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DOE OSTI2022

An adaptive scalable fully implicit algorithm based on stabilized finite element for reduced visco-resistive MHD

The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution methods for MHD are extremely challenging due to disparate time and length scales, strong hyperbolic phenomena, and nonlinearity. Additionally, therefore the development of scalable, implicit MHD algorithms and high-resolution adaptive mesh refinement strategies is of considerable importance. In this work, we develop a high-order stabilized finite-element algorithm for the reduced visco-resistive MHD equations based on the MFEM finite element library (mfem.org). The scheme is fully implicit, solved with the Jacobian-free Newton-Krylov (JFNK) method with a physics-based preconditioning strategy. Our preconditioning strategy is a generalization of the physics-based preconditioning methods in Chacón et al. (2002) to adaptive, stabilized finite elements. Algebraic multigrid methods are used to invert sub-block operators to achieve scalability. A parallel adaptive mesh refinement scheme with dynamic load-balancing is implemented to efficiently resolve the multi-scale spatial features of the system. Our implementation uses the MFEM framework, which provides arbitrary-order polynomials and flexible adaptive conforming and non-conforming meshes capabilities. Results demonstrate the accuracy, efficiency, and scalability of the implicit scheme in the presence of large scale disparity. The potential of the AMR approach is demonstrated on an island coalescence problem in the high Lundquist-number regime (≥ 10 7 ) with the successful resolution of plasmoid instabilities and thin current sheets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Petascale Orbital-Free Density Functional Theory Enabled by Small-Box Algorithms

Orbital-free density functional theory (OFDFT) is a quantum-mechanics-based method that utilizes electron density as its sole variable. The main computational cost in OFDFT is the ubiquitous use of the fast Fourier transform (FFT), which is mainly adopted to evaluate the kinetic energy density functional (KEDF) and electron–electron Coulomb interaction terms. We design and implement a small-box FFT (SBFFT) algorithm to overcome the parallelization limitations of conventional FFT algorithms. We also propose real-space truncation of the nonlocal Wang–Teter KEDF kernel. The scalability of the SBFFT is demonstrated by efficiently simulating one full optimization step (electron density, energies, forces, and stresses) of 1,024,000 lithium (Li) atoms on up to 65,536 cores. We perform other tests using Li as a test material, including calculations of physical properties of different phases of bulk Li, geometry optimizations of nanocrystalline Li, and molecular dynamics simulations of liquid Li. All of the tests yield excellent agreement with the original OFDFT results, suggesting that the OFDFT-SBFFT algorithm opens the door to efficient first-principles simulations of materials containing millions of atoms.

Chemistry↗

DOE OSTI2020

Striped Data Analysis Framework

A columnar data representation is known to be an efficient way for data storage, specifically in cases when the analysis is often done based only on a small fragment of the available data structures. A data representation like Apache Parquet is a step forward from a columnar representation, which splits data horizontally to allow for easy parallelization of data analysis. Based on the general idea of columnar data storage, working on the [LDRD Project], we have developed a striped data representation, which, we believe, is better suited to the needs of High Energy Physics data analysis. A traditional columnar approach allows for efficient data analysis of complex structures. While keeping all the benefits of columnar data representations, the striped mechanism goes further by enabling easy parallelization of computations without requiring special hardware. We will present an implementation and some performance characteristics of such a data representation mechanism using a distributed no-SQL database or a local file system, unified under the same API and data representation model. The representation is efficient and at the same time simple so that it allows for a common data model and APIs for wide range of underlying storage mechanisms such as distributed no-SQL databases and local file systems. Striped storage adopts Numpy arrays as its basic data representation format, which makes it easy and efficient to use in Python applications. The Striped Data Server is a web service, which allows to hide the server implementation details from the end user, easily exposes data to WAN users, and allows to utilize well known and developed data caching solutions to further increase data access efficiency. We are considering the Striped Data Server as the core of an enterprise scale data analysis platform for High Energy Physics and similar areas of data processing. We have been testing this architecture with a 2TB dataset from a CMS dark matter search and plan to expand it to multiple 100 TB or even PB scale. We will present the striped format, Striped Data Server architecture and performance test results.

Gutsche, Oliver↗

DOE OSTI2018

Striped Data Server for Scalable Parallel Data Analysis

A columnar data representation is known to be an efficient way for data storage, specifically in cases when the analysis is often done based only on a small fragment of the available data structures. A data representation like Apache Parquet is a step forward from a columnar representation, which splits data horizontally to allow for easy parallelization of data analysis. Based on the general idea of columnar data storage, working on the [LDRD Project], we have developed a striped data representation, which, we believe, is better suited to the needs of High Energy Physics data analysis. A traditional columnar approach allows for efficient data analysis of complex structures. While keeping all the benefits of columnar data representations, the striped mechanism goes further by enabling easy parallelization of computations without requiring special hardware. We will present an implementation and some performance characteristics of such a data representation mechanism using a distributed no-SQL database or a local file system, unified under the same API and data representation model. The representation is efficient and at the same time simple so that it allows for a common data model and APIs for wide range of underlying storage mechanisms such as distributed no-SQL databases and local file systems. Striped storage adopts Numpy arrays as its basic data representation format, which makes it easy and efficient to use in Python applications. The Striped Data Server is a web service, which allows to hide the server implementation details from the end user, easily exposes data to WAN users, and allows to utilize well known and developed data caching solutions to further increase data access efficiency. We are considering the Striped Data Server as the core of an enterprise scale data analysis platform for High Energy Physics and similar areas of data processing. As a result, we have been testing this architecture with a 2TB dataset from a CMS dark matter search and plan to expand it to multiple 100 TB or even PB scale. We will present the striped format, Striped Data Server architecture and performance test results.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

DOE OSTI2020

Scalable Knowledge Graph Analytics at 136 Petaflop/s

We are motivated by newly proposed methods for data mining large-scale corpora of scholarly publications, such as the full biomedical literature, which may consist of tens of millions of papers spanning decades of research. In this setting, analysts seek to discover how concepts relate to one another. They construct graph representations from annotated text databases and then formulate the relationship-mining problem as one of computing all-pairs shortest paths (APSP), which becomes a significant bottleneck. In this context, we present a new high-performance algorithm and implementation of the Floyd-Warshall algorithm for distributed-memory parallel computers accelerated by GPUs, which we call DSNAPSHOT (Distributed Accelerated Semiring All-Pairs Shortest Path). For our largest experiments, we ran DSNAPSHOT on a connected input graph with millions of vertices using 4, 096nodes (24,576GPUs) of the Oak Ridge National Laboratory's Summit supercomputer system. We find DSNAPSHOT achieves a sustained performance of 136×1015 floating-point operations per second (136petaflop/s) at a parallel efficiency of 90% under weak scaling and, in absolute speed, 70% of the best possible performance given our computation (in the single-precision tropical semiring or “min-plus” algebra). Looking forward, we believe this novel capability will enable the mining of scholarly knowledge corpora when embedded and integrated into artificial intelligence-driven natural language processing workflows at scale.

Kannan, Ramakrishnan {ramki}↗

DOE OSTI2017

Galactos: computing the anisotropic 3-point correlation function for 2 billion galaxies

The nature of dark energy and the complete theory of gravity are two central questions currently facing cosmology. A vital tool for addressing them is the 3-point correlation function (3PCF), which probes deviations from a spatially random distribution of galaxies. However, the 3PCF's formidable computational expense has prevented its application to astronomical surveys comprising millions to billions of galaxies. We present Galactos, a high-performance implementation of a novel, O( N 2 ) algorithm that uses a load-balanced k-d tree and spherical harmonic expansions to compute the anisotropic 3PCF. Our implementation is optimized for the Intel Xeon Phi architecture, exploiting SIMD parallelism, instruction and thread concurrency, and significant L1 and L2 cache reuse, reaching 39% of peak performance on a single node. Galactos scales to the full Cori system, achieving 9.8 PF (peak) and 5.06 PF (sustained) across 9636 nodes, making the 3PCF easily computable for all galaxies in the observable universe.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Efficient Scalable Contact Network Generation from Population Data

Modeling the contacts among a population is critical to understanding the dynamics of a disease outbreak. Contact networks, where nodes are individuals and edges are contacts among them, are used to represent these complex individual-level interactions. In this work, we are given the daily activity schedules of an urban population that represent the activity location and time of individuals in a population during a single twenty four hour period over multiple days. Using collocation to determine contact between individuals, our goal is to extract hourly contact networks from large-scale activity data. We improve upon the existing adjacency matrix-based method by implementing our custom sparse matrix multiplication algorithm. Starting with a Python implementation, we achieve a 1600x speed up in the computation with a fast custom designed sparse matrix multiplier algorithm implemented in the C++ language. This work is central to future parallel designs of the problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Machine Learning-Driven Conservative-to-Primitive Conversion in Hybrid Piecewise Polytropic and Tabulated Equations of State

We present a novel machine learning (ML)-based method to accelerate conservative-to-primitive inversion, focusing on hybrid piecewise polytropic and tabulated equations of state. Traditional root-finding techniques are computationally expensive, particularly for large-scale relativistic hydrodynamics simulations. To address this, we employ feedforward neural networks (NNC2PS and NNC2PL), trained in PyTorch (2.0+) and optimized for GPU inference using NVIDIA TensorRT (8.4.1), achieving significant speedups with minimal accuracy loss. The NNC2PS model achieves 𝐿 1 and 𝐿 ∞ errors of 4.54 × 10 −7 and 3.44 × 10−6, respectively, while the NNC2PL model exhibits even lower error values. TensorRT optimization with mixed-precision deployment substantially accelerates performance compared to traditional root-finding methods. Specifically, the mixed-precision TensorRT engine for NNC2PS achieves inference speeds approximately 400 times faster than a traditional single-threaded CPU implementation for a dataset size of 1,000,000 points. Ideal parallelization across an entire compute node in the Delta supercomputer (dual AMD 64-core 2.45 GHz Milan processors and 8 NVIDIA A100 GPUs with 40 GB HBM2 RAM and NVLink) predicts a 25-fold speedup for TensorRT over an optimally parallelized numerical method when processing 8 million data points. Moreover, the ML method exhibits sub-linear scaling with increasing dataset sizes. We release the scientific software developed, enabling further validation and extension of our findings. By exploiting the underlying symmetries within the equation of state, these findings highlight the potential of ML, combined with GPU optimization and model quantization, to accelerate conservative-to-primitive inversion in relativistic hydrodynamics simulations.

conservative-to-primitive conversion↗

DOE OSTI2021

Markov Chain Monte Carlo Predictions of Neutron-rich Lanthanide Properties as a Probe of r -process Dynamics

Lanthanide element signatures are key to understanding many astrophysical observables, from merger kilonova light curves to stellar and solar abundances. To learn about the lanthanide element synthesis that enriched our solar system, we apply the statistical method of Markov Chain Monte Carlo to examine the nuclear masses capable of forming the r-process rare-earth abundance peak. We describe the physical constraints we implement with this statistical approach and demonstrate the use of the parallel chains method to explore the multidimensional parameter space. We apply our procedure to three moderately neutron-rich astrophysical outflows with distinct types of r-process dynamics. We show that the mass solutions found are dependent on outflow conditions and are related to the r-process path. We describe in detail the mechanism behind peak formation in each case. We then compare our mass predictions for neutron-rich neodymium and samarium isotopes to the latest experimental data from the CPT at CARIBU. Here, we find our mass predictions given outflows that undergo an extended (n,γ)⇌(γ,n) equilibrium to be those most compatible with both observational solar abundances and neutron-rich mass measurements.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Massively parallel and universal approximation of nonlinear functions using diffractive processors

Nonlinear computation is essential for a wide range of information processing tasks, yet implementing nonlinear functions using optical systems remains a challenge due to the weak and power-intensive nature of optical nonlinearities. Overcoming this limitation without relying on nonlinear optical materials could unlock unprecedented opportunities for ultrafast and parallel optical computing systems. Here, we demonstrate that large-scale nonlinear computation can be performed using linear optics through optimized diffractive processors composed of passive phase-only surfaces. In this framework, the input variables of nonlinear functions are encoded into the phase of an optical wavefront—e.g., via a spatial light modulator (SLM)—and transformed by an optimized diffractive structure with spatially varying point-spread functions to yield output intensities that approximate a large set of unique nonlinear functions–all in parallel. We provide proof establishing that this architecture serves as a universal function approximator for an arbitrary set of bandlimited nonlinear functions, also covering wavelength-multiplexed nonlinear functions as well as multi-variate and complex-valued functions that are all-optically cascadable. Our analysis also indicates the successful approximation of typical nonlinear activation functions commonly used in neural networks, including the sigmoid, tanh, ReLU (rectified linear unit), and softplus. We numerically demonstrate the parallel computation of one million distinct nonlinear functions, accurately executed at wavelength-scale spatial density at the output of a diffractive optical processor. Furthermore, we experimentally validated this framework using in situ optical learning and approximated 35 unique nonlinear functions in a single shot using a compact setup consisting of an SLM and an image sensor. These results establish diffractive optical processors as a scalable platform for massively parallel universal nonlinear function approximation, paving the way for new capabilities in analog optical computing based on linear materials.

Rahman, Md Sadman Sakib [University of California,↗

DOE OSTI2021

FTK: A Simplicial Spacetime Meshing Framework for Robust and Scalable Feature Tracking

In this work, we present the Feature Tracking Kit (FTK), a framework that simplifies, scales, and delivers various feature-tracking algorithms for scientific data. The key of FTK is our simplicial spacetime meshing scheme that generalizes both regular and unstructured spatial meshes to spacetime while tessellating spacetime mesh elements into simplices. The benefits of using simplicial spacetime meshes include (1) reducing ambiguity cases for feature extraction and tracking, (2) simplifying the handling of degeneracies using symbolic perturbations, and (3) enabling scalable and parallel processing. The use of simplicial spacetime meshing simplifies and improves the implementation of several feature-tracking algorithms for critical points, quantum vortices, and isosurfaces. As a software framework, FTK provides end users with VTK/ParaView filters, Python bindings, a command line interface, and programming interfaces for feature-tracking applications. We demonstrate use cases as well as scalability studies through both synthetic data and scientific applications including tokamak, fluid dynamics, and superconductivity simulations. We also conduct end-to-end performance studies on the Summit supercomputer. FTK is open sourced under the MIT license: https://github.com/hguo/ftk.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Highly-scalable, physics-informed GANs for learning solutions of stochastic PDEs

Uncertainty quantification for forward and inverse problems is a central challenge across physical and biomedical disciplines. We address this challenge for the problem of modeling subsurface flow at the Hanford Site by combining stochastic computational models with observational data using physics-informed GAN models. The geographic extent, spatial heterogeneity, and multiple correlation length scales of the Hanford Site require training a computationally intensive GAN model to thousands of dimensions. We develop a highly optimized implementation that scales to {\herogpucount} NVIDIA Volta GPUs. We develop a hierarchical scheme based on a multi-player game-theoretic approach for exploiting domain parallelism, map discriminators and generators to multiple GPUs, and employ efficient communication schemes to ensure training stability and convergence. Our implementation scales to {\heronodecount} nodes on the Summit supercomputer with a \weakscalingeff\% scaling efficiency, achieving peak and sustained half-precision rates of {\heropeakperf} PF/s and {\herosustainedperf} PF/s.

physics informed ML, machine learning, generative ↗

DOE OSTI2023

Framework for Extensible, Asynchronous Task Scheduling (FEATS) in Fortran

Most parallel scientific programs contain compiler directives (pragmas) such as those from OpenMP, explicit calls to runtime library procedures such as those implementing the Message Passing Interface (MPI), or compiler-specific language extensions such as those provided by CUDA. By contrast, the recent Fortran standards empower developers to express parallel algorithms without directly referencing lower-level parallel programming models. Fortran’s parallel features place the language within the Partitioned Global Address Space (PGAS) class of programming models. When writing programs that exploit data-parallelism, application developers often find it straightforward to develop custom parallel algorithms. Problems involving complex, heterogeneous, staged calculations, however, pose much greater challenges. Such applications require careful coordination of tasks in a manner that respects dependencies prescribed by a directed acyclic graph. When rolling one’s own solution proves difficult, extending a customizable framework becomes attractive. The paper presents the design, implementation, and use of the Framework for Extensible Asynchronous Task Scheduling (FEATS), which we believe to be the first task-scheduling tool written in modern Fortran. We describe the benefits and compromises associated with choosing Fortran as the implementation language, and we propose ways in which future Fortran standards can best support the use case in this paper.

Richardson, Brad↗

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 OSTI2020

Towards Generic Parallel Programming in Computer Science Education with Kokkos

Parallel patterns, views, and spaces are promising abstractions to capture the programmer's intent as well as the contextual information that can be used by an underlying runtime to efficiently map software to parallel hardware. These abstractions can be valuable in cases where an algorithm must accommodate requirements of code and performance portability across hardware architectures and vendor programming models. Kokkos is a parallel programming model for host- and accelerator architectures that relies on these abstractions and targets these requirements. It consists of a pure C++ interface, a specification, and a programming library. The programming library exposes patterns and types and maps them to an underlying abstract machine model. The abstract machine model offers a generic view of parallel hardware. While Kokkos is gaining popularity in large-scale HPC applications at some DOE laboratories, we believe that the implemented concepts are of interest to a broader audience including academia as they may contribute to a generic, vendor, and architecture-independent education of parallel programming. In this work, we give an insight into the design considerations of this programming model and list important abstractions. Further, we document best practices obtained from giving virtual classes on Kokkos and give pointers to resources that the reader may consider valuable for a lecture on generic parallel programming for students with preexisting knowledge on this matter.

Ciesko, Jan↗

DOE OSTI2021

Parallel String Graph Construction and Transitive Reduction for De Novo Genome Assembly

One of the most computationally intensive tasks in computational biology is de novo genome assembly, the decoding of the sequence of an unknown genome from redundant and erroneous short sequences. A common assembly paradigm identifies overlapping sequences, simplifies their layout, and creates consensus. Despite many algorithms developed in the literature, the efficient assembly of large genomes is still an open problem. In this work, we introduce new distributed-memory parallel algorithms for overlap detection and layout simplification steps of de novo genome assembly, and implement them in the diBELLA 2D pipeline. Our distributed memory algorithms for both overlap detection and layout simplification are based on linear-algebra operations over semirings using 2D distributed sparse matrices. Our layout step consists of performing a transitive reduction from the overlap graph to a string graph. We provide a detailed communication analysis of the main stages of our new algorithms. diBELLA 2D achieves near linear scaling with over 80% parallel efficiency for the human genome, reducing the runtime for overlap detection by 1.2-1.3× for the human genome and 1.5-1.9× for C.elegans compared to the state-of-the-art. Our transitive reduction algorithm outperforms an existing distributed-memory implementation by 10.5-13.3× for the human genome and 18-29× for the C. elegans. Our work paves the way for efficient de novo assembly of large genomes using long reads in distributed memory.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2018

Algorithmic Patterns for $$\mathcal {H}$$-Matrices on Many-Core Processors

In this work, we consider the reformulation of hierarchical ( $\mathcal {H}$ ) matrix algorithms for many-core processors with a model implementation on graphics processing units (GPUs). $\mathcal {H}$ matrices approximate specific dense matrices, e.g., from discretized integral equations or kernel ridge regression, leading to log-linear time complexity in dense matrix–vector products. The parallelization of $\mathcal {H}$ matrix operations on many-core processors is difficult due to the complex nature of the underlying algorithms. While previous algorithmic advances for many-core hardware focused on accelerating existing $\mathcal {H}$ matrix CPU implementations by many-core processors, we here aim at totally relying on that processor type. As main contribution, we introduce the necessary parallel algorithmic patterns allowing to map the full $\mathcal {H}$ matrix construction and the fast matrix–vector product to many-core hardware. In this work, crucial ingredients are space filling curves, parallel tree traversal and batching of linear algebra operations. The resulting model GPU implementation hmglib is the, to the best of the authors knowledge, first entirely GPU-based Open Source $\mathcal {H}$ matrix library of this kind. We investigate application examples as present in kernel ridge regression, Gaussian Process Regression and kernel-based interpolation. In this context, an in-depth performance analysis and a comparative performance study against a standard multi-core CPU $\mathcal {H}$ matrix library highlights profound speedups of our many-core parallel approach.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Symplectic multi-particle tracking on GPUs

A symplectic multi-particle tracking model is implemented on the Graphic Processing Units (GPUs) using the Compute Unified Device Architecture (CUDA) language. The symplectic tracking model can preserve phase space structure and reduce non-physical effects in long term simulation, which is important for beam property evaluation in particle accelerators. Though this model is computationally expensive, it is very suitable for parallelization and can be accelerated significantly by using GPUs. In this paper, we optimized the implementation of the symplectic tracking model on both single GPU and multiple GPUs. Using a single GPU processor, the code achieves a factor of 2-10 speedup for a range of problem sizes compared with the time on a single state-of-the-art Central Processing Unit (CPU) node with similar power consumption and semiconductor technology. It also shows good scalability on a multi-GPU cluster at Oak Ridge Leadership Computing Facility. In an application to beam dynamics simulation, the GPU implementation helps save more than a factor of two total computing time in comparison to the CPU implementation.

43 PARTICLE ACCELERATORS↗