraction of meaningful statistics and data that are not within reach of stochastic sampling and generalized perturbation theory. This paper aims to demonstrate the advantages of spectral methods-especially when compared to current methods used in reactor physics for uncertainty quantification-and to illustrate their full potential. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

On a Simplified Approach to Achieve Parallel Performance and Portability Across CPU and GPU Architectures

This paper presents software advances to easily exploit computer architectures consisting of a multi-core CPU and CPU+GPU to accelerate diverse types of high-performance computing (HPC) applications using a single code implementation. The paper describes and demonstrates the performance of the open-source C++ matrix and array (MATAR) library that uniquely offers: (1) a straightforward syntax for programming productivity, (2) usable data structures for data-oriented programming (DOP) for performance, and (3) a simple interface to the open-source C++ Kokkos library for portability and memory management across CPUs and GPUs. The portability across architectures with a single code implementation is achieved by automatically switching between diverse fine-grained parallelism backends (e.g., CUDA, HIP, OpenMP, pthreads, etc.) at compile time. The MATAR library solves many longstanding challenges associated with easily writing software that can run in parallel on any computer architecture. This work benefits projects seeking to write new C++ codes while also addressing the challenges of quickly making existing Fortran codes performant and portable over modern computer architectures with minimal syntactical changes from Fortran to C++. We demonstrate the feasibility of readily writing new C++ codes and modernizing existing codes with MATAR to be performant, parallel, and portable across diverse computer architectures.

97 MATHEMATICS AND COMPUTING↗

Physics consistent machine learning framework for inverse modeling with applications to ICF capsule implosions

In high energy density physics (HEDP) and inertial confinement fusion (ICF), predictive modeling is complicated by uncertainty in parameters that characterize various aspects of the modeled system, such as those characterizing material properties, equation of state (EOS), opacities, and initial conditions. Typically, however, these parameters are not directly observable. What is observed instead is a time sequence of radiographic projections using X-rays. In this work, we define a set of sparse hydrodynamic features derived from the outgoing shock profile and outer material edge, which can be obtained from radiographic measurements, to directly infer such parameters. Our machine learning (ML)-based methodology involves a pipeline of two architectures, a radiograph-to-features network (R2FNet) and a features-to-parameters network (F2PNet), that are trained independently and later combined to approximate a posterior distribution for the parameters from radiographs. We show that the machine learning architectures are able to accurately infer initial conditions and EOS parameters, and that the estimated parameters can be used in a hydrodynamics code to obtain density fields, shocks, and material interfaces that satisfy thermodynamic and hydrodynamic consistency. Finally, we demonstrate that features resulting from an unknown EOS model can be successfully mapped onto parameters of a chosen analytical EOS model, implying that network predictions are learning physics, with a degree of invariance to the underlying choice of EOS model. To the best of our knowledge, our framework is the first demonstration of recovering both thermodynamic and hydrodynamic consistent density fields from noisy radiographs.

97 MATHEMATICS AND COMPUTING↗

SkyFACT: high-dimensional modeling of gamma-ray emission with adaptive templates and penalized likelihoods

We present SkyFACT (Sky Factorization with Adaptive Constrained Templates), a new approach for studying, modeling and decomposing diffuse gamma-ray emission. Like most previous analyses, the approach relies on predictions from cosmic-ray propagation codes like GALPROP and DRAGON. However, in contrast to previous approaches, we account for the fact that models are not perfect and allow for a very large number (∼> 10{sup 5}) of nuisance parameters to parameterize these imperfections. We combine methods of image reconstruction and adaptive spatio-spectral template regression in one coherent hybrid approach. To this end, we use penalized Poisson likelihood regression, with regularization functions that are motivated by the maximum entropy method. We introduce methods to efficiently handle the high dimensionality of the convex optimization problem as well as the associated semi-sparse covariance matrix, using the L-BFGS-B algorithm and Cholesky factorization. We test the method both on synthetic data as well as on gamma-ray emission from the inner Galaxy, |ℓ|<90{sup o} and | b |<20{sup o}, as observed by the Fermi Large Area Telescope. We finally define a simple reference model that removes most of the residual emission from the inner Galaxy, based on conventional diffuse emission components as well as components for the Fermi bubbles, the Fermi Galactic center excess, and extended sources along the Galactic disk. Variants of this reference model can serve as basis for future studies of diffuse emission in and outside the Galactic disk.

79 ASTRONOMY AND ASTROPHYSICS↗

O(N) Quantum Molecular Dynamics (QMD) Algorithms, Code Requirements, Release Notes, and Library Deployment

The Exascale Computing Project (ECP) Co-design Center for Particle Applications (CoPA) is addressing the challenges for particle applications to run on upcoming exascale computing architectures. This includes short- and long-range molecular dynamics (MD), particle-in-cell (PIC), and quantum molecular dynamics (QMD). This document addresses $\mathcal{O}(N)$ QMD. The goal of this CoPA team is to develop $\mathcal{O}(N)$ linear scaling methods for QMD optimized for new and next generation architectures. This will provide the capability to simulate larger systems and run for longer timeframes than is possible today. Focus is initially on the density matrix construction. This requires efficient matrix formats and linear algebra operations for distributed architectures. A significant reduction in the wallclock time for an MD timestep is necessary to achieve practical large scale QMD. Equally challenging is to develop scalable distributed implementations. This requires the exploration of efficient data formats (dense, sparse, etc.), data decomposition and distribution across compute nodes using block- and graph-based methods. Traditional programming models such as MPI/OpenMP, hybrid MPI/OpenMP/Accelerator, as well as asynchronous task-based models will be explored to achieve maximum parallelism. Parallelism at the level of a matrix operation, solver, and/or application needs to be explored to gain the most benefit on new and emerging architectures. This report serves as a “living document” of the additions and enhancements throughout the ECP CoPA project for $\mathcal{O}(N)$ QMD. The following sections address the applications we are working with, the quantum chemistry libraries (BML and PROGRESS), and our co-design exploration through the use of a proxy application.

36 MATERIALS SCIENCE↗

MO-FG-CAMPUS-IeP2-05: Feasibility Demonstration of High-Voltage Clinical CT and Impact On X-Ray Penetration Through Metal Objects

Purpose: To demonstrate the possibility and quantify the impact of operating a clinical CT scanner at exceptionally high x-ray tube voltage for better penetration through metal objects and facilitating metal artifact reduction. Methods: We categorize metal objects according to the data corruption severeness (level of distortion and complete photon starvation fraction). To demonstrate feasibility and investigate the impact of high voltage scanning we modified a commercial GE LightSpeed VCT scanner (generator and software) to enable CT scans with x-ray tube voltages as high as 175 kVp. A 20 cm diameter water phantom with two metal rods (10 mm stainless and 25 mm titanium) and a water phantom with realistic metal object (spine cage) were used to evaluate the data corruption and image artifacts in the absence of any algorithm correction. We also performed simulations to confirm our understanding of the transmitted photon levels through metal objects with different size and composition. Results: The reconstructed images at 175 kVp still have significant dark shading artifacts, as expected since no special scatter correction or beam hardening was performed but show substantially lower noise and photon starvation than at lower kVp due to better beam penetration. Analysis of the raw data shows that the photon starved data is reduced from over 4% at 140 kVp to below 0.2% at 175 kVp. The simulations indicate that for clinically relevant titanium and stainless objects a 175 kVp tube voltage effectively avoids photon starvation. Conclusion: The use of exceptionally high tube voltage on a clinical CT system is a practical and effective solution to avoid photon starvation caused by certain metal implants. Sparse and hybrid high-voltage protocols are being considered to maintain low patient dose. This opens the door to algorithmic physics-based corrections rather than treating the data as missing and relying on missing data algorithms. Some of the authors are employees of General Electric.

60 APPLIED LIFE SCIENCES↗

Parallel beamlet dose calculation via beamlet contexts in a distributed multi‐GPU framework

Purpose Dose calculation is one of the most computationally intensive, yet essential tasks in the treatment planning process. With the recent interest in automatic beam orientation and arc trajectory optimization techniques, there is a great need for more efficient model‐based dose calculation algorithms that can accommodate hundreds to thousands of beam candidates at once. Foundational work has shown the translation of dose calculation algorithms to graphical processing units ( GPU s), lending to remarkable gains in processing efficiency. But these methods provide parallelization of dose for only a single beamlet, serializing the calculation of multiple beamlets and under‐utilizing the potential of modern GPU s. In this paper, the authors propose a framework enabling parallel computation of many beamlet doses using a novel beamlet context transformation and further embed this approach in a scalable network of multi‐ GPU computational nodes. Methods The proposed context‐based transformation separates beamlet‐local density and TERMA into distinct beamlet contexts that independently provide sufficient data for beamlet dose calculation. Beamlet contexts are arranged in a composite context array with dosimetric isolation, and the context array is subjected to a GPU collapsed‐cone convolution superposition procedure, producing the set of beamlet‐specific dose distributions in a single pass. Dose from each context is converted to a sparse representation for efficient storage and retrieval during treatment plan optimization. The context radius is a new parameter permitting flexibility between the speed and fidelity of the dose calculation process. A distributed manager‐worker architecture is constructed around the context‐based GPU dose calculation approach supporting an arbitrary number of worker nodes and resident GPU s. Phantom experiments were executed to verify the accuracy of the context‐based approach compared to Monte Carlo and a reference CPU ‐ CCCS implementation for single beamlets and broad beams composed by addition of beamlets. Dose for representative 4 π beam sets was calculated in lung and prostate cases to compare its efficiency with that of an existing beamlet‐sequential GPU ‐ CCCS implementation. Code profiling was also performed to evaluate the scalability of the framework across many networked GPU s. Results The dosimetric accuracy of the context‐based method displays <1.35% and 2.35% average error from the existing serialized CPU ‐ CCCS algorithm and Monte Carlo simulation for beamlet‐specific PDD s in water and slab phantoms, respectively. The context‐based method demonstrates substantial speedup of up to two orders of magnitude over the beamlet‐sequential GPU ‐ CCCS method in the tested configurations. The context‐based framework demonstrates near linear scaling in the number of distributed compute nodes and GPU s employed, indicating that it is flexible enough to meet the performance requirements of most users by simply increasing the hardware utilization. Conclusions The context‐based approach demonstrates a new expectation of performance for beamlet‐based dose calculation methods. This approach has been successful in accelerating the dose calculation process for very large‐scale treatment planning problems ‐ such as automatic 4 π IMRT beam orientation and VMAT arc trajectory selection, with hundreds of thousands of beamlets ‐ in clinically feasible timeframes. The flexibility of this framework makes it as a strong candidate for use in a variety of other very large‐scale treatment planning tasks and clinical workflows.

Neph, Ryan↗

High-Performance Sparse Matrix-Matrix Products on Intel KNL and Multicore Architectures

Sparse matrix-matrix multiplication (SpGEMM) is a computational primitive that is vastly used in areas ranging from traditional numerical applications to recent big data analysis and machine learning. While many SpGEMM algorithms have been proposed, hardware specific optimizations for multi- and many-core processors are lacking and a detailed analysis of their performance under various use cases and matrices is not available. We firstly identify and mitigate multiple bottlenecks with memory management and thread scheduling on Intel Xeon Phi (Knights Landing or KNL). Specifically targeting multi- and many-core processors, we develop a hash-table-based algorithm and optimize a heap-based shared-memory SpGEMM algorithm. We investigate their performance together with other publicly available codes. Different from the literature, our evaluation also includes use cases that are representative of real graph algorithms, such as multi-source breadth-first search or triangle counting. Our hash-table and heap-based algorithms are showing significant speedups from libraries in the majority of the cases while different algorithms dominate the other scenarios with different matrix size, sparsity, compression factor and operation type. We wrap up in-depth evaluation results and make a recipe to give the best SpGEMM algorithm for target scenario. In conclusion, a critical finding is that hash-table-based SpGEMM gets a significant performance boost if the nonzeros are not required to be sorted within each row of the output matrix.

97 MATHEMATICS AND COMPUTING↗