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DOE OSTI2024

PANDORA: A Parallel Dendrogram Construction Algorithm for Single Linkage Clustering on GPU

This paper introduces Pandora, a parallel algorithm for computing dendrograms, the hierarchical cluster trees for single linkage clustering (SLC). Current parallel approaches construct dendrograms by partitioning a minimum spanning tree and removing edges. However, they struggle with skewed, hard-to-parallelize real-world dendrograms. Consequently, computing dendrograms is the sequential bottleneck in HDBSCAN*[21], a popular SLC variant. Pandora uses recursive tree contraction to address this limitation. Pandora contracts nodes to construct progressively smaller trees. It computes the smallest contracted dendrogram and expands it by inserting contracted edges. This recursive strategy is highly parallel, skew-independent, work-optimal, and well-suited for GPUs and multicores. We develop a performance portable implementation of Pandora in Kokkos[31] and evaluate its performance on multicore CPUs and multi-vendor GPUs (e.g., Nvidia, AMD) for dendrogram construction in HDBSCAN*. Multithreaded Pandora is 2.2x faster than the current best-multithreaded implementation. Our GPU version achieves 6-20x speedup on AMD GPUs and 10-37x on NVIDIA GPUs over multithreaded Pandora. Pandora removes HDBSCAN*’s sequential bottleneck, greatly boosting efficiency, particularly with GPUs.

Sao, Piyush↗

DOE OSTI2024

IRIS: Exploring Performance Scaling of the Intelligent Runtime System and its Dynamic Scheduling Policies

High-Performance Computing is becoming increasingly heterogeneous, relying on a diverse mix of hardware to achieve good performance. Paradoxically, current drivers and frameworks for these devices typically require separate languages and implementations for each vendor. Furthermore, there are few tools and little support to schedule codes between these devices in a truly heterogeneous manner-partly because of this fragmentation between vendors and the languages each supports. To overcome both limitations, the Intelligent Runtime System (IRIS) was developed. It allows a common task abstraction to automatically be shared among contemporary vendors and is run from a single host-side API. At runtime, IRIS queries the host system and registers which frameworks and drivers are available, these determine which kernels can be used by the scheduler-CPUs via OpenMP, Nvidia GPUs (CUDA), AMD GPUs (HIP), and Intel and Xilinx FPGAs with OpenCL. IRIS enables tasks to be scheduled to any heterogeneous device and resolves to the appropriate kernel binary at runtimeit only uses the devices supported by the system on which it is run. IRIS supports single-task and graph-based expressions of dependencies of tasks. Additionally, IRIS features a range of dynamic scheduling policies, allowing complex chains of tasks and interactions to be executed, relieving the programmer/user from considering the system to assign tasks to devices optimally. This paper presents the peak performance attainable by IRIS over a range of systems-each with different numbers and types of accelerator devices, it highlights the flexibility of IRIS since these devices are truly heterogeneous, relying on different backends (drivers, frameworks, and languages) which historically required unique implementations to utilize them. We then use this peak performance as a baseline to compare increasingly complex chains of tasks (with increasingly complex task dependencies) and evaluate how IRIS copes. Finally, we consider the performance of different IRIS scheduling policies on this range of task graphs.

Johnston, Beau↗

DOE OSTI2023

Newly Released Capabilities in the Distributed-Memory SuperLU Sparse Direct Solver

We present the new features available in the recent release of SuperLU_DIST, Version 8.1.1. SuperLU_DIST is a distributed-memory parallel sparse direct solver. The new features include (1) a 3D communication-avoiding algorithm framework that trades off inter-process communication for selective memory duplication, (2) multi-GPU support for both NVIDIA GPUs and AMD GPUs, and (3) mixed-precision routines that perform single-precision LU factorization and double-precision iterative refinement. Apart from the algorithm improvements, we also modernized the software build system to use CMake and Spack package installation tools to simplify the installation procedure. Throughout the article, we describe in detail the pertinent performance-sensitive parameters associated with each new algorithmic feature, show how they are exposed to the users, and give general guidance of how to set these parameters. We illustrate that the solver’s performance both in time and memory can be greatly improved after systematic tuning of the parameters, depending on the input sparse matrix and underlying hardware.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Cabana: A Performance Portable Library for Particle-Based Simulations

Particle-based simulations are ubiquitous throughout many fields of computational science and engineering, spanning the atomistic level with molecular dynamics (MD), to mesoscale particle-in-cell (PIC) simulations for solid mechanics, device-scale modeling with PIC methods for plasma physics, and massive N-body cosmology simulations of galaxy structures, with many other methods in between (Hockney & Eastwood, 1989). While these methods use particles to represent significantly different entities with completely different physical models, many low-level details are shared including performant algorithms for short- and/or long-range particle interactions, multi-node particle communication patterns, and other data management tasks such as particle sorting and neighbor list construction. Cabana is a performance portable library for particle-based simulations, developed as part of the Co-Design Center for Particle Applications (CoPA) within the Exascale Computing Project (ECP) (Alexander et al., 2020). The CoPA project and its full development scope, including ECP partner applications, algorithm development, and similar software libraries for quantum MD, is described in (Mniszewski et al., 2021). Cabana uses the Kokkos library for on-node parallelism (Edwards et al., 2014; Trott et al., 2022), enabling simulation on multi-core CPU and GPU architectures, and MPI for GPU-aware, multi-node communication. Cabana provides particle simulation capabilities on almost all current Kokkos backends, including serial execution, OpenMP (including OpenMP-Target for GPUs), CUDA (NVIDIA GPUs), HIP (AMD GPUs), and SYCL (Intel GPUs), providing a clear path for the coming generation of accelerator-based exascale hardware. Cabana builds on Kokkos by providing new particle data structures and particle algorithms resulting in a similar execution policy-based, node-level programming model that is intended to be used in addition to the core Kokkos library within an application. Cabana is designed as an application and physics agnostic, but particle-specific toolkit which can either be used to generate a new application, or to be used as needed in existing applications at various levels of invasiveness including through interfaces that wrap user memory in existing data structures.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

TChem-atm (v2.0.0): scalable performance-portable multiphase atmospheric chemistry

We present TChem-atm, a performance-portable approach that enables efficient simulation of chemically detailed and multiphase atmospheric chemistry on modern heterogeneous computing architectures. Unlike previous efforts that rely on architecture-specific code or focus exclusively on gas-phase chemistry, TChem-atm supports fully coupled gas–aerosol systems with execution across CPUs, NVIDIA GPUs, and AMD GPUs through the Kokkos programming model. It integrates the flexible multiphase capabilities of the Community Atmospheric Model Chemistry Package (CAMP) with the high-performance kinetic routines of TChem, and includes automatic Jacobian construction with support for a range of stiff ODE solvers. In a proof-of-concept integration with the particle-resolved model PartMC, TChem-atm reproduces the existing PartMC–CAMP implementation within solver tolerances and delivers substantial GPU speedups, especially for large particle populations. Performance benchmarks reveal substantial speedups on GPU platforms, particularly for large particle populations, with consistent results across hardware backends. TChem-atm enables performance-portable execution across CPUs and GPUs, though optimal efficiency may require modest architecture-specific tuning (e.g., team and vector sizes), with up to a twofold improvement on the NVIDIA H100. It directly supports sectional and particle-resolved host models, while modal aerosol schemes require minor adaptation to provide particle-scale quantities such as representative diameters. By enabling chemically detailed, multiphase simulations with performance portability and host-model flexibility, TChem-atm facilitates the incorporation of advanced chemistry into atmospheric models.

Díaz-Ibarra, Oscar Homero [Sandia National Laborat↗

NASA NTRSDate not supplied

Optimization of a Solver for Computational Materials and Structures Problems on NVIDIA Volta and AMD Instinct GPUs

The Scalable Implementation of Finite Elements by NASA (ScIFEN) is a software package developed to solve complex computational materials and structures problems using the finite element method (FEM). In this paper, we describe optimization techniques to speed up the linear solver computation that occurs within the ScIFEN application. We consider GPUs from two different vendors, NVIDIA and AMD as our target platforms for optimization and highlight differences in performance and optimization techniques. The NVIDIA GPU Volta V100 is used in the Summit system deployed at Oak Ridge National Laboratory, and the new exascale system, Frontier, will be using AMD Radeon Instinct GPU. We evaluated the performance of various optimization techniques on test matrices, ranging in size from100K to 4M, that are representative of ScIFEN applications. The linear solver computation is memory-bound on both GPUs. Our experiments show that on the NVIDIA GPU we obtained up to79%of the theoretical peak bandwidth, while the AMD GPU achieved 59%. Overall, the NVIDIA V100 GPU outperforms the AMD MI 25 GPU1. We observed an overall speedup of up to37X on an NVIDIA V100 compared to an Intel Skylake 12-coremachine. The solver for a 4M degree of freedom system took under 2.5 seconds.

Mohammad Zubair↗

DOE OSTI2022

Studying Performance Portability of LAMMPS across Diverse GPU-based Platforms

The molecular dynamics simulation software, LAMMPS, utilizes the Kokkos acceleration library to port computation to a diverse set of architectures including those based on GPU accelerators. In addition to Kokkos, LAMMPS contains a vast code base that leverages the CUDA application programming interface using library functions such as cuFFT, CUDA’s fast-fourier transform (FFT) library, and, more recently, also support for AMD’s Heterogeneous Interface for Portability (HIP) that is rapidly growing. While preparing LAMMPS tests for the AMD GPU-based test system precursors to Frontier, we investigated several strategies for accelerating LAMMPS on AMD GPUs, using the AMD Instinct MI100 and MI250X. In this work, we integrated the HIP FFT library, hipFFT, into the particle-particle particle-mesh (PPPM) long-range solver, which allowed the porting of PPPM calculations to the GPUs. Kokkos behavior on the MI100 and MI250X was also investigated through the package kokkos command of LAMMPS, targeting com- munication, memory usage, and particle grid decomposition. The Tersoff, Reax, Lennard-Jones (LJ), EAM, Granular, and PPPM potentials were investigated in this effort, and results from these experiments are provided. The selected potentials were run on Spock (AMD Instinct MI100), Crusher (AMD Instinct MI250X), AFW HPC11 (NVIDIA A100) and Summit (NVIDIA V100), for comparison. Operational roofline models were constructed and analyzed for the Tersoff, Reax, and Lennard-Jones potentials on Crusher and Summit.

Hagerty, Nick↗

DOE OSTI2023

Studying performance portability of LAMMPS across diverse GPU-based platforms

The molecular dynamics simulation software, LAMMPS, utilizes the Kokkos acceleration library to port computation to a diverse set of architectures including those based on GPU accelerators. In addition to Kokkos, LAMMPS contains a vast code base that leverages the CUDA application programming interface using library functions such as cuFFT, CUDA's fast-fourier transform (FFT) library, and, more recently, also support for AMD's Heterogeneous Interface for Portability (HIP) that is rapidly growing. While preparing LAMMPS tests for the AMD GPU-based test system precursors to Frontier, we investigated several strategies for accelerating LAMMPS on AMD GPUs, using the AMD Instinct MI100 and MI250X. In this work, we integrated the HIP FFT library, hipFFT, into the particle-particle particle-mesh (PPPM) long-range solver, which allowed the porting of PPPM calculations to the GPUs. Kokkos behavior on the MI100 and MI250X was also investigated through the package kokkos command of LAMMPS, targeting communication, memory usage, and particle grid decomposition. The Tersoff, Reax, Lennard-Jones (LJ), EAM, Granular, and PPPM potentials were investigated in this effort, and results from these experiments are provided. In conclusion, the selected potentials were run on Spock (AMD Instinct MI100), Crusher (AMD Instinct MI250X), AFW HPC11 (NVIDIA A100) and Summit (NVIDIA V100), for comparison. Operational roofline models were constructed and analyzed for the Tersoff, Reax, and Lennard–Jones potentials on Crusher and Summit.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

DIMPLES: Distributed Influence Maximization for Pandemic pLanning on Exascale Systems

We study exascale parallel algorithms for the selection of intervention or monitoring strategies in massive realistic socio-technical networks through scalable Influence Maximization (InfMax) algorithms. We employ novel techniques to enable efficient scaling on up to 8k nodes of OLCF Frontier, with 65k AMD GPUs and 458k AMD CPU cores. Current state-of-the-art InfMax tools are limited to networks with only a few million actors (vertices) and a few hundred million interactions (edges). By overcoming these limitations, we show that our approach is capable of processing a realistic social contact network of the United States with 285 million nodes and about 8 billion edges. This two orders-of-magnitude improvement over the previous state-of-the-art is obtained by leveraging algorithmic advancements for the InfMax problem and designing several problem-specific approaches to overlap communication with computation, improve GPU efficiency, and lower the application’s memory requirements. We evaluate strong scaling for computing 10k most influential seeds using up to 8k nodes of an exascale system, and weak scaling from 128 to 8k system nodes for seed sets ranging from 625 to 40k seeds. We achieve the fastest-known runtime of 25 minutes while performing 48 million diffusion simulations totaling 2.31 petabytes to identify 40k influential seeds using 8k nodes, and take 5.75 minutes to identify 10k seeds while using 4k nodes.

Minutoli, Marco [Pacific Northwest National Labora↗

DOE OSTI2024

A graphics processing unit accelerated sparse direct solver and preconditioner with block low rank compression

We present the GPU implementation efforts and challenges of the sparse solver package STRUMPACK. The code is made publicly available on github with a permissive BSD license. STRUMPACK implements an approximate multifrontal solver, a sparse LU factorization which makes use of compression methods to accelerate time to solution and reduce memory usage. Multiple compression schemes based on rank-structured and hierarchical matrix approximations are supported, including hierarchically semi-separable, hierarchically off-diagonal butterfly, and block low rank. Here, in this paper, we present the GPU implementation of the block low rank (BLR) compression method within a multifrontal solver. Our GPU implementation relies on highly optimized vendor libraries such as cuBLAS and cuSOLVER for NVIDIA GPUs, rocBLAS and rocSOLVER for AMD GPUs and the Intel oneAPI Math Kernel Library (oneMKL) for Intel GPUs. Additionally, we rely on external open source libraries such as SLATE (Software for Linear Algebra Targeting Exascale), MAGMA (Matrix Algebra on GPU and Multi-core Architectures), and KBLAS (KAUST BLAS). SLATE is used as a GPU-capable ScaLAPACK replacement. From MAGMA we use variable sized batched dense linear algebra operations such as GEMM, TRSM and LU with partial pivoting. KBLAS provides efficient (batched) low rank matrix compression for NVIDIA GPUs using an adaptive randomized sampling scheme. The resulting sparse solver and preconditioner runs on NVIDIA, AMD and Intel GPUs. Interfaces are available from PETSc, Trilinos and MFEM, or the solver can be used directly in user code. We report results for a range of benchmark applications, using the Perlmutter system from NERSC, Frontier from ORNL, and Aurora from ALCF. For a high frequency wave equation on a regular mesh, using 32 Perlmutter compute nodes, the factorization phase of the exact GPU solver is about 6.5× faster compared to the CPU-only solver. The BLR-enabled GPU solver is about 13.8× faster than the CPU exact solver. For a collection of SuiteSparse matrices, the STRUMPACK exact factorization on a single GPU is on average 1.9× faster than NVIDIA’s cuDSS solver.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

GPU-accelerated multitiered iterative phasing algorithm for fluctuation X-ray scattering

The multitiered iterative phasing (MTIP) algorithm is used to determine the biological structures of macromolecules from fluctuation scattering data. It is an iterative algorithm that reconstructs the electron density of the sample by matching the computed fluctuation X-ray scattering data to the external observations, and by simultaneously enforcing constraints in real and Fourier space. This paper presents the first ever MTIP algorithm acceleration efforts on contemporary graphics processing units (GPUs). The Compute Unified Device Architecture (CUDA) programming model is used to accelerate the MTIP algorithm on NVIDIA GPUs. The computational performance of the CUDA-based MTIP algorithm implementation outperforms the CPU-based version by an order of magnitude. Furthermore, the Heterogeneous-Compute Interface for Portability (HIP) runtime APIs are used to demonstrate portability by accelerating the MTIP algorithm across NVIDIA and AMD GPUs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

A MultiGPU Performance-Portable Solution for Array Programming Based on Kokkos

Today, multiGPU nodes are widely used in high-performance computing and data centers. However, current programming models do not provide simple, transparent, and portable support for automatically targeting multiple GPUs within a node on application areas of array programming. In this paper, we describe a new application programming interface based on the Kokkos programming model to enable array computation on multiple GPUs in a transparent and portable way across both NVIDIA and AMD GPUs. We implement different variations of this technique to accommodate the exchange of stencils (array boundaries) among different GPU memory spaces, and we provide autotuning to select the proper number of GPUs, depending on the computational cost of the operations to be computed on arrays, that is completely transparent to the programmer. We evaluate our multiGPU extension on Summit (#5 TOP500), with six NVIDIA V100 Volta GPUs per node, and Crusher that contains identical hardware/software as Frontier (#1 TOP500), with four AMD MI250X GPUs, each with 2 Graphics Compute Dies (GCDs)for a total of 8 GCDs per node. We also compare the performance of this solution against the use of MPI + Kokkos, which is the cur-rent de facto solution for multiple GPUs in Kokkos. Our evaluation shows that the new Kokkos solution provides good scalability for many GPUs and a faster and simpler solution (from a programming productivity perspective) than MPI + Kokkos.

Valero Lara, Pedro↗

DOE OSTI2023

Performance-Portable GPU Acceleration of the EFIT Tokamak Plasma Equilibrium Reconstruction Code

This paper presents the steps followed to GPU-offload parts of the core solver of EFIT-AI, an equilibrium reconstruction code suitable for tokamak experiments and burning plasmas. For this work, we will focus on the fitting procedure that consists of a Grad–Shafranov (GS) equation inverse solver that calculates equilibrium reconstructions on a grid. We will show profiling results of the original code (CPU-baseline), as well as the directives used to GPU-offload the most time-consuming function, initially to compare OpenACC and OpenMP on NVIDIA and AMD GPUs and later on to assess OpenMP performance portability on NVIDIA, AMD and Intel GPUs. We will make a performance comparison for different spatial grid sizes and show the speedup achieved on NVIDIA A100 (Perlmutter-NERSC), AMD MI250X (Frontier-OLCF) and Intel PVC GPUs (Sunspot-ALCF). Finally, we will draw some conclusions and recommendations to achieve high-performance portability for an equilibrium reconstruction code on the new HPC architectures

GPU↗

DOE OSTI2022

High performance sparse multifrontal solvers on modern GPUs

Here, we have ported the numerical factorization and triangular solve phases of the sparse direct solver STRUMPACK to GPU. STRUMPACK implements sparse LU factorization using the multifrontal algorithm, which performs most of its operations in dense linear algebra operations on so-called frontal matrices of various sizes. Our GPU implementation off-loads these dense linear algebra operations, as well as the sparse scatter–gather operations between frontal matrices. For the larger frontal matrices, our GPU implementation relies on vendor libraries such as cuBLAS and cuSOLVER for NVIDIA GPUs and rocBLAS and rocSOLVER for AMD GPUs. For the smaller frontal matrices we developed custom CUDA and HIP kernels to reduce kernel launch overhead. Overall, high performance is achieved by identifying submatrix factorizations corresponding to sub-trees of the multifrontal assembly tree which fit entirely in GPU memory. The multi-GPU setting uses SLATE (Software for Linear Algebra Targeting Exascale) as a modern GPU-aware replacement for ScaLAPACK. On 4 nodes of SUMMIT the code runs ~10X faster when using all 24 V100 GPUs compared to when it only uses the 168 POWER9 cores. On 8 SUMMIT nodes, using 48 V100 GPUs, the sparse solver reaches over 50TFlop/s. Compared to SuperLU, on a single V100, for a set of 17 matrices our implementation is faster for all but one matrix, and is on average 5X (median 4X) faster

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

The Simple Cloud-Resolving E3SM Atmosphere Model Running on the Frontier Exascale System

We present an efficient and performance portable implementation of the Simple Cloud Resolving E3SM Atmosphere Model (SCREAM). SCREAM is a full featured atmospheric global circulation model with a nonhydrostatic dynamical core and state-of-the-art parameterizations for microphysics, moist turbulence and radiation. It has been written from scratch in C++ with the Kokkos library used to abstract the on-node execution model for both CPUs and GPUs. SCREAM is one of only a few global atmosphere models to be ported to GPUs. As far as we know, SCREAM is the first such model to run on both AMD GPUs and NVIDIA GPUs, as well as the first to run on nearly an entire Exascale system (Frontier). On Frontier, we obtained a record setting performance of 1.26 simulated years per day for a realistic cloud resolving simulation.

Taylor, Mark↗

DOE OSTI2024

MAGMA: Enabling exascale performance with accelerated BLAS and LAPACK for diverse GPU architectures

MAGMA (Matrix Algebra for GPU and Multicore Architectures) is a pivotal open-source library in the landscape of GPU-enabled dense and sparse linear algebra computations. With a repertoire of approximately 750 numerical routines across four precisions, MAGMA is deeply ingrained in the DOE software stack, playing a crucial role in high-performance computing. Notable projects such as ExaConstit, HiOP, MARBL, and STRUMPACK, among others, directly harness the capabilities of MAGMA. In addition, the MAGMA development team has been acknowledged multiple times for contributing to the vendors’ numerical software stacks. Looking back over the time of the Exascale Computing Project (ECP), we highlight how MAGMA has adapted to recent changes in modern HPC systems, especially the growing gap between CPU and GPU compute capabilities, as well as the introduction of low precision arithmetic in modern GPUs. We also describe MAGMA’s direct impact on several ECP projects. Maintaining portable performance across NVIDIA and AMD GPUs, and with current efforts toward supporting Intel GPUs, MAGMA ensures its adaptability and relevance in the ever-evolving landscape of GPU architectures.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Evaluating Performance Portability with the CMS Heterogeneous Pixel Reconstruction code

In the past years the landscape of tools for expressing parallel algorithms in a portable way across various compute accelerators has continued to evolve significantly. There are many technologies on the market that provide portability between CPU, GPUs from several vendors, and in some cases even FPGAs. These technologies include C++ libraries such as Alpaka and Kokkos, compiler directives such as OpenMP, the SYCL open specification that can be implemented as a library or in a compiler, and standard C++ where the compiler is solely responsible for the offloading. Given this developing landscape, users have to choose the technology that best fits their applications and constraints. For example, in the CMS experiment the experience so far in heterogeneous reconstruction algorithms suggests that the full application contains a large number of relatively short computational kernels and memory transfer operations. In this work we use a stand-alone version of the CMS heterogeneous pixel reconstruction code as a realistic use case of HEP reconstruction software that is capable of leveraging GPUs effectively. We summarize the experience of porting this code base from CUDA to Alpaka, Kokkos, SYCL, std::par, and OpenMP offloading. We compare the event processing throughput achieved by each version on NVIDIA and AMD GPUs as well as on a CPU, and compare those to what a native version of the code achieves on each platform.

Andriotis, Nikolaos↗

DOE OSTI2026

AthenaK: A Performance-portable Version of the Athena++ Adaptive Mesh Refinement Framework

We describe AthenaK: a new implementation of the Athena++ block-based adaptive mesh refinement framework using the Kokkos programming model. Finite volume methods for Newtonian, special relativistic, and general relativistic (GR) hydrodynamics and magnetohydrodynamics (MHD), and GR-radiation hydrodynamics and MHD, as well as a module for evolving Lagrangian tracer or charged test particles (e.g., cosmic rays) are implemented using the framework. In two companion papers, we describe (1) a new solver for the Einstein equations based on the Z4c formalism, and (2) a GRMHD solver in dynamical spacetimes also implemented using the framework, enabling new applications in numerical relativity. By adopting Kokkos, the code can be run on virtually any hardware, including CPUs, GPUs from multiple vendors, and emerging Advanced RISC Machine processors. AthenaK shows excellent performance and weak scaling, achieving over 1 billion cell updates per second for hydrodynamics in three dimensions on a single NVIDIA Grace Hopper processor. It does this with a typical parallel efficiency of 80% on 65,536 AMD GPUs on the OLCF Frontier system. Such performance portability enables AthenaK to leverage modern exascale computing systems for challenging applications in astrophysical fluid dynamics, numerical relativity, and multimessenger astrophysics.

79 ASTRONOMY AND ASTROPHYSICS↗