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DOE OSTI2018

Scaling Structured Multigrid to 500K+ Cores Through Coarse-Grid Redistribution

The effcient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for common discretizations makes them a good candidate for an efficient parallel solver. Yet, modern architectures for high-performance computing systems continue to challenge the parallel scalability of multilevel solvers. While algebraic multigrid methods are robust for solving a variety of problems, the increasing importance of data locality and cost of data movement in modern architectures motivates the need to carefully exploit structure in the problem. Robust logically structured variational multigrid methods, such as Black Box Multigrid (BoxMG), maintain structure throughout the multigrid hierarchy. This avoids indirection and increased coarse- grid communication costs typical in parallel algebraic multigrid. Nevertheless, the parallel scalability of structured multigrid is challenged by coarse-grid problems where the overhead in communication dominates computation. In this paper, an algorithm is introduced for redistributing coarse-grid problems through incremental agglomeration. Guided by a predictive performance model, this algorithm provides robust redistribution decisions for structured multilevel solvers. A two-dimensional diffusion problem is used to demonstrate the significant gain in performance of this algorithm over the previous approach that used agglomeration to one processor. In addition, the parallel scalability of this approach

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

A Framework for Lattice QCD Calculations on GPUs

Efficient calculation of the greatest common divisor (GCD) for big integers each whose number of bits is greater than or equal to 1024 has drawn a considerable amount of attention because it can be used to detect a weakness of the RSA security infrastructure. This paper presents a parallel binary GCD algorithm and its implementation for big integers on the Intel Xeon Phi coprocessor. This algorithm is capable of computing GCDs efficiently on many pairs of big integers in parallel by utilizing all cores on a Xeon Phi coprocessor as well as taking advantage of all vector processing units of the coprocessor to speed up critical integer operations within the algorithm. Using 240 threads on a Xeon Phi coprocessor to carry out GCD calculations for a large amount of 2048-bit integers, the implementation achieves the speedup of 30 times over a sequential binary GCD algorithm implementation on a single CPU core, and it delivers twice amount of performance in comparison to the same sequential binary GCD implementation running on 240 threads of the Xeon Phi.

Winter, F. T.↗

DOE OSTI2026

Speedup of UEDGE Parameter Scans Using Machine-Learning Optimized OpenMP Parallelization and a Continuation Solver

This article presents the OpenMP parallelization of the preconditioning Jacobian assembly and right‐hand side residual evaluation in UEDGE. A continuation algorithm, utilizing the internal NKSOL implicit Jacobian‐Free Newton‐Krylov solver to efficiently scan physical parameters, is also presented. The implemented parallelization reduces the computational time for a benchmark scan run on 32 threads by compared to the serial version when using trained random forest regression models to identify the optimal decomposition of the system of equations. Random forest regression models applied to the UEDGE time‐dependent and continuation solver algorithms did not yield meaningful improvement in computational performance. A benchmark DIII‐D gas injection rate scan in the 0.35–0.75 kA interval, performed on a test cluster using the parallelized code and continuation solver, produced 1066 steady‐state solutions with a 22 s average wall‐clock computational time per steady‐state solution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

NEXTorch: A Design and Bayesian Optimization Toolkit for Chemical Sciences and Engineering

Automation and optimization of chemical systems require well-informed decisions on what experiments to run to reduce time, materials, and/or computations. Data-driven active learning algorithms have emerged as valuable tools to solve such tasks. Bayesian optimization, a sequential global optimization approach, is a popular active-learning framework. Past studies have demonstrated its efficiency in solving chemistry and engineering problems. Here we introduce NEXTorch, a library in Python/PyTorch, to facilitate laboratory or computational design using Bayesian optimization. NEXTorch offers fast predictive modeling, flexible optimization loops, visualization capabilities, easy interfacing with legacy software, and multiple types of parameters and data type conversions. It provides GPU acceleration, parallelization, and state-of-the-art Bayesian optimization algorithms and supports both automated an d human-in-the-loop optimization. The comprehensive online documentation introduces Bayesian optimization theory and several examples from catalyst synthesis, reaction condition optimization, parameter estimation, and reactor geometry optimization. NEXTorch is open-source and available on GitHub

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2013

GROMACS 4.5: A high-throughput and highly parallel open source molecular simulation toolkit

In this study, molecular simulation has historically been a low-throughput technique, but faster computers and increasing amounts of genomic and structural data are changing this by enabling large-scale automated simulation of, for instance, many conformers or mutants of biomolecules with or without a range of ligands. At the same time, advances in performance and scaling now make it possible to model complex biomolecular interaction and function in a manner directly testable by experiment. These applications share a need for fast and efficient software that can be deployed on massive scale in clusters, web servers, distributed computing or cloud resources. As a result, we present a range of new simulation algorithms and features developed during the past 4 years, leading up to the GROMACS 4.5 software package. The software now automatically handles wide classes of biomolecules, such as proteins, nucleic acids and lipids, and comes with all commonly used force fields for these molecules built-in. GROMACS supports several implicit solvent models, as well as new free-energy algorithms, and the software now uses multithreading for efficient parallelization even on low-end systems, including windows-based workstations. Together with hand-tuned assembly kernels and state-of-the-art parallelization, this provides extremely high performance and cost efficiency for high-throughput as well as massively parallel simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

An advanced algorithm for construction of Integral Transport Matrix Method operators using accumulation of single cell coupling factors

The Integral Transport Matrix Method (ITMM) has been shown to be an effective method for solving the neutron transport equation in large domains on massively parallel architectures. In the limit of very large number of processors, the speed of the algorithm, and its suitability for unstructured meshes, i.e. other than an ordered Cartesian grid, is limited by the construction of four matrix operators required for obtaining the solution in each sub-domain. The existing algorithm used for construction of these matrix operators, termed the differential mesh sweep, is computationally expensive and was developed for a structured grid. This work proposes the use of a new algorithm for construction of these operators based on the construction of a single, fundamental matrix representing the transport of a particle along every possible path throughout the sub-domain mesh. Each of the operators is constructed by multiplying an element of this fundamental matrix by two factors dependent only upon the operator being constructed and on properties of the emitting and incident cells. The ITMM matrix operator construction time for the new algorithm is demonstrated to be shorter than the existing algorithm in all tested cases with both isotropic and anisotropic scattering considered. While also being a more efficient algorithm on a structured Cartesian grid, the new algorithm is promising in its geometric robustness and potential for being applied to an unstructured mesh, with the ultimate goal of application to an unstructured tetrahedral mesh on a massively parallel architecture. (authors)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

SU-D-18A-02: Towards Real-Time On-Board Volumetric Image Reconstruction for Intrafraction Target Verification in Radiation Therapy

Purpose: To expedite on-board volumetric image reconstruction from limited-angle kV—MV projections for intrafraction verification. Methods: A limited-angle intrafraction verification (LIVE) system has recently been developed for real-time volumetric verification of moving targets, using limited-angle kV—MV projections. Currently, it is challenged by the intensive computational load of the prior-knowledge-based reconstruction method. To accelerate LIVE, we restructure the software pipeline to make it adaptable to model and algorithm parameter changes, while enabling efficient utilization of rapidly advancing, modern computer architectures. In particular, an innovative two-level parallelization scheme has been designed: At the macroscopic level, data and operations are adaptively partitioned, taking into account algorithmic parameters and the processing capacity or constraints of underlying hardware. The control and data flows of the pipeline are scheduled in such a way as to maximize operation concurrency and minimize total processing time. At the microscopic level, the partitioned functions act as independent modules, operating on data partitions in parallel. Each module is pre-parallelized and optimized for multi-core processors (CPUs) and graphics processing units (GPUs). Results: We present results from a parallel prototype, where most of the controls and module parallelization are carried out via Matlab and its Parallel Computing Toolbox. The reconstruction is 5 times faster on a data-set of twice the size, compared to recently reported results, without compromising on algorithmic optimization control. Conclusion: The prototype implementation and its results have served to assess the efficacy of our system concept. While a production implementation will yield much higher processing rates by approaching full-capacity utilization of CPUs and GPUs, some mutual constraints between algorithmic flow and architecture specifics remain. Based on a careful analysis of the prototype performance, it will be feasible to resolve such issues through appropriate algorithmic modifications or special-purpose hardware, thus enabling target verification in seconds with the LIVE system. This work was partially supported by a research grant from Varian Medical Systems.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

Enhancing scalability of a matrix-free eigensolver for studying many-body localization

We propose several techniques to enhance the parallel scalability of a matrix-free eigensolver designed for studying many-body localization (MBL) of quantum spin chain models with nearest-neighbor interactions and on-site disorder. This type of problem is computationally challenging because the dimension of the associated Hamiltonian matrix grows exponentially with respect to the number of spins L, and we need to average over different realizations of the random disorder to obtain relevant statistical behavior. For each disorder realization, we need to compute eigenvalues from different regions of the spectrum and their corresponding eigenvectors. In previous work, the interior eigenstates for a single eigenvalue problem are computed via the shift-and-invert Lanczos algorithm. Due to the extremely high memory footprint of the LU factorizations, this technique is not well suited for large L’s. For example, we need thousands of compute nodes on modern high performance computing infrastructures to go beyond L = 24. The matrix-free approach does not suffer from this memory bottleneck, however, its scalability is limited by a computation and communication load imbalance. To reduce this imbalance and to significantly enhance the scalability of the matrix-free eigensolver, we reorder the matrix and leverage the consistent space runtime, CSPACER. We also show its efficiency in managing irregular communication patterns at scale compared to optimized MPI non-blocking two-sided and one-sided RMA implementation variants. This effort enables us to study MBL for spin chains with a larger number of spins. The efficiency and effectiveness of the proposed algorithm is demonstrated by computing eigenstates on a massively parallel many-core high performance computer.

METIS↗

DOE OSTI2018

Concurrent implicit spectral deferred correction scheme for low-Mach number combustion with detailed chemistry

We present a parallel multi-implicit time integration scheme for the advection-diffusion-reaction systems arising from the equations governing low-Mach number combustion with complex chemistry. Here, our strategy employs parallelisation across the method to accelerate the serial Multi-Implicit Spectral Deferred Correction (MISDC) scheme used to couple the advection, diffusion, and reaction processes. In our approach, the diffusion solves and the reaction solves are performed concurrently by different processors. Our analysis shows that the proposed parallel scheme is stable for stiff problems and that the sweeps converge to the fixed-point solution at a faster rate than with serial MISDC. We present numerical examples to demonstrate that the new algorithm is high-order accurate in time, and achieves a parallel speedup compared to serial MISDC.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Towards a more general understanding of the algorithmic utility of recurrent connections

Lateral and recurrent connections are ubiquitous in biological neural circuits. Yet while the strong computational abilities of feedforward networks have been extensively studied, our understanding of the role and advantages of recurrent computations that might explain their prevalence remains an important open challenge. Foundational studies by Minsky and Roelfsema argued that computations that require propagation of global information for local computation to take place would particularly benefit from the sequential, parallel nature of processing in recurrent networks. Such “tag propagation” algorithms perform repeated, local propagation of information and were originally introduced in the context of detecting connectedness, a task that is challenging for feedforward networks. Here, we advance the understanding of the utility of lateral and recurrent computation by first performing a large-scale empirical study of neural architectures for the computation of connectedness to explore feedforward solutions more fully and establish robustly the importance of recurrent architectures. In addition, we highlight a tradeoff between computation time and performance and construct hybrid feedforward/recurrent models that perform well even in the presence of varying computational time limitations. We then generalize tag propagation architectures to propagating multiple interacting tags and demonstrate that these are efficient computational substrates for more general computations of connectedness by introducing and solving an abstracted biologically inspired decision-making task. Our work thus clarifies and expands the set of computational tasks that can be solved efficiently by recurrent computation, yielding hypotheses for structure in population activity that may be present in such tasks.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2019

PaKman: Scalable Assembly of Large Genomes on Distributed Memory Machines

De novo genome assembly is a fundamental problem in the field of bioinformatics, that aims to assemble the DNA sequence of an unknown genome from numerous short DNA fragments (aka reads) obtained from it. With the advent of high-throughput sequencing technologies, billions of reads can be generated in a matter of hours, necessitating efficient parallelization of the assembly process. While multiple parallel solutions have been proposed in the past, conducting a large- scale assembly at scale remains a challenging problem because of the inherent complexities associated with data movement, and irregular access footprints of memory and I/O operations. In this paper, we present a novel algorithm, called PaKman, to address the problem of performing large-scale genome assemblies on a distributed memory parallel computer. Our approach focuses on improving performance through a combination of novel data structures and algorithmic strategies for reducing the communication and I/O footprint during the assembly process. A key aspect of our algorithm is its graph data structure, which comprises fat nodes (or what we call "macro-nodes") that reduce the communication burden during contig generation. We present an extensive performance and qualitative evaluation of our algorithm, including comparisons to other state-of-the-art parallel assemblers. Our results demonstrate the ability to achieve near-linear speedups on up to 8K cores (tested); outperform state-of-the-art distributed memory and shared memory tools in performance while delivering comparable (if not better) quality; and reduce time to solution significantly. For instance, PaKman is able to complete an assembly of the full human genome in just over a minute on 8K cores.

Ghosh, Priyanka↗

DOE OSTI2015

Batched matrix computations on hardware accelerators based on GPUs

Scientific applications require solvers that work on many small size problems that are independent from each other. At the same time, the high-end hardware evolves rapidly and becomes ever more throughput-oriented and thus there is an increasing need for an effective approach to develop energy-efficient, high-performance codes for these small matrix problems that we call batched factorizations. The many applications that need this functionality could especially benefit from the use of GPUs, which currently are four to five times more energy efficient than multicore CPUs on important scientific workloads. This study, consequently, describes the development of the most common, one-sided factorizations, Cholesky, LU, and QR, for a set of small dense matrices. The algorithms we present together with their implementations are, by design, inherently parallel. In particular, our approach is based on representing the process as a sequence of batched BLAS routines that are executed entirely on a GPU. Importantly, this is unlike the LAPACK and the hybrid MAGMA factorization algorithms that work under drastically different assumptions of hardware design and efficiency of execution of the various computational kernels involved in the implementation. Thus, our approach is more efficient than what works for a combination of multicore CPUs and GPUs for the problems sizes of interest of the application use cases. The paradigm where upon a single chip (a GPU or a CPU) factorizes a single problem at a time is not at all efficient in our applications’ context. We illustrate all of these claims through a detailed performance analysis. With the help of profiling and tracing tools, we guide our development of batched factorizations to achieve up to two-fold speedup and three-fold better energy efficiency as compared against our highly optimized batched CPU implementations based on MKL library. Finally, the tested system featured two sockets of Intel Sandy Bridge CPUs and we compared with a batched LU factorizations featured in the CUBLAS library for GPUs, we achieve as high as 2.5× speedup on the NVIDIA K40 GPU.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Efficient First-Order Algorithms for Large-Scale, Non-Smooth Maximum Entropy Models with Application to Wildfire Science

Maximum entropy (MaxEnt) models are a class of statistical models that use the maximum entropy principle to estimate probability distributions from data. Due to the size of modern data sets, MaxEnt models need efficient optimization algorithms to scale well for big data applications. State-of-the-art algorithms for MaxEnt models, however, were not originally designed to handle big data sets; these algorithms either rely on technical devices that may yield unreliable numerical results, scale poorly, or require smoothness assumptions that many practical MaxEnt models lack. In this paper, we present novel optimization algorithms that overcome the shortcomings of state-of-the-art algorithms for training large-scale, non-smooth MaxEnt models. Our proposed first-order algorithms leverage the Kullback–Leibler divergence to train large-scale and non-smooth MaxEnt models efficiently. For MaxEnt models with discrete probability distribution of n elements built from samples, each containing m features, the stepsize parameter estimation and iterations in our algorithms scale on the order of O(mn) operations and can be trivially parallelized. Moreover, the strong ℓ1 convexity of the Kullback–Leibler divergence allows for larger stepsize parameters, thereby speeding up the convergence rate of our algorithms. To illustrate the efficiency of our novel algorithms, we consider the problem of estimating probabilities of fire occurrences as a function of ecological features in the Western US MTBS-Interagency wildfire data set. Our numerical results show that our algorithms outperform the state of the art by one order of magnitude and yield results that agree with physical models of wildfire occurrence and previous statistical analyses of wildfire drivers.

Physics↗

DOE OSTI2015

Modeling of fracture of protective concrete structures under impact loads

This paper presents results of numerical simulation of interaction between a Boeing 747-400 aircraft and the protective shell of a nuclear power plant. The shell is presented as a complex multilayered cellular structure consisting of layers of concrete and fiber concrete bonded with steel trusses. Numerical simulation was performed three-dimensionally using the original algorithm and software taking into account algorithms for building grids of complex geometric objects and parallel computations. Dynamics of the stress-strain state and fracture of the structure were studied. Destruction is described using a two-stage model that allows taking into account anisotropy of elastic and strength properties of concrete and fiber concrete. It is shown that wave processes initiate destruction of the cellular shell structure; cells start to destruct in an unloading wave originating after the compression wave arrival at free cell surfaces.

36 MATERIALS SCIENCE↗

DOE OSTI2018

A practical guide to replica-exchange Wang—Landau simulations

This paper is based on a series of tutorial lectures about the replica-exchange Wang-Landau (REWL) method given at the IX Brazilian Meeting on Simulational Physics (BMSP 2017). It provides a practical guide for the implementation of the method. A complete example code for a model system is available online. In this paper, we discuss the main parallel features of this code after a brief introduction to the REWL algorithm. The tutorial section is mainly directed at users who have written a single-walker Wang–Landau program already but might have just taken their first steps in parallel programming using the Message Passing Interface (MPI). In the last section, we answer "frequently asked questions" from users about the implementation of REWL for different scientific problems.

Vogel, Thomas↗

DOE OSTI2016

Extreme-scale Algorithms and Solver Resilience

A widening gap exists between the peak performance of high-performance computers and the performance achieved by complex applications running on these platforms. Over the next decade, extreme-scale systems will present major new challenges to algorithm development that could amplify this mismatch in such a way that it prevents the productive use of future DOE Leadership computers due to the following; Extreme levels of parallelism due to multicore processors; An increase in system fault rates requiring algorithms to be resilient beyond just checkpoint/restart; Complex memory hierarchies and costly data movement in both energy and performance; Heterogeneous system architectures (mixing CPUs, GPUs, etc.); and Conflicting goals of performance, resilience, and power requirements.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Scalable quantum computational science: A perspective from block-encodings and polynomial transformations

Significant developments made in quantum hardware and error correction recently have been driving quantum computing toward practical utility. However, gaps remain between abstract quantum algorithmic development and practical applications in computational sciences. In this perspective article, we propose several properties that scalable quantum computational science methods should possess. We further discuss how block-encodings and polynomial transformations can potentially serve as a unified framework with the desired properties. Recent advancements on these topics are presented, including the construction and assembly of block-encodings, and various generalizations of quantum signal processing (QSP) algorithms to perform polynomial transformations. The scalability of QSP methods on parallel and distributed quantum architectures is also highlighted. Promising applications in simulation and observable estimation in chemistry, physics, and optimization problems are presented. We hope this perspective serves as a gentle introduction to state-of-the-art quantum algorithms for the computational science community and inspires future development of scalable quantum computational science methodologies that bridge theory and practice.

Bayesian inference↗

DOE OSTI2024

The VTK-m User's Guide (V. 2.2)

High-performance computing relies on ever finer threading. Advances in processor technology include ever greater numbers of cores, hyperthreading, accelerators with integrated blocks of cores, and special vectorized instructions, all of which require more software parallelism to achieve peak performance. Traditional visualization solutions cannot support this extreme level of concurrency. Extreme scale systems require a new programming model and a fundamental change in how we design algorithms. To address these issues we created VTK-m: the visualization toolkit for multi-/many-core architectures. VTK-m supports a number of algorithms and the ability to design further algorithms through a top-down design with an emphasis on extreme parallelism. VTK-m also provides support for finding and building links across topologies, making it possible to perform operations that determine manifold surfaces, interpolate generated values, and find adjacencies. Although VTK-m provides a simplified high-level interface for programming, its template-based code removes the overhead of abstraction.

97 MATHEMATICS AND COMPUTING↗