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DOE OSTI2019

An Efficient Parallel-in-Time Method for Optimization with Parabolic PDEs

To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the necessity of solving both the state equation and a backward-in-time adjoint equation to evaluate the reduced gradient in each iteration of the optimization method. In this study, we investigate the use of the parallel-in-time method PFASST in the setting of PDE-constrained optimization. In order to develop an efficient fully time-parallel algorithm, we discuss different options for applying PFASST to adjoint gradient computation, including the possibility of doing PFASST iterations on both the state and the adjoint equations simultaneously. Here, we also explore the additional gains in efficiency from reusing information from previous optimization iterations when solving each equation. Numerical results for both a linear and a nonlinear reaction-diffusion optimal control problem demonstrate the parallel speedup and efficiency of different approaches.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

A derivation and scalable implementation of the synchronous parallel kinetic Monte Carlo method for simulating long-time dynamics

Kinetic Monte Carlo (KMC) simulations are used to study long-time dynamics of a wide variety of systems. Unfortunately, the conventional KMC algorithm is not scalable to larger systems, since its time scale is inversely proportional to the simulated system size. A promising approach to resolving this issue is the synchronous parallel KMC (SPKMC) algorithm, which makes the time scale size-independent. This paper introduces a formal derivation of the SPKMC algorithm based on local transition-state and time-dependent Hartree approximations, as well as its scalable parallel implementation based on a dual linked-list cell method. The resulting algorithm has achieved a weak-scaling parallel efficiency of 0.935 on 1024 Intel Xeon processors for simulating biological electron transfer dynamics in a 4.2 billion-heme system, as well as decent strong-scaling parallel efficiency. The parallel code has been used to simulate a lattice of cytochrome complexes on a bacterial-membrane nanowire, and it is broadly applicable to other problems such as computational synthesis of new materials.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Multithreaded parallelization of the energy and analytic gradient in the fragment molecular orbital method

The fragment molecular orbital method in GAMESS is parallelized in a multithreaded OpenMP implementation combined with the MPI version of the two-level generalized distributed data interface. The energy and analytic gradient in gas phase and the polarizable continuum model of solvation are parallelized in this hybrid three-level scheme, achieving a large memory footprint reduction and a high parallel efficiency on Intel Xeon Phi processors. The parallel efficiency is demonstrated on the Stampede2 and Theta supercomputers using up to 2048 nodes (262 144 threads).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

A survey on software methods to improve the energy efficiency of parallel computing

Energy consumption is one of the top challenges for achieving the next generation of supercomputing. Codesign of hardware and software is critical for improving energy efficiency (EE) for future large-scale systems. Many architectural power-saving techniques have been developed, and most hardware components are approaching physical limits. Accordingly, parallel computing software, including both applications and systems, should exploit power-saving hardware innovations and manage efficient energy use. In addition, new power-aware parallel computing methods are essential to decrease energy usage further. This article surveys software-based methods that aim to improve EE for parallel computing. It reviews the methods that exploit the characteristics of parallel scientific applications, including load imbalance and mixed precision of floating-point (FP) calculations, to improve EE. In addition, this article summarizes widely used methods to improve power usage at different granularities, such as the whole system and per application. In particular, it describes the most important techniques to measure and to achieve energy-efficient usage of various parallel computing facilities, including processors, memories, and networks. Overall, this article reviews the state-of-the-art of energy-efficient methods for parallel computing to motivate researchers to achieve optimal parallel computing under a power budget constraint.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2011

A Cut-Cell Approach for 2D Cartesian Meshes that Preserves Orthogonal Grid Sweep Ordering

In this paper, we present a cut-cell methodology for solving the two-dimensional neutral-particle transport equation on an orthogonal Cartesian grid. We allow the rectangular cell to be subdivided into two polygonal subcells. We ensure that this division (or cut) conserves the volumes of the materials in the subcells and we utilize a step-characteristics (SC) slice balance approach (SBA) to calculate the angular fluxes exiting the cell as well as the average scalar fluxes in each subcell. Solving the discrete ordinates transport equation on an arbitrary mesh has historically been difficult to parallelize while maintaining good parallel efficiency. However on Cartesian meshes, the KBA algorithm maintains good parallel efficiency using a direct solve. The ability to preserve this algorithm was a driving factor in the development of our cut-cell method. This method also provides a more accurate depiction of a material interface in a cell, which leads to more accurate solutions downstream of this cell. As a result, fewer spatial cells can be utilized, resulting in reduced memory requirements. We apply this approach in the 2D/3D discrete ordinates neutral-particle transport code Denovo, where we analyze a 2D 3 x 3 lattice of pincells. We show that, for eigenvalue problems, a significant increase in accuracy for a given mesh size is gained by utilizing the cut-cell, SC equations instead of the standard homogenized-cell, SC equations.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2016

Multi-node and Multi-core Performance Studies of a Monte Carlo code RMC

Over the past 15 years the architecture of high-performance computing systems has become increasingly heterogeneous with individual computing cores being subdivided into nodes and even auxiliary co-processing units such as graphics processing units or the Intel many integrated core co-processors. In fact, future computer platforms is moving toward a larger number of nodes and cores with lower memory available per node. Today, several production Monte Carlo codes use some types of hybrid parallelism strategy that makes use of shared-memory parallelism within a computing node and message-passing parallelism between nodes, which enables the codes to utilize available computing resources as much as possible, both among and within computing nodes on a cluster. The so-called hybrid parallelization is also possible with Reactor Monte Carlo Code RMC by activating both MPI and OpenMP parallel algorithms together. On HPC' which typically consists of several or several-ten thousand nodes equipping 16-32 computing intra-cores per node, simulation of RMC can be carried out in the hybrid parallelization with the MPI inter-node parallelization and the OpenMP intra-node parallelization. RMC has adopted a hybrid message-passing and shared-memory approach to parallelism, which enables the code to utilize available computing resources, both among and within computing nodes on a cluster. Shared-memory parallelism is especially valuable for large-model simulations because it enables multiple compute cores within a node to share common model information such as the geometry description, material, cross section and tally data, thus reducing the memory usage per processor. The calculation on the Tianhe-2 supercomputer took 6144 cores, resulting in a rate of 173,314,000 neutrons/minute for BEAVRS benchmark. While pin-wise full core H-M benchmark burnup calculations with millions of depletion regions was selected using MPI/OpenMP parallelism, the speed of 6,144 cores reach 1,843,200 burnable regions per minute. Keeping up with the continuing trend for increases in the number of computing resources within modern HPC systems is a significant challenge for teams that develop and maintain high-performance MC radiation transport solvers. order to address this challenge, RMC has adopted a hybrid message-passing and shared-memory approach to parallelism, which enables the code to utilize available computing resources, both among and within computing nodes on a cluster. Shared-memory parallelism is especially valuable for large-model simulations because it enables multiple compute cores within a node to share common model information such as the geometry description, material and composition definitions, and cross section data, thus reducing the memory usage per processor. The parallel performance has been studied by using two complex and representative benchmarks, H-M and BEAVRS benchmark. All simulations were run on Intel Xeon E5-2692 12 core, 2.2 GHz processors at MilkyWay-2 Super Computer with up to 12,288 available computing cores. While employing MPI parallelism, excellent parallel efficiency is achieved even above 12,000 processors and RMC reaches the parallel efficiency of 96% on 12,288 cores for the pin-by-pin computation of the BEAVRS benchmark. While BEAVRS criticality benchmark was selected using MPI/OpenMP parallelism, the speed of 6,144 cores reach 173,314,000 particles per minute. While pin-wise full core H-M benchmark burnup calculations with millions of depletion regions was selected using MPI/OpenMP parallelism, the speed of 6,144 cores reach 1,843,200 burnable regions per minute. Results from these studies demonstrate that RMC, using the hybrid parallel model described in this paper, is able to handle pin-wise full core burnup calculations with millions of depletion regions and scales well through thousands of processors. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Enabling kilometer-scale E3SM land model simulation over North America: A new integrated framework solution

This study introduces a novel framework designed to enhance the performance, scalability, and portability of the kilometer-scale E3SM Land Model (km-ELM) within the E3SM modeling infrastructure. By seamlessly integrating cutting-edge data tools, we address existing challenges such as slow performance, limited scalability, and difficulties in software integration in current data-driven ELM simulation over large geographic areas. Our innovative approach leverages the KiloCraft data toolkit to generate unified inputs for simulations ranging from a single-cite case, to a 72,083-cell regional case to a continental configuration encompassing 21.6 million land grid cells at a 1 km × 1 km resolution. We conduct extensive strong- and weak-scaling experiments on three state-of-the-art supercomputers, utilizing up to 100,800 CPU cores across 2400 compute nodes to evaluate end-to-end metrics including wall-clock time, simulation-years-per-day (SYPD), initialization costs, and I/O throughput. Our results reveal the land (LND) component’s efficient scaling, demonstrating near-ideal weak scaling and strong-scaling parallel efficiencies reaching up to 87% at 50,400 cores. We confirm portability and reproducibility through bitwise-equivalent outputs across different machines using identical inputs over supported machines. Notably, at extreme scales, we identify I/O as a critical bottleneck and that leads to effective solution with the SCORPIO/ADIOS stack. Collectively, these findings validate the deployment of km-ELM at a continental scale with high parallel efficiency and provide essential guidance on configuration, decomposition, and I/O settings for optimized kilometer-scale land simulations in E3SM. This work emphasizes the innovative design and practical solutions that enhance the operational capabilities of km-ELM, focusing on software performance and scalability while leaving detailed scientific evaluations of simulated land processes for future investigations.

E3SM land model (ELM), km-ELM, scalability, perfor↗

DOE OSTI2021

Twelve Ways to Fool the Masses When Giving Parallel-in-Time Results

Getting good speedup—let alone high parallel efficiency—for parallel-in-time (PinT) integration examples can be frustratingly difficult. The high complexity and large number of parameters in PinT methods can easily (and unintentionally) lead to numerical experiments that overestimate the algorithm’s performance. In the tradition of Bailey’s article “Twelve ways to fool the masses when giving performance results on parallel computers”, we discuss and demonstrate pitfalls to avoid when evaluating the performance of PinT methods. Despite being written in a light-hearted tone, this paper is intended to raise awareness that there are many ways to unintentionally fool yourself and others and that by avoiding these fallacies more meaningful PinT performance results can be obtained.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Counting Kmers for Biological Sequences at Large Scale

Counting the abundance of all the distinct kmers in biological sequence data is a fundamental step in bioinformatics. These applications include de novo genome assembly, error correction, etc. With the development of sequencing technology, the sequence data in a single project can reach Petabyte-scale or Terabyte-scale nucleotides. Counting demand for the abundance of these sequencing data is beyond the memory and computing capacity of single computing node, and how to process it efficiently is a challenge on a high-performance computing cluster. As such, we propose SWAPCounter, a highly scalable distributed approach for kmer counting. This approach is embedded with an MPI streaming I/O module for loading huge data set at high speed, and a counting bloom filter module for both memory and communication efficiency. By overlapping all the counting steps, SWAPCounter achieves high scalability with high parallel efficiency. In this work, the experimental results indicate that SWAPCounter has competitive performance with two other tools on shared memory environment, KMC 2 , and MSPKmerCounter. Moreover, SWAPCounter also shows the highest scalability under strong scaling experiments. In our experiment on Cetus supercomputer, SWAPCounter scales to 32,768 cores with 79% parallel efficiency (using 2048 cores as baseline) when processing 4 TB sequence data of 1000 Genomes. The source code of SWAPCounter is publicly available at https://github.com/mengjintao/SWAPCounter.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2011

Simplified Parallel Domain Traversal

Many data-intensive scientific analysis techniques require global domain traversal, which over the years has been a bottleneck for efficient parallelization across distributed-memory architectures. Inspired by MapReduce and other simplified parallel programming approaches, we have designed DStep, a flexible system that greatly simplifies efficient parallelization of domain traversal techniques at scale. In order to deliver both simplicity to users as well as scalability on HPC platforms, we introduce a novel two-tiered communication architecture for managing and exploiting asynchronous communication loads. We also integrate our design with advanced parallel I/O techniques that operate directly on native simulation output. We demonstrate DStep by performing teleconnection analysis across ensemble runs of terascale atmospheric CO{sub 2} and climate data, and we show scalability results on up to 65,536 IBM BlueGene/P cores.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2010

Factors impacting performance of multithreaded sparse triangular solve.

As computational science applications grow more parallel with multi-core supercomputers having hundreds of thousands of computational cores, it will become increasingly difficult for solvers to scale. Our approach is to use hybrid MPI/threaded numerical algorithms to solve these systems in order to reduce the number of MPI tasks and increase the parallel efficiency of the algorithm. However, we need efficient threaded numerical kernels to run on the multi-core nodes in order to achieve good parallel efficiency. In this paper, we focus on improving the performance of a multithreaded triangular solver, an important kernel for preconditioning. We analyze three factors that affect the parallel performance of this threaded kernel and obtain good scalability on the multi-core nodes for a range of matrix sizes.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2010

Factors impacting performance of multithreaded triangular solve.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2013

HACC: extreme scaling and performance across diverse architectures, In: SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis

Supercomputing is evolving towards hybrid and accelerator-based architectures with millions of cores. The HACC (Hardware/Hybrid Accelerated Cosmology Code) framework exploits this diverse landscape at the largest scales of problem size, obtaining high scalability and sustained performance. Developed to satisfy the science requirements of cosmological surveys, HACC melds particle and grid methods using a novel algorithmic structure that flexibly maps across architectures, including CPU/GPU, multi/many-core, and Blue Gene systems. We demonstrate the success of HACC on two very different machines, the CPU/GPU system Titan and the BG/Q systems Sequoia and Mira, attaining unprecedented levels of scalable performance. We demonstrate strong and weak scaling on Titan, obtaining up to 99.2% parallel efficiency, evolving 1.1 trillion particles. On Sequoia, we reach 13.94 PFlops (69.2% of peak) and 90% parallel efficiency on 1,572,864 cores, with 3.6 trillion particles, the largest cosmological benchmark yet performed. HACC design concepts are applicable to several other supercomputer applications.

Computer Science↗

DOE OSTI2021

AENET–LAMMPS and AENET–TINKER : Interfaces for accurate and efficient molecular dynamics simulations with machine learning potentials

Machine-learning potentials (MLPs) trained on data from quantum-mechanics based first-principles methods can approach the accuracy of the reference method at a fraction of the computational cost. To facilitate efficient MLP-based molecular dynamics and Monte Carlo simulations, an integration of the MLPs with sampling software is needed. Here, we develop two interfaces that link the atomic energy network (ænet) MLP package with the popular sampling packages TINKER and LAMMPS. The three packages, ænet, TINKER, and LAMMPS, are free and open-source software that enable, in combination, accurate simulations of large and complex systems with low computational cost that scales linearly with the number of atoms. Scaling tests show that the parallel efficiency of the ænet–TINKER interface is nearly optimal but is limited to shared-memory systems. The ænet–LAMMPS interface achieves excellent parallel efficiency on highly parallel distributed memory systems and benefits from the highly optimized neighbor list implemented in LAMMPS. We demonstrate the utility of the two MLP interfaces for two relevant example applications: the investigation of diffusion phenomena in liquid water and the equilibration of nanostructured amorphous battery materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

HBMax: Optimizing Memory Efficiency for Parallel Influence Maximization on Multicore Architectures

The goal of influence maximization is to select k most-influential vertices or seeds in a network, where influence is defined by a given diffusion process. The problem has a number of important applications such as viral marketing, information spread, and epidemic control. Although computing optimal seed set is NP-Hard, due to the submodular nature of the problem efficient approximation algorithms exist. However, even state-of-the-art parallel implementations are limited by a sampling step that incurs large memory footprints. This in turn limits the problem size reach and approximation quality. In this work, we study the memory footprint of the sampling process collecting reverse reachability information in the IMM algorithm over large real-world social networks. We present an adaptive and memory-efficient optimization approach for a state-of-the-art multi-threaded parallel influence maximization algorithm. Our approach,HuffMax, uses a portion of the reverse reachable (RR) sets collected by the algorithm to learn the characteristics of the graph. Then, it compresses the intermediate reverse reachability information with Huffman coding, and queries directly on the compressed data to preserve the memory savings obtained through compression. We also propose an efficient sampling strategy based on the distribution of RR sets, which can further reduce the computation time for typical social networks with long-tail distributions. Considering a NUMA architecture, we scale up our solution on 128-core CPUs and reduce the memory footprint by up to 45.7% with negligible time overhead (or even faster) and without perceivable loss of accuracy.

Chen, Xinyu↗

DOE OSTI2020

Scalable All-pairs Shortest Paths for Huge Graphs on Multi-GPU Clusters

We present an optimized Floyd-Warshall (Floyd-Warshall) algorithm that computes the All-pairs shortest path (APSP) for GPU accelerated clusters. The Floyd-Warshall algorithm due to its structural similarities to matrix-multiplication is well suited for highly parallel GPU architectures. To achieve high parallel efficiency, we address two key algorithmic challenges: reducing high communication overhead and addressing limited GPU memory. To reduce high communication costs, we redesign the parallel (a) to expose more parallelism, (b) aggressively overlap communication and computation with pipelined and asynchronous scheduling of operations, and (c) tailored MPI-collective. To cope with limited GPU memory, we employ an offload model, where the data resides on the host and is transferred to GPU on-demand. The proposed optimizations are supported with detailed performance models for tuning. Our optimized parallel Floyd-Warshall implementation is up to 5x faster than a strong baseline and achieves 8.1 PetaFLOPS/sec on 256~nodes of the Summit supercomputer at Oak Ridge National Laboratory. This performance represents 70% of the theoretical peak and 80% parallel efficiency. The offload algorithm can handle 2.5x larger graphs with a 20% increase in overall running time.

Sao, Piyush↗

DOE OSTI2021

Domain decomposition in the GPU-accelerated Shift Monte Carlo code

The GPU solver within the Shift continuous-energy Monte Carlo neutron transport code has been extended to provide domain decomposition in addition to domain replication to enable the solution of problems with memory requirements exceeding the capacity of a single GPU. The strategy follows the Multiple Set, Overlapping Domain (MSOD) approach that is used in Shift’s CPU solver and integrates into the event-based algorithm used for Shift’s GPU solver. Furthermore, the ability to assign processors to spatial domains non-uniformly has been maintained. In this work, two different approaches for communicating particle data between domains are considered, and multiple criteria for load balancing problems have been investigated. Numerical results are presented for both fresh and depleted small modular nuclear reactor (SMR) cores. A parallel efficiency of approximately 80% was achieved with up to 16 spatial domains measured relative to full domain replication. A scaling study on the Summit supercomputer demonstrates a weak scaling parallel efficiency of over 90% on over 24000 GPUs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

Petascale turbulence simulation using a highly parallel fast multipole method on GPUs

This paper reports large-scale direct numerical simulations of homogeneous-isotropic fluid turbulence, achieving sustained performance of 1.08 petaflop/s on gpu hardware using single precision. The simulations use a vortex particle method to solve the Navier–Stokes equations, with a highly parallel fast multipole method (fmm) as numerical engine, and match the current record in mesh size for this application, a cube of computational points solved with a spectral method. The standard numerical approach used in this field is the pseudo-spectral method, relying on the fft algorithm as the numerical engine. The particle-based simulations presented in this paper quantitatively match the kinetic energy spectrum obtained with a pseudo-spectral method, using a trusted code. In terms of parallel performance, weak scaling results show the fmm-based vortex method achieving 74% parallel efficiency on 4096 processes (one gpu per mpi process, 3 gpus per node of the tsubame-2.0 system). The fft-based spectral method is able to achieve just 14% parallel efficiency on the same number of mpi processes (using only cpu cores), due to the all-to-all communication pattern of the fft algorithm. The calculation time for one time step was 108 s for the vortex method and 154 s for the spectral method, under these conditions. Computing with 69 billion particles, this work exceeds by an order of magnitude the largest vortex-method calculations to date.

Computer Science↗