Speedup Research Articles

Refactoring BZIP2 on the new‐generation sunway supercomputer

AbstractHigh‐performance computing is progressively assuming a fundamental role in advancing scientific research and engineering domains. However, the ever‐expanding scales of scientific simulations pose challenges for efficient data I/O and storage. The data compression technology has garnered significant attention as a solution to reduce data transmission and storage costs while enhancing performance. In particular, the BZIP2 lossless compression algorithm has been widely used due to its exceptional compression ratio, moderate compression speed, high reliability, and open‐source nature. This paper focuses on the design and realization of a parallelized BZIP2 algorithm tailored for deployment on the New‐Generation Sunway supercomputing platform. By leveraging the unique cache patterns of the New‐Generation Sunway processor, we propose the highly tuned multi‐threading and multi‐node implementations of the BZIP2 applications for different scenarios. Moreover, we also propose the efficient BZIP2 libraries based on the management processing element and computing processing element which support the commonly used high‐level (de)compression interfaces. The test results indicate that the our multi‐threading implementation achieves maximum speedup of 23.09 (8.57) in decompression(compression) compared to the sequential implementation. Furthermore, the multi‐node implementation achieves 50.81% (26.35%) parallel efficiency and peak performance of 16.6 GB/s (52.8 GB/s) for compression(decompression) when scaling up to 2048 processes.

AdaSAM: Boosting sharpness-aware minimization with adaptive learning rate and momentum for training deep neural networks

Sharpness aware minimization (SAM) optimizer has been extensively explored as it can generalize better for training deep neural networks via introducing extra perturbation steps to flatten the landscape of deep learning models. Integrating SAM with adaptive learning rate and momentum acceleration, dubbed AdaSAM, has already been explored empirically to train large-scale deep neural networks without theoretical guarantee due to the triple difficulties in analyzing the coupled perturbation step, adaptive learning rate and momentum step. In this paper, we try to analyze the convergence rate of AdaSAM in the stochastic non-convex setting. We theoretically show that AdaSAM admits a O(1/bT) convergence rate, which achieves linear speedup property with respect to mini-batch size b. Specifically, to decouple the stochastic gradient steps with the adaptive learning rate and perturbed gradient, we introduce the delayed second-order momentum term to decompose them to make them independent while taking an expectation during the analysis. Then we bound them by showing the adaptive learning rate has a limited range, which makes our analysis feasible. To the best of our knowledge, we are the first to provide the non-trivial convergence rate of SAM with an adaptive learning rate and momentum acceleration. At last, we conduct several experiments on several NLP tasks and the synthetic task, which show that AdaSAM could achieve superior performance compared with SGD, AMSGrad, and SAM optimizers.

Dimensioning the pending interest table in content-centric networks

In chunk-based interest-driven content-centric networks, each interest packet forwarded upstream by a node on a face implies the return of at most one data chunk to the node from that face shortly after. As a consequence, the congestion of the downstream transmission buffer in the data path of the node is highly correlated with the occupancy of the pending interest table (PIT). Therefore a systematic study and analysis of the PIT occupancy are of paramount importance to understanding congestion in CCN. In particular, in this paper, we propose an analytical model to estimate the PIT occupancy distribution via a continuous-time Markov chain (CTMC) model that considers the effects of interest blocking, interest timeout and retries. To validate our model and assumptions, we invoke simulation with realistic traffic streams and show how the filtering effects of caching and interest aggregation make the Markov assumption reasonable in the nodes that are the most susceptible to experiencing congestion. To solve the model numerically, we use two alternative approximations, state space truncation and state aggregation, and then give some numerical results to demonstrate the accuracy of our approximations.

Local Second-Order Møller-Plesset Theory with a Single Threshold Using Orthogonal Virtual Orbitals: Theory, Implementation, and Assessment.

It has long been clear that electron correlation methods exhibit unphysical compute scalings with molecular size, which has motivated the development of local correlation methods to discard effectively zero contributions in a controlled way to yield an approximate correlation energy. The ideal local correlation method should have a single numerical threshold that controls the dropping of terms with the ability to have that threshold set small enough so that the correlation energy is reproduced to enough significant figures such that the result is chemically identical. This work reports such a method for the second-order Møller-Plesset (MP2) theory. The theory, implementation, and testing of this local MP2 theory are reported. Thresholds ranging from 10-5 to 10-8 and basis sets ranging from split valence plus polarization through to quadruple-ζ are assessed for local MP2 calculations on a range of molecules, including linear chains and molecules with two- and three-dimensional character. The implementation is shared memory parallel via OpenMP and yields roughly 50% parallel efficiency with 16 cores for a large job. Considerable efforts were made to minimize memory demands, which increased as thresholds were tightened. A variety of relative energy calculations are presented as a function of threshold to provide some guidance to users on how to obtain adequate precision at a low compute cost. It is particularly clear that derivative properties require tighter thresholds in order to achieve an adequate precision.

Accelerating Coupled-Cluster Calculations with GPUs: An Implementation of the Density-Fitted CCSD(T) Approach for Heterogeneous Computing Architectures Using OpenMP Directives.

An algorithm is presented for the coupled-cluster singles, doubles, and perturbative triples correction [CCSD(T)] method based on the density fitting or the resolution-of-the-identity (RI) approximation for performing calculations on heterogeneous computing platforms composed of multicore CPUs and graphics processing units (GPUs). The directive-based approach to GPU offloading offered by the OpenMP application programming interface has been employed to adapt the most compute-intensive terms in the RI-CCSD amplitude equations with computational costs scaling as , , and (where NO and NV denote the numbers of correlated occupied and virtual orbitals, respectively) and the perturbative triples correction to execute on GPU architectures. The pertinent tensor contractions are performed using an accelerated math library such as cuBLAS or hipBLAS. Optimal strategies are discussed for splitting large data arrays into tiles to fit them into the relatively small memory space of the GPUs, while also minimizing the low-bandwidth CPU-GPU data transfers. The performance of the hybrid CPU-GPU RI-CCSD(T) code is demonstrated on pre-exascale supercomputers composed of heterogeneous nodes equipped with NVIDIA Tesla V100 and A100 GPUs and on the world's first exascale supercomputer named "Frontier", the nodes of which consist of AMD MI250X GPUs. Speedups within the range 4-8× relative to the recently reported CPU-only algorithm are obtained for the GPU-offloaded terms in the RI-CCSD amplitude equations. Applications to polycyclic aromatic hydrocarbons containing 16-66 carbon atoms demonstrate that the acceleration of the hybrid CPU-GPU code for the perturbative triples correction relative to the CPU-only code increases with the molecule size, attaining a speedup of 5.7× for the largest circumovalene molecule (C66H20). The GPU-offloaded code enables the computation of the perturbative triples correction for the C60 molecule using the cc-pVDZ/aug-cc-pVTZ-RI basis sets in 7 min on Frontier when using 12,288 AMD GPUs with a parallel efficiency of 83.1%.

Virtual lattice method for efficient Monte Carlo transport simulation of dispersion nuclear fuels

The randomly dispersed Tristructural-isotropic (TRISO) particle fuel is an attractive nuclear fuel type widely used in advanced reactor designs. However, the massive randomly-distributed fuel elements and the prohibitive computational costs pose challenges for high-fidelity modeling and simulation of dispersion fuels. To address this, we present a virtual lattice optimization method for accelerating the Monte Carlo particle transport simulation of nuclear systems with dispersion fuels. The new method involves using a regular overlaid mesh on the dispersed fuel region to improve geometry processing in Monte Carlo simulations. We describe the optimization methodology in our paper and construct a theoretical performance model to determine the optimal lattice pitch size that minimizes calculation cost. We then develop and implement the algorithm of the virtual method in the open-source Monte Carlo code OpenMC. To demonstrate the efficacy of the new algorithm, high-fidelity HTR-PM full core models based on the Shidao-Bay nuclear power plant are constructed, including an explicit representation of up to 420,000 fuel pebbles. Criticality and depletion simulations are performed on large-scale models. Results show that the k-effective derived by the optimized code agrees well with both the experiment and the original code. Further performance comparison shows that the virtual lattice method exhibits lower time consumption, higher parallel efficiency, and lower storage requirement in comparison to the conventional physical lattice method. The study establishes the effectiveness of the proposed methodology in facilitating efficient and accurate high-fidelity simulations of large-scale dispersion fuel models.

A massive MPI parallel framework of smoothed particle hydrodynamics with optimized memory management for extreme mechanics problems

The dynamic failure process of structures under extreme loadings is very common in many fields of engineering and science. The smoothed particle hydrodynamics (SPH) method offers inherent benefits in dealing with complex interfaces and large material deformations in extreme mechanics problems. However, SPH simulations for 3D engineering applications are time-consuming. To address this issue, we introduce MPI (Message Passing Interface) in our SPH scheme to reduce computational time. Some optimizations are adopted to ensure the massive computation of the SPH method. In particular, an optimized memory management strategy is developed to control the memory footprint. With the present MPI-based massive parallelization of the SPH method, several validation examples are tested and analyzed. By comparing the present numerical results with the reference data, the dynamic failure process of complex structures subjected to extreme loadings like explosive and impact loadings can be well captured. A large number of particles, up to 2.04 billion, are adopted in the present simulations. The scaling tests show that the scalability of the massively parallel SPH program achieves a maximum parallel efficiency of 97% on 10020 CPU cores.

An improved dynamical Poisson equation solver for self-gravity

ABSTRACT Since self-gravity is crucial in the structure formation of the Universe, many hydrodynamics simulations with the effect of self-gravity have been conducted. The multigrid method is widely used as a solver for the Poisson equation of the self-gravity; however, the parallelization efficiency of the multigrid method becomes worse when we use a massively parallel computer, and it becomes inefficient with more than 104 cores, even for highly tuned codes. To perform large-scale parallel simulations (>104 cores), developing a new gravity solver with good parallelization efficiency is beneficial. In this article, we develop a new self-gravity solver using the telegraph equation with a damping coefficient, κ. Parallelization is much easier than the case of the elliptic Poisson equation since the telegraph equation is a hyperbolic partial differential equation. We analyse convergence tests of our telegraph equations solver and determine that the best non-dimensional damping coefficient of the telegraph equations is $\tilde{\kappa } \simeq 2.5$. We also show that our method can maintain high parallelization efficiency even for massively parallel computations due to the hyperbolic nature of the telegraphic equation by weak-scaling tests. If the time-step of the calculation is determined by heating/cooling or chemical reactions, rather than the Courant–Friedrichs–Lewy (CFL) condition, our method may provide the method for calculating self-gravity faster than other previously known methods such as the fast Fourier transform and multigrid iteration solvers because gravitational phase velocity determined by the CFL condition using these time-scales is much larger than the fluid velocity plus sound speed.

Lifex-ep: a robust and efficient software for cardiac electrophysiology simulations

BackgroundSimulating the cardiac function requires the numerical solution of multi-physics and multi-scale mathematical models. This underscores the need for streamlined, accurate, and high-performance computational tools. Despite the dedicated endeavors of various research teams, comprehensive and user-friendly software programs for cardiac simulations, capable of accurately replicating both normal and pathological conditions, are still in the process of achieving full maturity within the scientific community.ResultsThis work introduces texttt {life}^{text{x}}-ep, a publicly available software for numerical simulations of the electrophysiology activity of the cardiac muscle, under both normal and pathological conditions. texttt {life}^{text{x}}-ep employs the monodomain equation to model the heart’s electrical activity. It incorporates both phenomenological and second-generation ionic models. These models are discretized using the Finite Element method on tetrahedral or hexahedral meshes. Additionally, texttt {life}^{text{x}}-ep integrates the generation of myocardial fibers based on Laplace–Dirichlet Rule-Based Methods, previously released in Africa et al., 2023, within texttt {life}^{text{x}}-fiber. As an alternative, users can also choose to import myofibers from a file. This paper provides a concise overview of the mathematical models and numerical methods underlying texttt {life}^{text{x}}-ep, along with comprehensive implementation details and instructions for users. texttt {life}^{text{x}}-ep features exceptional parallel speedup, scaling efficiently when using up to thousands of cores, and its implementation has been verified against an established benchmark problem for computational electrophysiology. We showcase the key features of texttt {life}^{text{x}}-ep through various idealized and realistic simulations conducted in both normal and pathological scenarios. Furthermore, the software offers a user-friendly and flexible interface, simplifying the setup of simulations using self-documenting parameter files.Conclusionstexttt {life}^{text{x}}-ep provides easy access to cardiac electrophysiology simulations for a wide user community. It offers a computational tool that integrates models and accurate methods for simulating cardiac electrophysiology within a high-performance framework, while maintaining a user-friendly interface. texttt {life}^{text{x}}-ep represents a valuable tool for conducting in silico patient-specific simulations.

Two different parallel approaches for a hybrid fractional order Coronavirus model

In this paper, two different parallel approaches for a hybrid fractional order Coronavirus (2019-nCov) mathematical model are presented. Both parallel approaches are implemented using Julia high level language. Parallel algorithm implementations are developed for the HPC cluster using Message Passing Interface (MPI) technology and general-purpose computing on GPUs (GPGPU) using Compute Unified Device Architecture (CUDA) based on hardware environments. The algorithm implementation are used to solve the real-world problem of the hybrid fractional order Coronavirus (2019-nCov) mathematical model and to study the parallel efficiency. The introduced hybrid fractional order derivative is defined as a linear combination of the integral of Riemann-Liouville and the fractional order Caputo derivative. A parallel algorithm is designed based on the predictor-corrector method with the discretization of the Caputo proportional constant fractional hybrid operator for solving the model problem numerically. Simulation results show that, both the new parallel approaches achieve significant efficiency.

Enhanced Ant Colony Algorithm for Discrete Dynamic Berth Allocation in a Case Container Terminal

Berth allocation is a critical concern in container terminal port logistics, involving the precise determination of where and when arriving vessels should dock along a quay. With berth space limitations and a continuous surge in container handling demands, ensuring an effective berth allocation is paramount for the smooth and efficient operation of container ports. However, due to the randomness of vessel arrival times and uncertainties surrounding container ship loading capacities, berth allocation problems (BAP) often present discrete and dynamic challenges. This paper addresses these challenges by considering real-world terminal operational factors, formulating relevant assumptions, and establishing a model for dynamic berth allocation and efficient ship berthing scheduling. The primary motivation stems from the parallels observed between the BAP problem and ant foraging path selection, leading to the proposal of a novel Parallel Search Structure Enhanced Ant Colony Algorithm (PACO). A proper set of parameters of the algorithm are selected based upon sensitivity analyses on the convergence and parallelism efficiency of the algorithm. To validate our method, a real-world case-container terminal operation in Shanghai Port was studied. The experimental comparison results show that the PACO algorithm outperforms other commonly used algorithms, making it more effective and efficient for the Discrete Dynamic Berth Allocation Problem (DDBAP).

Analysis of the Influence Path of Confucianism in the Civic Education of Contemporary College Students in the Context of Big Data

Abstract Under the background of big data, college students’ Civic Education has realized the adjustment of teaching technology and educational paradigm, and the value of big data technology for college students’ Civic Education has become increasingly intuitive. In this paper, firstly, the data points designated for clustering are selected in the dataset as the initial clustering centroids. In response to the Euclidean distance treating variables equally, the coefficient of variation method is proposed for subjective weighting. The support vector machine for solving the two-class classification problem is obtained as a real-valued function to test the parallel efficiency of different clustering mining algorithms in the same experimental setting. Finally, for the training sample input data, it is concluded that the algorithm has a better clustering effect and improves the speed and accuracy of clustering. The feasibility of the proposed influence path is demonstrated by comparing it with the data application of the subjective empirical weighting method. The results show that 8% of students before the experiment thought that integrating Confucianism into Civic Education was valuable and meaningful, and after the experiment, the number of students who thought it was valuable and meaningful increased from 8% to 58%. It indicates that the integration of excellent traditional Confucianism into the ideological and political education of college students is very important to strengthen the ideological and political education of college students.

Fast parallel IGA-ADS solver for time-dependent Maxwell's equations

We propose a simulator for time-dependent Maxwell's equations with linear computational cost. We employ B-spline basis functions as considered in the isogeometric analysis (IGA). We focus on non-stationary Maxwell's equations defined on a regular patch of elements. We employ the idea of alternating-directions splitting (ADS) and employ a second-order accurate time-integration scheme for the time-dependent Maxwell's equations in a weak form. After discretization, the resulting stiffness matrix exhibits a Kronecker product structure. Thus, it enables linear computational cost LU factorization. Additionally, we derive a formulation for absorbing boundary conditions (ABCs) suitable for direction splitting. We perform numerical simulations of the scattering problem (traveling pulse wave) to verify the ABC. We simulate the radiation of electromagnetic (EM) waves from the dipole antenna. We verify the order of the time integration scheme using a manufactured solution problem. We then simulate magnetotelluric measurements. Our simulator is implemented in a shared memory parallel machine, with the GALOIS library supporting the parallelization. We illustrate the parallel efficiency with strong and weak scalability tests corresponding to non-stationary Maxwell simulations.

Computational performance of musculoskeletal simulation in OpenSim Moco using parallel computing.

Optimal control musculoskeletal simulation is a valuable approach for studying fundamental and clinical aspects of human movement. However, the high computational demand has long presented a substantial challenge, creating a need to improve simulation performance. The OpenSim Moco software package permits musculoskeletal simulation problems to be solved in parallel on multicore processors using the CasADi optimal control library, potentially reducing the computational demand. However, the computational performance of this framework has not been thoroughly examined. Thus, we aimed to investigate the computational speed-up obtained via multicore parallel computing relative to solving problems serially (i.e., using a single core) in optimal control simulations of human movement in OpenSim Moco. Simulations were solved using up to 18 cores with a variety of temporal mesh interval densities and using two different initial guess strategies. We examined a range of musculoskeletal models and movements that included two- and three-dimensional models, tracking and predictive simulations, and walking and reaching tasks. The maximum overall parallel speed-up was problem specific and ranged from 1.7 to 7.7 times faster than serial, with most of the speed-up achieved by about 6 processor cores. Parallel speed-up was generally greater on finer temporal meshes, while the initial guess strategy had minimal impact on speed-up. Considerable speed-up can be achieved for some optimal control simulation problems in OpenSim Moco by leveraging the multicore processors often available in modern computers. However, since improvements are problem specific, achieving optimal computational performance will require some degree of exploration by the end user.

Design and Development of Effective Multi-Level Cache Memory Model

An algorithm to determine the effectiveness and efficiency of a multi-level cache was developed in this paper. The developed model was used to test the efficiency rate, the relationships and the performance output level of a computer concerning the cache properties. This research paper showed that the level of cache and access time increases with the absolute hit rate but decreases with the relative hit rate. The number of cache levels varies directly with absolute access time and inversely with relative access time. The level one cache with set associativity of one has the highest access time and as the associativity and cache levels increase the memory access time decreases. The increase in the number of set associativity leads to an increase in cache performance and as well increases the performance speed of a computer.

Orthogonal Layers of Parallelism in Large-Scale Eigenvalue Computations

We address the communication overhead of distributed sparse matrix-(multiple)-vector multiplication in the context of large-scale eigensolvers, using filter diagonalization as an example. The basis of our study is a performance model, which includes a communication metric that is computed directly from the matrix sparsity pattern without running any code. The performance model quantifies to which extent scalability and parallel efficiency are lost due to communication overhead. To restore scalability, we identify two orthogonal layers of parallelism in the filter diagonalization technique. In the horizontal layer the rows of the sparse matrix are distributed across individual processes. In the vertical layer bundles of multiple vectors are distributed across separate process groups. An analysis in terms of the communication metric predicts that scalability can be restored if, and only if, one implements the two orthogonal layers of parallelism via different distributed vector layouts. Our theoretical analysis is corroborated by benchmarks for application matrices from quantum and solid state physics, road networks, and nonlinear programming. We finally demonstrate the benefits of using orthogonal layers of parallelism with two exemplary application cases—an exciton and a strongly correlated electron system—which incur either small or large communication overhead.

Approximating Inverse Cumulative Distribution Functions to Produce Approximate Random Variables

For random variables produced through the inverse transform method, approximate random variables are introduced, which are produced using approximations to a distribution’s inverse cumulative distribution function. These approximations are designed to be computationally inexpensive and much cheaper than library functions, which are exact to within machine precision and, thus, highly suitable for use in Monte Carlo simulations. The approximation errors they introduce can then be eliminated through use of the multilevel Monte Carlo method. Two approximations are presented for the Gaussian distribution: a piecewise constant on equally spaced intervals and a piecewise linear using geometrically decaying intervals. The errors of the approximations are bounded and the convergence demonstrated, and the computational savings are measured for C and C++ implementations. Implementations tailored for Intel and Arm hardware are inspected alongside hardware agnostic implementations built using OpenMP. The savings are incorporated into a nested multilevel Monte Carlo framework with the Euler-Maruyama scheme to exploit the speedups without losing accuracy, offering speed ups by a factor of 5–7. These ideas are empirically extended to the Milstein scheme and the non-central χ 2 distribution for the Cox-Ingersoll-Ross process, offering speedups of a factor of 250 or more.

Exploring model complexity in machine learned potentials for simulated properties

Machine learning (ML) enables the development of interatomic potentials with the accuracy of first principles methods while retaining the speed and parallel efficiency of empirical potentials. While ML potentials traditionally use atom-centered descriptors as inputs, different models such as linear regression and neural networks map descriptors to atomic energies and forces. This begs the question: what is the improvement in accuracy due to model complexity irrespective of descriptors? We curate three datasets to investigate this question in terms of ab initio energy and force errors: (1) solid and liquid silicon, (2) gallium nitride, and (3) the superionic conductor Li_{10}Ge(PS_{6})_{2} (LGPS). We further investigate how these errors affect simulated properties and verify if the improvement in fitting errors corresponds to measurable improvement in property prediction. By assessing different models, we observe correlations between fitting quantity (e.g. atomic force) error and simulated property error with respect to ab initio values.Graphical abstract

A fast, dense Chebyshev solver for electronic structure on GPUs.

Matrix diagonalization is almost always involved in computing the density matrix needed in quantum chemistry calculations. In the case of modest matrix sizes (≲4000), performance of traditional dense diagonalization algorithms on modern GPUs is underwhelming compared to the peak performance of these devices. This motivates the exploration of alternative algorithms better suited to these types of architectures. We newly derive, and present in detail, an existing Chebyshev expansion algorithm [Liang et al., J. Chem. Phys. 119, 4117-4125 (2003)] whose number of required matrix multiplications scales with the square root of the number of terms in the expansion. Focusing on dense matrices of modest size, our implementation on GPUs results in large speed ups when compared to diagonalization. Additionally, we improve upon this existing method by capitalizing on the inherent task parallelism and concurrency in the algorithm. This improvement is implemented on GPUs by using CUDA and HIP streams via the MAGMA library and leads to a significant speed up over the serial-only approach for smaller (≲1000) matrix sizes. Finally, we apply our technique to a model system with a high density of states around the Fermi level, which typically presents significant challenges.

Domain pattern formation in tetragonal ferroelectric ceramics

We present the results of high-resolution simulations of the ferroelectric domain evolution in polycrystalline lead zirconate titanate (PZT), using a phase-field framework that accounts for thermal fluctuations. Leveraging the parallel efficiency of a Fourier spectral scheme, we model micron-sized ceramic samples with thousands of grains at atomic-unit-cell spatial resolution. We introduce a method to automatically identify and track different types of domain walls from phase-field data, which we exploit to study their role during polarization reversal under applied electric fields. Results indicate that the density of domain walls and the domain width obey the Kittel-Mitsui-Furuichi-Roitburd square-root law with implications on the macroscopically observable piezo- and dielectric material properties. Moreover, analyzing the statistics of the domain pattern formation in simulated samples reveals correlations between the average polarization and strain within a grain and its crystallographic orientation, which is in agreement with high-energy x-ray diffraction experiments. Furthermore, we study the occurrence of the two predominant types of domain patterns – monodomain and laminate/twin domain structures – whose emergence within gains of a polycrystal is traced back to the grain orientation. Phase-field statistics are supported by a simple analytical model, which is based on minimizing the electric enthalpy and accurately predicts some of the reported correlations and allows us to further study the behavior of monodomains vs. laminate patterns in ferroelectric ceramics.