Arbitrary-level coarse mesh finite difference acceleration with hierarchical coarsening in space and energy
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Hackemack, Michael W.↗
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A Hyperspherical Adaptive Sparse-Grid Method for High-Dimensional Discontinuity Detection
This study proposes and analyzes a hyperspherical adaptive hierarchical sparse-grid method for detecting jump discontinuities of functions in high-dimensional spaces. The method is motivated by the theoretical and computational inefficiencies of well-known adaptive sparse-grid methods for discontinuity detection. Our novel approach constructs a function representation of the discontinuity hypersurface of an N-dimensional discontinuous quantity of interest, by virtue of a hyperspherical transformation. Then, a sparse-grid approximation of the transformed function is built in the hyperspherical coordinate system, whose value at each point is estimated by solving a one-dimensional discontinuity detection problem. Due to the smoothness of the hypersurface, the new technique can identify jump discontinuities with significantly reduced computational cost, compared to existing methods. In addition, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. Rigorous complexity analyses of the new method are provided as are several numerical examples that illustrate the effectiveness of the approach.
97 MATHEMATICS AND COMPUTING↗
A hyper-spherical adaptive sparse-grid method for high-dimensional discontinuity detection
This work proposes and analyzes a hyper-spherical adaptive hierarchical sparse-grid method for detecting jump discontinuities of functions in high-dimensional spaces is proposed. The method is motivated by the theoretical and computational inefficiencies of well-known adaptive sparse-grid methods for discontinuity detection. Our novel approach constructs a function representation of the discontinuity hyper-surface of an N-dimensional dis- continuous quantity of interest, by virtue of a hyper-spherical transformation. Then, a sparse-grid approximation of the transformed function is built in the hyper-spherical coordinate system, whose value at each point is estimated by solving a one-dimensional discontinuity detection problem. Due to the smoothness of the hyper-surface, the new technique can identify jump discontinuities with significantly reduced computational cost, compared to existing methods. Moreover, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. Rigorous error estimates and complexity analyses of the new method are provided as are several numerical examples that illustrate the effectiveness of the approach.
97 MATHEMATICS AND COMPUTING↗
Test-particle acceleration in a hierarchical three-dimensional turbulence model
The acceleration of charged particles is relevant to the solar corona over a broad range of scales and energies. High-energy particles are usually detected in concomitance with large energy release events like solar eruptions and flares. Nevertheless, acceleration can occur at smaller scales, characterized by dynamical activity near current sheets. To gain insight into the complex scenario of coronal charged particle acceleration, we investigate the properties of acceleration with a test-particle approach using three-dimensional magnetohydrodynamic (MHD) models. These are obtained from direct solutions of the reduced MHD equations, well suited for a plasma embedded in a strong axial magnetic field, relevant to the inner heliosphere. A multi-box, multiscale technique is used to solve the equations of motion for protons. This method allows us to resolve an extended range of scales present in the system, namely, from the ion inertial scale of the order of a meter up to macroscopic scales of the order of 10 km (1/100th of the outer scale of the system). This new technique is useful to identify the mechanisms that, acting at different scales, are responsible for acceleration to high energies of a small fraction of the particles in the coronal plasma. We report results that describe acceleration at different stages over a broad range of time, length, and energy scales.
79 ASTRONOMY AND ASTROPHYSICS↗
Hyperspherical Sparse Approximation Techniques for High-Dimensional Discontinuity Detection
This work proposes a hyperspherical sparse approximation framework for detecting jump discontinuities in functions in high-dimensional spaces. The need for a novel approach results from the theoretical and computational inefficiencies of well-known approaches, such as adaptive sparse grids, for discontinuity detection. Our approach constructs the hyperspherical coordinate representation of the discontinuity surface of a function. Then sparse approximations of the transformed function are built in the hyperspherical coordinate system, with values at each point estimated by solving a one-dimensional discontinuity detection problem. Due to the smoothness of the hypersurface, the new technique can identify jump discontinuities with significantly reduced computational cost, compared to existing methods. Several approaches are used to approximate the transformed discontinuity surface in the hyperspherical system, including adaptive sparse grid and radial basis function interpolation, discrete least squares projection, and compressed sensing approximation. Moreover, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. In conclusion, rigorous complexity analyses of the new methods are provided, as are several numerical examples that illustrate the effectiveness of our approach.
97 MATHEMATICS AND COMPUTING↗
ARCHIE: Data Analysis Acceleration with Array Caching in Hierarchical Storage
© 2018 IEEE. Scientific data analysis typically involves reading massive amounts of data that was generated by simulations, experiments, and observations. Performance of reading such large volumes of data from disk-based file systems is often poor because of the slow and mechanical components in the disks. Recent supercomputing systems are adding non-volatile storage layers in a hierarchy to handle the performance gap between fast main memory and slow disk-based storage. Software libraries for managing this hierarchy not only need efficient reading of data but also reduce user-involvement for cross-layer data movement. Furthermore, these libraries need to support array data access patterns into hierarchical storage management as scientific data is often organized in array-based data structures. Existing software typically manage individual storage layers requiring significant manual process in moving data among them. In this paper, we introduce a new array caching in hierarchical storage (ARCHIE) to accelerate array data analysis in a seamless fashion. ARCHIE evaluates array access patterns and prefetches data with array semantics between storage layers. Our evaluation shows that ARCHIE outperforms state-of-the-art file systems, i.e., Lustre and DataWarp, on a production supercomputing system by up to 5.8× in accessing data by scientific analysis applications.
Dong, Bin↗
Accelerating Multigrid-based Hierarchical Scientific Data Refactoring on GPUs
Rapid growth in scientific data and a widening gap between computational speed and I/O bandwidth make it increasingly infeasible to store and share all data produced by scientific simulations. Instead, we need methods for reducing data volumes: ideally, methods that can scale data volumes adaptively so as to enable negotiation of performance and fidelity tradeoffs in different situations. Multigrid-based hierarchical data representations hold promise as a solution to this problem, allowing for flexible conversion between different fidelities so that, for example, data can be created at high fidelity and then transferred or stored at lower fidelity via logically simple and mathematically sound operations. However, the effective use of such representations has been hindered until now by the relatively high costs of creating, accessing, reducing, and otherwise operating on such representations. We describe here highly optimized data refactoring kernels for GPU accelerators that enable efficient creation and manipulation of data in multigrid-based hierarchical forms. We demonstrate that our optimized design can achieve up to 250 TB/s aggregated data refactoring throughput—83% of theoretical peak—on 1024 nodes of the Summit supercomputer. We showcase our optimized design by applying it to a large-scale scientific visualization workflow and the MGARD lossy compression software.
Data refactoring↗
Accelerating Multigrid-based Hierarchical Scientific Data Refactoring on GPUs
Rapid growth in scientific data and a widening gap between computational speed and I/O bandwidth make it increasingly infeasible to store and share all data produced by scientific simulations. Instead, we need methods for reducing data volumes: ideally, methods that can scale data volumes adaptively so as to enable negotiation of performance and fidelity tradeoffs in different situations. Multigrid-based hierarchical data representations hold promise as a solution to this problem, allowing for flexible conversion between different fidelities so that, for example, data can be created at high fidelity and then transferred or stored at lower fidelity via logically simple and mathematically sound operations. However, the effective use of such representations has been hindered until now by the relatively high costs of creating, accessing, reducing, and otherwise operating on such representations. We describe here highly optimized data refactoring kernels for GPU accelerators that enable efficient creation and manipulation of data in multigrid-based hierarchical forms. We demonstrate that our optimized design can achieve up to 250 TB/s aggregated data refactoring throughput—83% of theoretical peak—on 1024 nodes of the Summit supercomputer. We showcase our optimized design by applying it to a large-scale scientific visualization workflow and the MGARD lossy compression software.
Chen, Jieyang↗
Accelerating Bilevel Optimization With Hierarchical Many-Threaded Parallel Differential Evolution
Bilevel optimization is encountered in many relevant real-world applications. The main feature of this type of problem is that an upper-level optimization problem is constrained by a nested lower-level optimization problem. Because of this nested structure, bilevel problems (BLPs) are usually computationally expensive to solve. Differential evolution (DE) has demonstrated promising results in solving BLPs of relatively small scales. As the problem scale increases, the decision space becomes intrinsically larger, requiring a growing number of function evaluations for the method to work properly. In this context, heavy parallelization and high-performance computing techniques are indispensable to enable the resolution of more complex and challenging optimization problems. Hence, we propose a hierarchical many-threaded parallel DE approach for BLPs, where both levels are parallelized. The computational experiments demonstrate that the parallel implementation achieved runtime speeds ranging from 44 to 2559 times faster than the sequential version on a well-known scalable SMD benchmark test problem when executed on an NVIDIA A100 GPU. The findings indicate that the algorithm’s convergence is strongly influenced by the number of both upper- and lower-level generations. Moreover, the success of experiments with large-scale problems is closely linked to the choice of small population sizes.
Dufek, Amanda S↗
Design for dependability: A simulation-based approach
This research addresses issues in simulation-based system level dependability analysis of fault-tolerant computer systems. The issues and difficulties of providing a general simulation-based approach for system level analysis are discussed and a methodology that address and tackle these issues is presented. The proposed methodology is designed to permit the study of a wide variety of architectures under various fault conditions. It permits detailed functional modeling of architectural features such as sparing policies, repair schemes, routing algorithms as well as other fault-tolerant mechanisms, and it allows the execution of actual application software. One key benefit of this approach is that the behavior of a system under faults does not have to be pre-defined as it is normally done. Instead, a system can be simulated in detail and injected with faults to determine its failure modes. The thesis describes how object-oriented design is used to incorporate this methodology into a general purpose design and fault injection package called DEPEND. A software model is presented that uses abstractions of application programs to study the behavior and effect of software on hardware faults in the early design stage when actual code is not available. Finally, an acceleration technique that combines hierarchical simulation, time acceleration algorithms and hybrid simulation to reduce simulation time is introduced.
Goswami, Kumar K.↗
HIERARCHICAL FORMATION IN ACTION: CHARACTERIZING ACCELERATED GALAXY EVOLUTION IN COMPACT GROUPS USING WHOLE-SKY WISE DATA
Compact groups provide an environment to study the growth of galaxies amid multiple prolonged interactions. With their dense galaxy concentrations and relatively low velocity dispersions, compact groups mimic the conditions of hierarchical galaxy assembly. Compact group galaxies are known to show a bimodality in Spitzer IRAC infrared color space: galaxies are preferentially either quiescent with low specific star formation rates (SSFRs) or prolifically forming stars—galaxies with moderate levels of specific star formation are rare. Previous Spitzer IRAC studies identifying this “canyon” have been limited by small number statistics. We utilize whole-sky Wide-field Infrared Survey Explorer (WISE) data to study 163 compact groups, thereby tripling our previous sample and including more galaxies with intermediate mid-IR colors indicative of moderate SSFRs. We define a distinct WISE mid-IR color space (log[((f{sub 12})/(f{sub 4.6}))]) versus (log[((f{sub 22})/(f{sub 3.4}))]) that we use to identify canyon galaxies from the larger sample. We confirm that compact group galaxies show a bimodal distribution in the mid-infrared and identify 37 canyon galaxies with reliable photometry and intermediate mid-IR colors. Morphologically, we find that the canyon harbors a large population of both Sa–Sbc and E/S0 type galaxies, and that they fall on the optical red sequence rather than the green valley. Finally, we provide a catalog of WISE photometry for 567 of 652 galaxies selected from the sample of 163 compact groups.
79 ASTRONOMY AND ASTROPHYSICS↗
Hierarchical Roofline analysis for GPUs: Accelerating performance optimization for the NERSC‐9 Perlmutter system
Summary The Roofline performance model provides an intuitive and insightful approach to identifying performance bottlenecks and guiding performance optimization. In preparation for the next‐generation supercomputer Perlmutter at NERSC, this paper presents a methodology to construct a hierarchical Roofline on NVIDIA GPUs and extends it to support reduced precision and Tensor Cores. The hierarchical Roofline incorporates L1, L2, device memory, and system memory bandwidths into one single figure, and it offers more profound insights into performance analysis than the traditional DRAM‐only Roofline. We use our Roofline methodology to analyze three proxy applications: GPP from BerkeleyGW, HPGMG from AMReX, and conv2d from TensorFlow. In doing so, we demonstrate the ability of our methodology to readily understand various aspects of performance and performance bottlenecks on NVIDIA GPUs and motivate code optimizations.
Yang, Charlene↗
A Performance Portable, Fully Implicit Landau Collision Operator with Batched Linear Solvers
Modern accelerators use hierarchical parallel programming models that enable massive multithreading within a processing element (PE), with multiple PEs per device driven by traditional processes. Batching is a technique for exposing PE-level parallelism in algorithms that have traditionally run on MPI processes or multiple threads within a single process. Opportunities for batching arise in, for example, kinetic discretizations of magnetized plasmas where collisions are advanced in velocity space at each spatial point independently. This paper builds on previous work on a high-performance, fully nonlinear, Landau collision operator by batching the linear solver, as well as batching the spatial point problems and adding new support for multiple grids for multiscale, multispecies problems. An anisotropic relaxation verification test that agrees well with previously published results and analytical models is presented. The performance results from NVIDIA A100 and AMD MI250X nodes are presented with hardware utilization analysis for each architecture. Finally, the entire implicit Landau operator time advance is implemented in Kokkos for performance portability, running entirely on the device and is available in the PETSc numerical library.
97 MATHEMATICS AND COMPUTING↗
Hierarchical Particle Mesh: An FFT-accelerated Fast Multipole Method
I observe a modification to the original Fast Multipole Method (FMM) of Greengard & Rokhlin that approximates the gravitation field of an FMM cell as a small uniform grid (a “gridlet”) of effective masses. The effective masses on a gridlet are set from the requirement that the multipole moments of the FMM cells are reproduced exactly, thus preserving the accuracy of the gravitational field representation. The measurement of the gravitational field from a multipole expansion can then be computed for all multipole orders simultaneously, with a single Fast Fourier Transform, significantly reducing the computational cost at a given value of the required accuracy. The described approach belongs to the class of “kernel independent” variants of the FMM method and works with any Green function.
79 ASTRONOMY AND ASTROPHYSICS↗
Ab Initio-Based Bond Order Potential for Arsenene Polymorphs Developed via Hierarchical Reinforcement Learning
Arsenene, a less-explored two-dimensional material, holds the potential for applications in wearable electronics, memory devices, and quantum systems. This study introduces a bond-order potential model with Tersoff formalism, the ML-Tersoff, which leverages multireward hierarchical reinforcement learning (RL), trained on an ab initio data set. This data set covers a spectrum of properties for arsenene polymorphs, enhancing our understanding of its mechanical and thermal behaviors without the complexities of traditional models requiring multiple parameter sets. Our RL strategy utilizes decision trees coupled with a hierarchical reward strategy to accelerate convergence in high-dimensional continuous search spaces. Unlike the Stillinger-Weber approach, which demands separate formalisms for buckled and puckered forms, the ML-Tersoff model concurrently captures multiple properties of the two polymorphs by effectively representing the local environment, thereby avoiding the need for different atomic types. Here, we apply the ML model to understand the mechanical and thermal properties of the arsenene polymorphs and nanostructures. We observe an inverse relationship between the critical strain and temperature in arsenene. Thermal conductivity calculations in nanosheets show good agreement with ab initio data, reflecting a decrease in thermal conductivity attributable to increased anharmonic effects at higher temperatures. We also apply the model to predict the thermal behavior of arsenene nanotubes.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Time-Critical Volume Rendering
For the past twelve months, we have conducted and completed a joint research entitled "Time- Critical Volume Rendering" with NASA Ames. As expected, High performance volume rendering algorithms have been developed by exploring some new faster rendering techniques, including object presence acceleration, parallel processing, and hierarchical level-of-detail representation. Using our new techniques, initial experiments have achieved real-time rendering rates of more than 10 frames per second of various 3D data sets with highest resolution. A couple of joint papers and technique reports as well as an interactive real-time demo have been compiled as the result of this project.
Kaufman, Arie↗
Accelerated Voltage Regulation in Multi-Phase Distribution Networks Based on Hierarchical Distributed Algorithm
Here, we introduce a hierarchical distributed algorithm to solve optimal power flow (OPF) problems that aim at dispatching controllable distributed energy resources (DERs) for voltage regulation at minimum cost. The proposed algorithm highlights unprecedented scalability to large multi-phase distribution networks by jointly exploring the tree/subtrees structure of a large radial distribution network and the structure of the linearized distribution power flow (LinDistFlow) model to derive a hierarchical, distributed implementation of the primal-dual gradient algorithm that solves OPF. The proposed implementation significantly reduces the computation loads compared to the centrally coordinated implementation of the same primal-dual algorithm without compromising optimality. Numerical findings on a 4,521-node test feeder show that the designed algorithm achieves more than 10-fold acceleration in the speed of convergence compared to the centrally coordinated primal-dual algorithm through reducing and distributing computational loads.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Confronting the Challenge of Modeling Cloud and Precipitation Microphysics
In the atmosphere, microphysics refers to the microscale processes that affect cloud and precipitation particles and is a key linkage among the various components of Earth’s atmospheric water and energy cycles. The representation of microphysical processes in models continues to pose a major challenge leading to uncertainty in numerical weather forecasts and climate simulations. In this paper, the problem of treating microphysics in models is divided into two parts: i) how to represent the population of cloud and precipitation particles, given the impossibility of simulating all particles individually within a cloud, and ii) uncertainties in the microphysical process rates owing to fundamental gaps in knowledge of cloud physics. The recently-developed Lagrangian particle-based method is advocated as a way to address several conceptual and practical challenges of representing particle populations using traditional bulk and bin microphysics parameterization schemes. For addressing critical gaps in cloud physics knowledge, sustained investment for observational advances from laboratory experiments, new probe development, and next-generation instruments in space is needed. Greater emphasis on laboratory work, which has apparently declined over the past several decades relative to other areas of cloud physics research, is argued to be an essential ingredient for improving process-level understanding. More systematic use of natural cloud and precipitation observations to constrain microphysics schemes is also advocated. Because it is generally difficult to quantify individual microphysical process rates from these observations directly, this presents an inverse problem that can be viewed from the standpoint of Bayesian statistics. Following this idea, a probabilistic framework is proposed that combines elements from statistical and physical modeling. Besides providing rigorous constraint of schemes, there is an added benefit of quantifying uncertainty systematically. Finally, a broader hierarchical approach is proposed to accelerate improvements in microphysics schemes, leveraging the advances described in this paper related to process modeling (using Lagrangian particle-based schemes), laboratory experimentation, cloud and precipitation observations, and statistical methods.
54 ENVIRONMENTAL SCIENCES↗