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DOE OSTI2022

Assessing MP2 frozen natural orbitals in relativistic correlated electronic structure calculations

The high computational scaling with the basis set size and the number of correlated electrons is a bottleneck limiting applications of coupled cluster algorithms, in particular for calculations based on two- or four-component relativistic Hamiltonians, which often employ uncontracted basis sets. This problem may be alleviated by replacing canonical Hartree–Fock virtual orbitals by natural orbitals (NOs). Here, in this paper, we describe the implementation of a module for generating NOs for correlated wavefunctions and, in particular, second order Møller–Plesset perturbation frozen natural orbitals (MP2FNOs) as a component of our novel implementation of relativistic coupled cluster theory for massively parallel architectures [Pototschnig et al. J. Chem. Theory Comput. 17, 5509, (2021)]. Our implementation can manipulate complex or quaternion density matrices, thus allowing for the generation of both Kramers-restricted and Kramers-unrestricted MP2FNOs. Furthermore, NOs are re-expressed in the parent atomic orbital (AO) basis, allowing for generating coupled cluster singles and doubles NOs in the AO basis for further analysis. By investigating the truncation errors of MP2FNOs for both the correlation energy and molecular properties—electric field gradients at the nuclei, electric dipole and quadrupole moments for hydrogen halides HX (X = F–Ts), and parity-violating energy differences for H 2 Z 2 (Z = O–Se)—we find MP2FNOs accelerate the convergence of the correlation energy in a roughly uniform manner across the Periodic Table. It is possible to obtain reliable estimates for both energies and the molecular properties considered with virtual molecular orbital spaces truncated to about half the size of the full spaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

2016 High Performance Computing Annual Report

Sandia National Laboratories’ California site is celebrating its 60th anniversary (1956 to 2016), and high performance computing has been a key enabler for its scientists and engineers throughout much of its history. Since its founding, Sandia California has helped pioneer the use of HPC platforms including hosting Sandia’s first Cray-1 supercomputer in the 1970s and supporting development of scalable cluster computing platforms to create a new paradigm for cost-effective supercomputing in the 1990s. Recent decades of investment in creation of scalable application frameworks for scientific computing have also enabled new generations of modeling and simulation codes. These resources have facilitated computational analysis of complex phenomena in diverse applications spanning national defense, energy, and homeland security. Today, Sandia California researchers work with partners in academia, industry, and national labs to evolve the state-of-the-art in HPC, modeling, and data analysis (including foundational capabilities for exascale computing platforms) and apply them in transformational ways. Research efforts include mitigating the effects of silent hardware failures that can jeopardize the results of large-scale computations, developing exascale-capable asynchronous task-parallel programming models and runtime systems, formulating new techniques to better explore and analyze extreme-scale data sets, and increasing our understanding of materials and chemical sciences which has applications spanning nuclear weapons stockpile stewardship to more efficient automobile engines. The following section highlights some of these research and applications projects and further illustrates the breadth of our HPC capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Multigrid Reduction in Time for Nonlinear Parabolic Problems: A Case Study

The need for parallelism in the time dimension is being driven by changes in computer architectures, where performance increases are now provided through greater concurrency, not faster clock speeds. This creates a bottleneck for sequential time marching schemes because they lack parallelism in the time dimension. Multigrid reduction in time (MGRIT) is an iterative procedure that allows for temporal parallelism by utilizing multigrid reduction techniques and a multilevel hierarchy of coarse time grids. MGRIT has been shown to be effective for linear problems, with speedups of up to 50 times. The goal of this work is the efficient solution of nonlinear problems with MGRIT, where efficiency is defined as achieving similar performance when compared to an equivalent linear problem. The benchmark nonlinear problem is the p-Laplacian, where p=4 corresponds to a well-known nonlinear diffusion equation and p=2 corresponds to the standard linear diffusion operator, our benchmark linear problem. The key difficulty encountered is that the nonlinear time-step solver becomes progressively more expensive on coarser time levels as the time-step size increases. To overcome such difficulties, multigrid research has historically targeted an accumulated body of experience regarding how to choose an appropriate solver for a specific problem type. To that end, this paper develops a library of MGRIT optimizations and modifications, most important an alternate initial guess for the nonlinear time-step solver and delayed spatial coarsening, that will allow many nonlinear parabolic problems to be solved with parallel scaling behavior comparable to the corresponding linear problem.

parareal↗

DOE OSTI2023

Editorial: Neuroscience, computing, performance, and benchmarks: Why it matters to neuroscience how fast we can compute

At the turn of the millennium the computational neuroscience community realized that neuroscience was in a software crisis: software development was no longer progressing as expected and reproducibility declined. The International Neuroinformatics Coordinating Facility (INCF) was inaugurated in 2007 as an initiative to improve this situation. The INCF has since pursued its mission to help the development of standards and best practices. In a community paper published this very same year, Brette et al. tried to assess the state of the field and to establish a scientific approach to simulation technology, addressing foundational topics, such as which simulation schemes are best suited for the types of models we see in neuroscience. In 2015, a Frontiers Research Topic “Python in neuroscience” by Muller et al. triggered and documented a revolution in the neuroscience community, namely in the usage of the scripting language Python as a common language for interfacing with simulation codes and connecting between applications. The review by Einevoll et al. documented that simulation tools have since further matured and become reliable research instruments used by many scientific groups for their respective questions. Open source and community standard simulators today allow research groups to focus on their scientific questions and leave the details of the computational work to the community of simulator developers. A parallel development has occurred, which has been barely visible in neuroscientific circles beyond the community of simulator developers: Supercomputers used for large and complex scientific calculations have increased their performance from ~10 TeraFLOPS (10 13 floating point operations per second) in the early 2000s to above 1 ExaFLOPS (10 18 floating point operations per second) in the year 2022. This represents a 100,000-fold increase in our computational capabilities, or almost 17 doublings of computational capability in 22 years. Moore's law (the observation that it is economically viable to double the number of transistors in an integrated circuit every other 18–24 months) explains a part of this; our ability and willingness to build and operate physically larger computers, explains another part. It should be clear, however, that such a technological advancement requires software adaptations and under the hood, simulators had to reinvent themselves and change substantially to embrace this technological opportunity. It actually is quite remarkable that—apart from the change in semantics for the parallelization—this has mostly happened without the users knowing. The current Research Topic was motivated by the wish to assemble an update on the state of neuroscientific software (mostly simulators) in 2022, to assess whether we can see more clearly which scientific questions can (or cannot) be asked due to our increased capability of simulation, and also to anticipate whether and for how long we can expect this increase of computational capabilities to continue.

biophysically detailed models↗

DOE OSTI2016

Proper orthogonal decomposition analysis of parallel twin jets measured using particle image velocimetry - 18685

The mixing of turbulent jets has been found in several locations of High Temperature Gas-cooled Reactors (HTGRs) including upper and lower plenums, where jets impinge into open space from coolant channels. In the present work, a parallel twin jets experimental facility was used to generate velocity field of mixing jets by means of Particle Image Velocimetry (PIV), which can be eventually used for validation of Computational Fluid Dynamics (CFD) simulations. The facility has two fixed parallel rectangular jet nozzles (5.8 mm in width, 87.8 mm in length) submerged in the middle of the water tank, which allows an assumption of free jet mixing. In order to compare the experimental data produced to existing data, Re = 4000 {approx} 5000 at the jet outlet was selected. In the past, several statistically meaningful data have been reported using Laser Doppler Velocimetry (LDV) and Hot Wire Anemometer (HWA), which can support Reynolds Averaged Navier-Stokes turbulent models. However, recent CFD simulations using Large Eddy Simulation (LES) require high resolution experimental data in time and space. Thus, in this study, in addition to statistically enough number of data sets for RANS models validation, high temporal and spatial resolution data were collected for the validation of LES calculations. In order to study the turbulent structure Reynolds decomposition and Proper Orthogonal Decomposition (POD) were applied to the data obtained. These decomposition analyses visualized multi-scale vortices and the transportation of eddies. In terms of twin jets structure, the present experimental data showed good agreement with other techniques for the important characteristic parameters including the length of the converging region and the location of the merging point. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2016

Comparison of Parallel and Series Hybrid Power Trains for Transit Bus Applications

The fuel economy and emissions of conventional and hybrid buses equipped with emissions after treatment were evaluated via computational simulation for six representative city bus drive cycles. Both series and parallel configurations for the hybrid case were studied. The simulation results indicated that series hybrid buses have the greatest overall advantage in fuel economy. The series and parallel hybrid buses were predicted to produce similar carbon monoxide and hydrocarbon tailpipe emissions but were also predicted to have reduced tailpipe emissions of nitrogen oxides compared with the conventional bus in higher speed cycles. For the New York bus cycle, which has the lowest average speed among the cycles evaluated, the series bus tailpipe emissions were somewhat higher than they were for the conventional bus; the parallel hybrid bus had significantly lower tailpipe emissions. All three bus power trains were found to require periodic active diesel particulate filter regeneration to maintain control of particulate matter. Finally, plug-in operation of series hybrid buses appears to offer significant fuel economy benefits and is easily employed because of the relatively large battery capacity that is typical of the series hybrid configuration.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2019

Parallel-In-Time Multigrid with Adaptive Spatial Coarsening for The Linear Advection and Inviscid Burgers Equations

We apply a multigrid reduction-in-time (MGRIT) algorithm to hyperbolic partial differential equations in one spatial dimension. This study is motivated by the observation that sequential time-stepping is a computational bottleneck when attempting to implement highly concurrent algorithms; thus parallel-in-time methods are desirable. MGRIT adds parallelism by using a hierarchy of successively coarser temporal levels to accelerate the solution on the finest level. In the case of explicit time-stepping, spatial coarsening is a suitable approach to ensure that stability conditions are satisfied on all levels, and it may be useful for implicit time-stepping by producing cheaper multigrid cycles. Unfortunately, uniform spatial coarsening results in extremely slow convergence when the wave speed is near zero, even if only locally. We present an adaptive spatial coarsening strategy that addresses this issue for the variable coefficient linear advection equation and the inviscid Burgers equation using first-order explicit or implicit time-stepping methods. Serial numerical results show this method offers significant improvements over uniform coarsening and is convergent for the inviscid Burgers equation with and without shocks. Parallel scaling tests on up to 128K cores indicate that run-time improvements over serial time-stepping strategies are possible when spatial parallelism alone saturates, and that scalability is robust for oscillatory solutions which change on the scale of the grid spacing.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Parallel Randomized Tucker Decomposition Algorithms

The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. Here, we propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two algorithms that scale to large data and many processors, significantly reduce both computation and communication cost compared to previous deterministic and randomized approaches, and obtain nearly the same approximation errors. The key idea in our algorithms is to perform randomized sketches with Kronecker-structured random matrices, which reduces computation compared to unstructured matrices and can be implemented using a fundamental tensor computational kernel. We provide probabilistic error analysis of our algorithms and implement a new parallel algorithm for the structured randomized sketch. Our experimental results demonstrate that our combination of randomization and parallelization achieves accurate Tucker decompositions much faster than alternative approaches. We observe up to a 16X speedup over the fastest deterministic parallel implementation on 3D simulation data.

Tucker decompositions↗

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 OSTI2017

A parallel orbital-updating based plane-wave basis method for electronic structure calculations

Highlights: • Propose three parallel orbital-updating based plane-wave basis methods for electronic structure calculations. • These new methods can avoid the generating of large scale eigenvalue problems and then reduce the computational cost. • These new methods allow for two-level parallelization which is particularly interesting for large scale parallelization. • Numerical experiments show that these new methods are reliable and efficient for large scale calculations on modern supercomputers. - Abstract: Motivated by the recently proposed parallel orbital-updating approach in real space method , we propose a parallel orbital-updating based plane-wave basis method for electronic structure calculations, for solving the corresponding eigenvalue problems. In addition, we propose two new modified parallel orbital-updating methods. Compared to the traditional plane-wave methods, our methods allow for two-level parallelization, which is particularly interesting for large scale parallelization. Numerical experiments show that these new methods are more reliable and efficient for large scale calculations on modern supercomputers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Parallel projection—An improved return mapping algorithm for finite element modeling of shape memory alloys

Here, we present a novel finite element analysis of inelastic structures containing Shape Memory Alloys (SMAs). Phenomenological constitutive models for SMAs lead to material nonlinearities, that require substantial computational effort to resolve. Finite element analysis methods, which rely on Gauss quadrature integration schemes, must solve two sets of coupled differential equations: one at the global level and the other at the local, i.e. Gauss point level. In contrast to the conventional return mapping algorithm, which solves these two sets of coupled differential equations separately using a nested Newton procedure, we propose a scheme to solve the local and global differential equations simultaneously. In the process we also derive closed-form expressions used to update the internal/constitutive state variables, and unify the popular closest-point and cutting plane methods with our formulas. Numerical testing indicates that our method allows for larger thermomechanical loading steps and provides increased computational efficiency, over the standard return mapping algorithm.

42 ENGINEERING↗

DOE OSTI2017

Axom

The Axom library consists of n collection of software components that provide core computer science infrastructure capabilities that can be shared by diverse high performance computing (HPC) applications. The current set of capabilities that Axom provides includes: Customizable support for error/warning and diagnostic message reporting and coordination among components of integrated applications (e.g., physics packages, libraries, etc.); Scalable parallel aggregation and filtering of message logging; In memory datastore for hierarchical, mesh-aware simulation data. The datastore supports data description, allocation, deallocation. parallel l/0, etc; Mesh data model abstractions that enable the development of mesh-based computational algorithms that work with many diverse, application· specific mesh types; and Computational geometry primitives for developing high performance parallel algorithms based on spatial geometry and meshes, e.g., spatial acceleration data structures, sets, maps, relations, etc.

Hornung, RichardD.↗

DOE OSTI2021

PandAna: A Python Analysis Framework for Scalable High Performance Computing in High Energy Physics

Modern experiments in high energy physics analyze millions of events recorded in particle detectors to select the events of interest and make measurements of physics parameters. These data can often be stored as tabular data in files with detector information and reconstructed quantities. Current techniques for event selection in these files lack the scalability needed for high performance computing environments. We describe our work to develop a high energy physics analysis framework suitable for high performance computing. This new framework utilizes modern tools for reading files and implicit data parallelism. Framework users analyze tabular data using standard, easy-to-use data analysis techniques in Python while the framework handles the file manipulations and parallelism without the user needing advanced experience in parallel programming. In future versions, we hope to provide a framework that can be utilized on a personal computer or a high performance computing cluster with little change to the user code.

Groh, Micah↗

DOE OSTI2020

Parallelization and Performance Portability in Hydrodynamics Codes

With the eve of Exascale computing, performance and portability are at the forefront of all scientific codes. Adding more cores and more energy to a system is no longer a sustainable way to achieve performance, and extra effort must now be made to improve performance in all areas of code and code development. Using hydrodynamic codes as a basis, this work explores numerous techniques to achieve performance in different ways. Adaptive mesh refinement (AMR) is a necessary technique to improve memory optimization in mesh-based simulations. However it is invasive and conventionally difficult to integrate into existing applications, so we present a new branch of AMR to create a smooth transition to these optimizations, which not only improves performance, but also greatly reduces developer effort. We introduce the concept of this improvement as Phantom-Cell AMR, and assess theoretically the improvements, as well as present an application of its use. Other work included involves and investigation into an efficient data structure that ensures optimal memory layout for cache performance, with a target of making codes performant and portable across all architectures. All of the work targets both performance and portability, not just on CPU hardware, but specifically across GPU architectures. Parallel performance is key to all of the methods presented, but the research makes a great effort to improve the portability of all applications to prepare for current high performance computing systems and those on the horizon.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Convergence of the multigrid reduction in time algorithm for the linear elasticity equations

This paper presents some recent advances for parallel-in-time methods applied to linear elasticity. With recent computer architecture changes leading to stagnant clock speeds, but ever increasing numbers of cores, future speedups will be available through increased concurrency. Thus, sequential algorithms, such as time stepping, will suffer a bottleneck. This paper explores multigrid reduction in time (MGRIT) for an important application area, linear elasticity. Previously, efforts at parallel-in-time for elasticity have experienced difficulties, for example, the beating phenomenon. As a result, practical parallel-in-time algorithms for this application area currently do not exist. This paper proposes some solutions made possible by MGRIT (e.g., slow temporal coarsening and FCF-relaxation) and, more importantly, a different formulation of the problem that is more amenable to parallel-in-time methods. Using a recently developed convergence theory for MGRIT and Parareal, we show that the changed formulation of the problem avoids the instability issues and allows the reduction of the error using two temporal grids. We then extend our approach to the multilevel case, where we demonstrate how slow temporal coarsening improves convergence. Finally, the paper ends with supporting numerical results showing a practical algorithm enjoying speedup benefits over the sequential algorithm.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

All-Atom Simulation of 3D Hot Spot Formation in Shocked TATB Explosive

TATB is an insensitive high explosive (IHE) critical to the stockpile that is challenging to model at the continuum scale. Advanced detonation models in the Cheetah high explosive chemistry code require validation though subscale simulations. High explosive initiation is determined by micron-scale physics of hot spots formed a shock-collapsed pores. Pore sizes between 100 nm and 1 μm are believed to be the most important for determining the shock sensitivity of TATB. This range of pore sizes is difficult to access at the atomic scale through allatom molecular dynamics (MD) simulations, even with Sierra-class computers. Quasi-2D simulations are widely used and allow much larger pore sizes (up to 400 nm) to be studied, but the applicability of 2D simulations to the actual 3D pore response is not understood. Resolving these uncertainties through “full physics” MD modeling is key for generalizing, parameterizing, and validating the kinds of continuum models used to inform design, safety, and performance. This work was a continuation of FY20 efforts pushing simulations to full 3D with the largest-ever all-atom simulations of an explosive. These were the first all-atom full-3D simulations of large hot spots thought to govern explosive detonation and required over a billion atoms. Simulations were performed using LAMMPS, an open SNL science code. MD explosive models present unique challenges, even for established codes such as LAMMPS. Their model forms are more complex than typical models for metals, while simulating high temperature-pressure conditions is demanding and increases computational cost. Scaling problems in GPU-enabled MD algorithms initially limited simulations to <100 million atoms but were resolved through collaboration with SNL. An overall 24x speedup was obtained relative to CPU machines. Specialized analysis of these simulations required a bottom-up refactoring and algorithm parallelization of in-house codes and application of computer vision algorithms to extract meaningful information.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Asynchronous Iterative Solvers for Extreme-Scale Computing (Final Report)

This is the final report for the project: Asynchronous Iterative Solvers for Extreme-Scale Computing. This was a collaborative project. This report only covers the activities specific to Georgia Institute of Technology. The project investigated and developed iterative solvers that operate asynchronously, thereby avoiding the high cost of synchronization that is apparent when using standard, synchronous iterative solvers at extreme levels of parallelism.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Energy-efficient Mott activation neuron for full-hardware implementation of neural networks

To circumvent the von Neumann bottleneck, substantial progress has been made towards in-memory computing with synaptic devices. However, compact nanodevices implementing non-linear activation functions are required for efficient full-hardware implementation of deep neural networks. Here, in this work, we present an energy-efficient and compact Mott activation neuron based on vanadium dioxide and its successful integration with a conductive bridge random access memory (CBRAM) crossbar array in hardware. The Mott activation neuron implements the rectified linear unit function in the analogue domain. The neuron devices consume substantially less energy and occupy two orders of magnitude smaller area than those of analogue complementary metal–oxide semiconductor implementations. The LeNet-5 network with Mott activation neurons achieves 98.38% accuracy on the MNIST dataset, close to the ideal software accuracy. We perform large-scale image edge detection using the Mott activation neurons integrated with a CBRAM crossbar array. Our findings provide a solution towards large-scale, highly parallel and energy-efficient in-memory computing systems for neural networks.

electrical and electronic engineering↗