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DOE OSTI2021

Local time stepping for the shallow water equations in MPAS

In this work we assess the performance of a set of local time-stepping (LTS) schemes for the shallow water equations implemented in the Model for Prediction Across Scales (MPAS). The goal of LTS is to speed up the simulation by allowing different time-steps on different regions of the computational grid. The LTS schemes considered here were originally introduced by Hoang et al. (2019) [26], who laid out the mathematical foundation of the methods. Here, the authors take on the task of presenting a fast, efficient and scalable parallel implementation of these LTS methods on high performance computing machines, with the aim to provide a recipe for other climate modeling groups that may be interested in employing LTS algorithms in their codes. As a matter of fact, even if MPAS is our framework of choice, our approach is general enough and could be of interest to other groups beyond the MPAS community. Due to their nature, LTS methods possess an inherent load imbalance that needs to be carefully addressed in order to obtain efficient scalability. Even more important is the far from trivial task of computing the right-hand side terms only on specific LTS regions during the time-stepping procedure. An inefficient handling of this task causes a drastic decay of the CPU time performance, making the LTS algorithms practically of no use. The emphasis of the present work is therefore on the computational and parallel aspects of the LTS methods, whose proper treatment is crucial to make the methods run faster against existing strategies, such as for instance high-order explicit global time-stepping schemes. This is in fact the ultimate goal of using an LTS procedure and it is the one to which we direct all our optimization efforts.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Dual-pace transient heat conduction in vertically aligned carbon nanotube arrays induced by structure separation

Vertically aligned arrays of carbon nanotubes (CNTs) are attractive for a wide range of macroscopic applications which can exploit the remarkable properties of individual nanotubes. In this work, an abnormal behavior of CNT bundles in heat conduction is discovered under the transient electro-thermal characterization. The measured voltage change over the sample shows a dual-pace thermal response (DTR), which could not be fitted using a single thermal diffusivity heat transfer model. Instead, two thermal diffusivities are determined from the DTR phenomenon. Three rounds of cryogenic experiments are conducted to investigate the physics behind DTR phenomenon. It starts to emerge when the temperature is reduced to a certain level. After two rounds of cryogenic experiments, the DTR phenomenon becomes permanent from 295 K to 10 K. The nano-scale structure separation induced by the increased thermal strain leads to macroscale structure separation, which results in two parallel heat conduction paths responsible for the DTR phenomenon. By building a new parallel heat transfer model taking both the transient and steady-state electrical and thermal response into consideration, the area ratio of separated CNTs is determined. Furthermore, this result uncovers the existence of coiled morphology and nano-structure evolution of CNTs under cryogenic state and its effect on thermal and electrical transport, especially on their transient behaviors. Knowledge of the thermal transport in these CNTs arrays is important considering the fact that transient thermal response strongly affects their mechanical, optical, and electrical behaviors.

42 ENGINEERING↗

DOE OSTI2022

Low-synch Gram–Schmidt with delayed reorthogonalization for Krylov solvers

The parallel strong-scaling of iterative methods is often determined by the number of global reductions at each iteration. Low-synch Gram-Schmidt algorithms are applied here to the Arnoldi algorithm to reduce the number of global reductions and therefore to improve the parallel strong-scaling of iterative solvers for nonsymmetric matrices such as the GMRES and the Krylov-Schur iterative methods. In the Arnoldi context, the factorization is "left-looking" and processes one column at a time. Among the methods for generating an orthogonal basis for the Arnoldi algorithm, the classical Gram-Schmidt algorithm, with reorthogonalization (CGS2) requires three global reductions per iteration. A new variant of CGS2 that requires only one reduction per iteration is presented and applied to the Arnoldi algorithm. Delayed CGS2 (DCGS2) employs the minimum number of global reductions per iteration (one) for a one-column at-a-time algorithm. The main idea behind the new algorithm is to group global reductions by rearranging the order of operations. DCGS2 must be carefully integrated into an Arnoldi expansion or a GMRES solver. Numerical stability experiments assess robustness for Krylov-Schur eigenvalue computations. Performance experiments on the ORNL Summit supercomputer then establish the superiority of DCGS2 over CGS2.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

From NWChem to NWChemEx: Evolving with the Computational Chemistry Landscape

Since the advent of the first computers, chemists have been at the forefront of using computers to understand and solve complex chemical problems. As the hardware and software have evolved, so have the theoretical and computational chemistry methods and algorithms. Parallel computers clearly changed the common computing paradigm in the late 1970s and 80s, and the field has again seen a paradigm shift with the advent of graphical processing units. This review explores the challenges and some of the solutions in transforming software from the terascale to the petascale and now to the upcoming exascale computers. While discussing the field in general, NWChem and its redesign, NWChemEx, will be highlighted as one of the early codesign projects to take advantage of massively parallel computers and emerging software standards to enable large scientific challenges to be tackled.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

A Task Based Approach for Co-Scheduling Ensemble Workloads on Heterogeneous Nodes

Scientific workflows consist of multiple, connected applications, with data and results flowing from one to another in a pipeline. Traditionally, such workflows are executed in sequential order, storing intermediate data in storage disks. Co-scheduling application workflows concurrently on the same compute nodes would greatly reduce the cost of moving data to/from storage and allow real-time analysis of intermediate results. Nevertheless, most parallel programming runtimes do not allow seamless integration of various applications in a scientific workflow, in part due to the complexity of managing data and resources. The situation is even more complicated for heterogeneous systems. In this work we extend the Minos Computing Library (MCL) runtime to accelerate pipe-lined and parallel workloads where multiple applications are running in the same system. MCL’s asynchronous task library and runtime dynamically manages resources to allow co-scheduling of multiple processes sharing heterogeneous resources. In addition, we design a custom ex- tension of the Open Compute Language (OpenCL) to enable multiple processes to share device memory. We enable MCL to coordinate these shared buffers to allow for easy, fast data sharing between applications. Using malleable micro-benchmarks and two application workflows that combine scientific simulation and AI-based analysis, we show that our method outperforms traditional approaches.

Index Terms—Parallel systems, Scheduling and Task ↗

DOE OSTI2020

Analyzing the Performance Trade-Off in Implementing User-Level Threads

User-level threads have been widely adopted as a means of achieving lightweight concurrent execution without the costs of OS-level threads. Nevertheless, the costs of managing user-level threads represent a performance barrier that dictates how fine grained the concurrency exposed by an application can be without incurring significant overheads; this in turn may translate into insufficient parallelism to exploit highly parallel systems. This article is a deep dive into the fundamental costs in implementing user-level threads. We first identify that one of the highest sources of fork-join overheads stems from deviations, events that incur context switching during the execution of a thread and disrupt a run-to-completion execution. We then conduct an in-depth investigation of a wide spectrum of methods with respect to how they handle deviations while covering both parent- and child-first scheduling policies. Our methodology involves a comprehensive instruction- and cache-level analysis of all methods on several modern CPU architectures. Finally, the primary finding of our evaluation is that dynamic promotion methods that assume the absence of deviation and dynamically provide context-switching support offer the best trade-off between performance and capability when the likelihood of deviation is low.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Distributed Augmentation, Hypersweeps, and Branch Decomposition of Contour Trees for Scientific Exploration

Contour trees describe the topology of level sets in scalar fields and are widely used in topological data analysis and visualization. A main challenge of utilizing contour trees for large-scale scientific data is their computation at scale using highperformance computing. To address this challenge, recent work has introduced distributed hierarchical contour trees for distributed computation and storage of contour trees. However, effective use of these distributed structures in analysis and visualization requires subsequent computation of geometric properties and branch decomposition to support contour extraction and exploration. In this work, we introduce distributed algorithms for augmentation, hypersweeps, and branch decomposition that enable parallel computation of geometric properties, and support the use of distributed contour trees as query structures for scientific exploration. Finally, we evaluate the parallel performance of these algorithms and apply them to identify and extract important contours for scientific visualization.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A New Class of AMG Interpolation Methods Based on Matrix-Matrix Multiplications

A new class of distance-two interpolation methods for algebraic multigrid (AMG) that can be formulated in terms of sparse matrix-matrix multiplications is presented and analyzed. Compared with similar distance-two prolongation operators, the proposed algorithms exhibit improved efficiency and portability to various computing platforms, since they allow one to easily exploit existing high-performance sparse matrix kernels. The new interpolation methods have been implemented in hypre, a widely used parallel multigrid solver library. With the proposed interpolations, the overall time of hypre's BoomerAMG setup can be considerably reduced, while sustaining equivalent, sometimes improved, convergence rates. Numerical results for a variety of test problems on parallel machines are presented that support the superiority of the proposed interpolation operators over the existing ones in hypre.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Fast Multigrid Reduction-in-Time for Advection via Modified Semi-Lagrangian Coarse-Grid Operators

Many iterative parallel-in-time algorithms have been shown to be highly efficient for diffusion-dominated partial differential equations (PDEs) but are inefficient or even divergent when applied to advection-dominated PDEs. We consider the application of the multigrid reduction-in-time (MGRIT) algorithm to linear advection PDEs. Here, the key to efficient time integration with this method is using a coarse-grid operator that provides a sufficiently accurate approximation to the so-called ideal coarse-grid operator. For certain classes of semi-Lagrangian discretizations, we present a novel semi-Lagrangian-based coarse-grid operator that leads to fast and scalable multilevel time integration of linear advection PDEs. The coarse-grid operator is composed of a semi-Lagrangian discretization followed by a correction term, with the correction designed so that the leading-order truncation error of the composite operator is approximately equal to that of the ideal coarse-grid operator. Parallel results show substantial speed-ups over sequential time integration for variable-wave-speed advection problems in one and two spatial dimensions, and using high-order discretizations up to order five. The proposed approach establishes the first practical method that provides small and scalable MGRIT iteration counts for advection problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Communication Lower Bounds and Optimal Algorithms for Multiple Tensor-Times-Matrix Computation

Multiple tensor-times-matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. Here, we establish communication lower bounds that determine how much data movement is required (under mild conditions) to perform the Multi-TTM computation in parallel. The crux of the proof relies on analytically solving a constrained, nonlinear optimization problem. We also present a parallel algorithm to perform this computation that organizes the processors into a logical grid with twice as many modes as the input tensor. We show that, with correct choices of grid dimensions, the communication cost of the algorithm attains the lower bounds and is therefore communication optimal. Finally, we show that our algorithm can significantly reduce communication compared to the straightforward approach of expressing the computation as a sequence of tensor-times-matrix operations when the input and output tensors vary greatly in size.

HBL-inequalities↗

DOE OSTI2023

Scalable Incremental Checkpointing using GPU-Accelerated De-Duplication

Writing large amounts of data concurrently to stable storage is a typical I/O pattern of many HPC workflows. This pattern introduces high I/O overheads and results in increased storage space utilization especially for workflows that need to capture the evolution of data structures with high frequency as checkpoints. In this context, many applications, such as graph pattern matching, perform sparse updates to large data structures between checkpoints. For these applications, incremental checkpointing techniques that save only the differences from one checkpoint to another can dramatically reduce the checkpoint sizes, I/O bottlenecks, and storage space utilization. However, such techniques are not without challenges: it is non-trivial to transparently determine what data has changed since a previous checkpoint and assemble the differences in a compact fashion that does not result in excessive metadata. State-of-art data reduction techniques (e.g., compression and de-duplication) have significant limitations when applied to modern HPC applications that leverage GPUs: slow at detecting the differences, generate a large amount of metadata to keep track of the differences, and ignore crucial spatiotemporal checkpoint data redundancy. This paper addresses these challenges by proposing a Merkle tree-based incremental checkpointing method to exploit GPUs' high memory bandwidth and massive parallelism. Experimental results at scale show a significant reduction of the I/O overhead and space utilization of checkpointing compared with state-of-the-art incremental checkpointing and compression techniques.

Tan, Nigel↗

DOE OSTI2022

Scalable training of graph convolutional neural networks for fast and accurate predictions of HOMO-LUMO gap in molecules

Abstract Graph Convolutional Neural Network (GCNN) is a popular class of deep learning (DL) models in material science to predict material properties from the graph representation of molecular structures. Training an accurate and comprehensive GCNN surrogate for molecular design requires large-scale graph datasets and is usually a time-consuming process. Recent advances in GPUs and distributed computing open a path to reduce the computational cost for GCNN training effectively. However, efficient utilization of high performance computing (HPC) resources for training requires simultaneously optimizing large-scale data management and scalable stochastic batched optimization techniques. In this work, we focus on building GCNN models on HPC systems to predict material properties of millions of molecules. We use HydraGNN, our in-house library for large-scale GCNN training, leveraging distributed data parallelism in PyTorch. We use ADIOS, a high-performance data management framework for efficient storage and reading of large molecular graph data. We perform parallel training on two open-source large-scale graph datasets to build a GCNN predictor for an important quantum property known as the HOMO-LUMO gap. We measure the scalability, accuracy, and convergence of our approach on two DOE supercomputers: the Summit supercomputer at the Oak Ridge Leadership Computing Facility (OLCF) and the Perlmutter system at the National Energy Research Scientific Computing Center (NERSC). We present our experimental results with HydraGNN showing (i) reduction of data loading time up to 4.2 times compared with a conventional method and (ii) linear scaling performance for training up to 1024 GPUs on both Summit and Perlmutter.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Validation of a Generalized Formulation for Load-Sharing Behavior in Epicyclic Gears for Wind Turbines: Preprint

In an ideal epicyclic gear set every parallel gear path transmits the same amount of torque. However, it is well known that certain manufacturing variations result in unequal load sharing between the parallel gear paths. Previous works have developed and validated a general closed-form analytical model of this phenomenon that describes the load sharing characteristics of epicyclic gear sets from three to six planets at any torque level. More recently, this analytical model has been reformulated to include the effects of gravity, carrier bearing clearance, and external applied moments, all of which are relevant to most gearboxes and their mounting configuration in horizontal-axis wind turbines. In this paper, the reformulated model is compared to load measurements collected from two similar wind turbine gearboxes with three-planet epicyclic gear sets. The resulting load sharing values are also compared to the mesh load factor requirements in the AGMA 6006 and IEC 61400-4 wind turbine gearbox design standards. Load sharing factors as high as 1.16 at extreme rotor moments and 1.08 with no moment were measured for the gearbox with cylindrical roller bearings, but the load sharing factor remained below 1.10 for the gearbox with tapered roller bearings The results show that in the wind turbine application, load sharing is not equal - even for three-planet systems with a floating central member because of the effects of gravity, rotor moments, and the resulting relative motions among the epicyclic gear components within the carrier bearing clearance.

closed-form analytical model↗

DOE OSTI2020

Validation of a Generalized Formulation for Load Sharing Behavior in Epicyclic Gears for Wind Turbines

closed-form analytical model↗

DOE OSTI2020

Triangle Counting with Cyclic Distributions

Triangles are the simplest non-trivial subgraphs and triangle counting is used in a number of different applications. The order in which vertices are processed in triangle counting strongly effects the amount of work that needs to be done (and thus the overall performance). Ordering vertices by degree has been shown to be one particularly effective ordering approach. However, for graphs with skewed degree distributions (such as power-law graphs), ordering by degree effects the distribution of work; parallelization must account for this distribution in order to balance work among workers. In this paper we provide an in- depth analysis of the ramifications of degree-based ordering on parallel triangle counting. We present approach for partitioning work in triangle counting, based on cyclic distribution and some surprisingly simple C++ implementations. Experimental results demonstrate the effectiveness of our approach, particularly for power-law (and social network) graphs.

Graph algorithms, parallel algorithms↗

DOE OSTI2022

Performance enhancement of planar MOC calculation in hexagonal geometries by assembly-wise domain decomposition

The parallelization of planar Method of Characteristics (MOC) calculation with the higher order scattering in the hexagonal version of the nTRACER direct whole core calculation code is enhanced by adopting assembly-wise domain decomposition and other techniques. In order to augment the hexagonal domain decomposition, the three-color scheme, the angular decomposition, and the angular flux storage scheme are examined. The parallel performance assessed for the VVER benchmark problems demonstrates that the hexagonal assembly-wise domain decomposition significantly reduces the computing time in ray tracing by up to 64 %. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

High-Speed Ionic Synaptic Memory Based on 2D Titanium Carbide MXene

Synaptic devices with linear high-speed switching can accelerate learning in artificial neural networks (ANNs) embodied in hardware. Conventional resistive memories however suffer from high write noise and asymmetric conductance tuning, preventing parallel programming of ANN arrays. Electrochemical random-access memories (ECRAMs), where resistive switching occurs by ion insertion into a redox-active channel, aim to address these challenges due to their linear switching and low noise. ECRAMs using 2D materials and metal oxides however suffer from slow ion kinetics, whereas organic ECRAMs enable high-speed operation but face challenges toward on-chip integration due to poor temperature stability of polymers. Here, ECRAMs using 2D titanium carbide (Ti 3 C 2 T x ) MXene that combine the high speed of organics and the integration compatibility of inorganic materials in a single high-performance device are demonstrated. These ECRAMs combine the speed, linearity, write noise, switching energy, and endurance metrics essential for parallel acceleration of ANNs, and importantly, they are stable after heat treatment needed for back-end-of-line integration with Si electronics. The high speed and performance of these ECRAMs introduces MXenes, a large family of 2D carbides and nitrides with more than 30 stoichiometric compositions synthesized to date, as promising candidates for devices operating at the nexus of electrochemistry and electronics.

2D materials↗

DOE OSTI2023

Nonvolatile Magnetoelectric Switching of Magnetic Tunnel Junctions with Dipole Interaction

The magnetoelectric effect is technologically appealing because of its ability to manipulate magnetism using an electric field rather than magnetic field or current, thus providing a promising solution for the development of energy-efficient spintronics. Although 180° magnetization switching is vital to spintronic devices, the achievement of 180° magnetization switching via magnetoelectric coupling is still a fundamental challenge. Here, in this work, voltage-driven full resistance switching of a magnetic tunnel junction (MTJ) with dipole interaction on a ferroelectric substrate through switchable parallel/antiparallel magnetization alignment is demonstrated. Parallel magnetization alignment along the y direction is obtained under a bias magnetic field. By rotating the magnetic easy axis via strain-mediated magnetoelectric coupling, the parallel magnetizations in the MTJ reorient to the x axis with opposite paths because of dipole interaction, thus resulting in antiparallel alignment. Moreover, this voltage switching of MTJs is nonvolatile owing to variations in dipole interaction and can be well understood via phase field simulations. The results provide an avenue to realize electrical switching of MTJs and are significant for exploring energy-efficient spintronic devices.

36 MATERIALS SCIENCE↗