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DOE OSTI2022

Stochastic Vector Techniques in Ground-State Electronic Structure

Herein we review a suite of stochastic vector computational approaches for studying the electronic structure of extended condensed matter systems. These techniques help reduce algorithmic complexity, facilitate efficient parallelization, simplify computational tasks, accelerate calculations, and diminish memory requirements. While their scope is vast, we limit our study to ground-state and finite temperature density functional theory (DFT) and second-order many-body perturbation theory. More advanced topics, such as quasiparticle (charge) and optical (neutral) excitations and higher-order processes, are covered elsewhere. We start by explaining how to use stochastic vectors in computations, characterizing the associated statistical errors. Next, we show how to estimate the electron density in DFT and discuss effective techniques to reduce statistical errors. Finally, we review the use of stochastic vectors for calculating correlation energies within the second-order Møller-Plesset perturbation theory and its finite temperature variational form. Example calculation results are presented and used to demonstrate the efficacy of the methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Hyper-Differential Sensitivity Analysis of Uncertain Parameters in PDE-Constrained Optimization

Many problems in engineering and sciences require the solution of large scale optimization constrained by partial differential equations (PDEs). Though PDE-constrained optimization is itself challenging, most applications pose additional complexity, namely, uncertain parameters in the PDEs. Uncertainty quantification (UQ) is necessary to characterize, prioritize, and study the influence of these uncertain parameters. Sensitivity analysis, a classical tool in UQ, is frequently used to study the sensitivity of a model to uncertain parameters. In this article, we introduce "hyper-differential sensitivity analysis" which considers the sensitivity of the solution of a PDE-constrained optimization problem to uncertain parameters. Our approach is a goal-oriented analysis which may be viewed as a tool to complement other UQ methods in the service of decision making and robust design. We formally define hyper-differential sensitivity indices and highlight their relationship to the existing optimization and sensitivity analysis literatures. Assuming the presence of low rank structure in the parameter space, computational efficiency is achieved by leveraging a generalized singular value decomposition in conjunction with a randomized solver which converts the computational bottleneck of the algorithm into an embarrassingly parallel loop. Two multi-physics examples, consisting of nonlinear steady state control and transient linear inversion, demonstrate efficient identification of the uncertain parameters which have the greatest influence on the optimal solution.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

PeleLMeX: an AMR Low Mach Number Reactive Flow Simulation Code without level sub-cycling

PeleLMeX simulates chemically reacting low Mach number flows with block-structured adaptive mesh refinement (AMR). The code is built upon the AMReX library, which provides the underlying data structures and tools to manage and operate on them across massively parallel computing architectures. PeleLMeX algorithmic features are inherited from its predecessor PeleLM but key improvements allow representation of more complex physical processes. Together with its compressible flow counterpart PeleC, the thermo-chemistry library PelePhysics and the multi-physics library PeleMP, it forms the Pele suite of open-source reactive flow simulation codes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

FLC Nomination: Stephen R. Lee

STEM Mentorship Award: Given to an individual who may or may not be a direct employee of a government laboratory or facility in the Mid Continent Region, but has demonstrated exceptional character, mentorship, and creativity in the areas of science and math or by promoting the development of young people in grades K-12 or higher in technical career fields. Contributions must be unique and show measurable benefit to the laboratory, school system/students and must have occurred within the past three calendar years. Stephen R. Lee is the division leader of the Computer, Computational, and Statistical Sciences Division (CCS) at Los Alamos National Laboratory (LANL or the Laboratory). He holds a Bachelor of Science in Physics from New Mexico State University and a Master of Science in Physics from Kansas State University and began his 27-year career at the Laboratory in 1986. As division leader of CCS, Stephen is responsible for the management and oversight of CCS and all of its activities, as well as approximately 200 technical staff engaged in computer and computational, and statistical sciences. His experience and interests include computational algorithm development for largescale parallel computing (peta-scale and beyond), predictive simulations for nuclear weapons, simulation capabilities for non-nuclear weapons applications such as bioscience, homeland defense, nanotechnology, advanced computational platform research and development.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Computation Annual Report (2013)

Computation provides the intellectual electricity that helps make Lawrence Livermore National Laboratory (LLNL) a thriving and innovative research and development (R&D) institution. Our hardware, software, and discipline experts are integrated into almost every field of research at LLNL. Our in-house programs, software applications, and support initiatives help achieve mission-critical national-security objectives for the U.S. Departments of Energy, Homeland Security, and Defense, as well as other federal and state agencies. We deliver comprehensive support to a wide set of scientific disciplines that include physical sciences (materials modeling, fluid dynamics), biology (genomic sequencing), mathematics (scalable algorithms), and computer sciences (parallel processing, real-time control systems). This year, we have expanded our outreach with high performance computing (HPC) collaborations and made great strides in our capabilities related to mathematical computation, control systems, and computation infrastructure, many of them in concert with partners in industry and academia. The Computation workforce remains highly motivated and passionate about melding computational expertise with cutting-edge science and technology to enable breakthroughs. 2013 has once again proven that Computation provides the foundation and support that are essential for productivity at LLNL. Every scientific discipline and program leverages the tools and expertise provided by our staff. We remain at the forefront of HPC moving towards exascale and have developed the infrastructure and proficiency to make this an achievable goal. Our researchers repeatedly deliver outstanding research, attracting collaborations with the biggest names in academia and industry, while joining forces with other national laboratories to further push the bounds of what is scientifically possible. Computation’s mission is echoed by the President of the United States in his assertion that “our future depends on reaffirming America’s role as the world’s engine of scientific discovery and technological innovation.” Driven by this lofty goal, we employ our state-of-the-art computational capabilities to ensure LLNL’s position as a global science and technology leader.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

HPC-enabled computation of demand models at scale

The purpose of this project is to examine the energy impact of urban-scale traffic for the Los Angeles Basin by developing and implementing a scalable traffic assignment model. An energy optimization function will be posed and when integrated into the optimization code for travel assignment it can be mathematically proven to converge. The energy optimization function can then be compared to the typical travel time optimization that is traditionally used in traffic assignment models. The analysis will begin with static traffic assignment models with the routing for all origin and destinations computed in parallel on high performance computing facilities. Convergence of the numerical methods rely on the solution of convex programs (or extensions of these). This step will mostly consist of demonstrating the ability to parallelize the Frank Wolfe algorithm on various platforms.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2020

HPC4Mobilty w/ UCB

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2024

Progressive Hedging Decomposition for Solutions of Large-Scale Process Family Design Problems

In previous work, we have introduced a mathematical model for solving a discretized version of the process family design problem. This involves two sets of decision variables. One set selects which unit module designs are included in the process platform out of a candidate set of options; the other set determines which of these unit module designs are assigned to each variant. In this work, we exploit a parallelized Progressive Hedging (PH) algorithm to solve even larger scale design problems. PH is a well-known algorithm traditionally used to solve stochastic programming problems. While our problem is not a two-stage stochastic programming problem, the structure is similar, and it can be directly mapped to the PH approach, which we employ here to solve this deterministic optimization problem. We decompose our problem by process variant. We treat the platform unit module design variables as first-stage and the assignment of unit module designs to variants as second-stage, solving the problem using mpi-sppy. We demonstrate this approach on case studies of CC, water desalination, and refrigeration.

Stinchfield, Georgia↗

DOE OSTI2014

Performance of Replica-Exchange Wang-Landau Sampling for the 2D Ising Model: A Brief Survey

We report a brief performance study of the replica-exchange Wang-Landau algorithm, a recently proposed parallel realization of Wang-Landau sampling, using the 2D Ising model as a test case. The simulation time is found to scale inversely with the square root of the number of subwindows (and thus number of processors) used to span the global parameter space. We also investigate the time profiles for random walkers in dierent subwindows to complete iterations, which will aid the development of and adaptive load-balancing scheme.

Zhao, Yiwei↗

DOE OSTI2015

BASTet (Berkeley Analysis and Storage Toolkit)

BASTet is an advanced software library written in Python. BASTet serves as the analysis and storage library for the OpenMSI project. BASTet is an integrate framework for: i) storage of spectral imaging data, ii) storage of derived analysis data, iii) provenance of analyses, iv) integration and execution of analyses via complex workflows. BASTet implements the API for the HDF5 storage format used by OpenMSI. Analyses that are developed using BASTet benefit from direct integration with storage format, automatic tracking of provenance, and direct integration with command-line and workflow execution tools. BASTet also defines interfaces to enable developers to directly integrate their analysis with OpenMSI's web-based viewing infrastruture without having to know OpenMSI. BASTet also provides numerous helper classes and tools to assist with the conversion of data files, ease parallel implementation of analysis algorithms, ease interaction with web-based functions, description methods for data reduction. BASTet also includes detailed developer documentation, user tutorials, iPython notebooks, and other supporting documents.

Bowen, Benjamin↗

DOE OSTI2019

Multi-View, Deep Learning, and Contextual Analysis: Promising Approaches for sUAS Land Cover Classification

Small Unmanned Aircraft System (sUAS) image collection and preprocessing to produce orthoimages, point clouds, and digital surface models have made great leaps forward in the past years. These advances and the wide spectrum of existing and emerging sUAS applications mandate parallel improvements in the algorithms used for image classification that take into consideration the specific characteristics of sUAS imagery. This chapter presents several alternative approaches to improve classification accuracy using redundant information in overlapped sUAS imagery captured in a typical sUAS mission. These include Deep Convolution Neural Network (DCNN) classification, Fully Convolutional Neural (FCN) Network, and contextual relationships under an Object-Based Image Analysis (OBIA) framework. The chapter synthesizes the results of implementing the introduced classification approaches using a case study of high-resolution sUAS images captured in a wetland area in Central Florida.

Liu, Tao↗

DOE OSTI2013

Phase-space finite elements in a least-squares solution of the transport equation

The linear Boltzmann transport equation is solved using a least-squares finite element approximation in the space, angular and energy phase-space variables. The method is applied to both neutral particle transport and also to charged particle transport in the presence of an electric field, where the angular and energy derivative terms are handled with the energy/angular finite elements approximation, in a manner analogous to the way the spatial streaming term is handled. For multi-dimensional problems, a novel approach is used for the angular finite elements: mapping the surface of a unit sphere to a two-dimensional planar region and using a meshing tool to generate a mesh. In this manner, much of the spatial finite-elements machinery can be easily adapted to handle the angular variable. The energy variable and the angular variable for one-dimensional problems make use of edge/beam elements, also building upon the spatial finite elements capabilities. The methods described here can make use of either continuous or discontinuous finite elements in space, angle and/or energy, with the use of continuous finite elements resulting in a smaller problem size and the use of discontinuous finite elements resulting in more accurate solutions for certain types of problems. The work described in this paper makes use of continuous finite elements, so that the resulting linear system is symmetric positive definite and can be solved with a highly efficient parallel preconditioned conjugate gradients algorithm. The phase-space finite elements capability has been built into the Sceptre code and applied to several test problems, including a simple one-dimensional problem with an analytic solution available, a two-dimensional problem with an isolated source term, showing how the method essentially eliminates ray effects encountered with discrete ordinates, and a simple one-dimensional charged-particle transport problem in the presence of an electric field. (authors)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

Multi-cycle boiling water reactor fuel cycle optimization

In this work a new computer code, BWROPT (Boiling Water Reactor Optimization), is presented. BWROPT uses the Parallel Simulated Annealing (PSA) algorithm to solve the out-of-core optimization problem coupled with an in-core optimization that determines the optimum fuel loading pattern. However it uses a Haling power profile for the depletion instead of optimizing the operating strategy. The result of this optimization is the optimum new fuel inventory and the core loading pattern for the first cycle considered in the optimization. Several changes were made to the optimization algorithm with respect to other nuclear fuel cycle optimization codes that use PSA. Instead of using constant sampling probabilities for the solution perturbation types throughout the optimization as is usually done in PSA optimizations the sampling probabilities are varied to get a better solution and/or decrease runtime. The new fuel types available for use can be sorted into an array based on any number of parameters so that each parameter can be incremented or decremented, which allows for more precise fuel type selection compared to random sampling. Also, the results are sorted by the new fuel inventory of the first cycle for ease of comparing alternative solutions. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2019

Direct simulation Monte Carlo on petaflop supercomputers and beyond

The gold-standard definition of the Direct Simulation Monte Carlo (DSMC) method is given in the 1994 book by Bird [Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon Press, Oxford, UK, 1994)], which refined his pioneering earlier papers in which he first formulated the method. In the intervening 25 years, DSMC has become the method of choice for modeling rarefied gas dynamics in a variety of scenarios. The chief concern to applying DSMC to more dense or even continuum flows is its computational expense compared to continuum computational fluid dynamics methods. The dramatic (nearly billion-fold) increase in speed of the largest supercomputers over the last 30 years has thus been a key enabling factor in using DSMC to model a richer variety of flows, due to the method’s inherent parallelism. We have developed the open-source SPARTA DSMC code with the goal of running DSMC efficiently on the largest machines, both current and future. It is largely an implementation of Bird’s 1994 formulation. In this work, we describe algorithms used in SPARTA to enable DSMC to operate in parallel at the scale of many billions of particles or grid cells, or with billions of surface elements. We highlight a few examples of the kinds of fundamental physics questions and engineering applications that DSMC can address at these scales.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Accuracy of the explicit energy-conserving particle-in-cell method for under-resolved simulations of capacitively coupled plasma discharges

The traditional explicit electrostatic momentum-conserving particle-in-cell algorithm requires strict resolution of the electron Debye length to deliver numerical stability and accuracy. The explicit electrostatic energy-conserving particle-in-cell algorithm alleviates this constraint with minimal modification to the traditional algorithm, retaining its simplicity, ease of parallelization, and acceleration on modern supercomputing architectures. In this article, we apply the algorithm to model a one-dimensional radio frequency capacitively coupled plasma discharge relevant to industrial applications. The energy-conserving approach closely matches the results from the momentum-conserving algorithm and retains accuracy even for cell sizes up to 8 times the electron Debye length. For even larger cells, the algorithm loses accuracy due to poor resolution of steep gradients within the radio frequency sheath. Accuracy can be recovered by adopting a non-uniform grid, which resolves the sheath and allows for cell sizes up to 32 times the electron Debye length in the quasi-neutral bulk of the discharge. The effect is an up to 8 times reduction in the number of required simulation cells, an improvement that can compound in higher-dimensional simulations. We therefore consider the explicit energy-conserving algorithm as a promising approach to significantly reduce the computational cost of full-scale device simulations and a pathway to delivering kinetic simulation capabilities of use to industry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2017

The Pointing Self-calibration Algorithm for Aperture Synthesis Radio Telescopes

This paper is concerned with algorithms for calibration of direction-dependent effects (DDE) in aperture synthesis radio telescopes (ASRT). After correction of direction-independent effects (DIE) using self-calibration, imaging performance can be limited by the imprecise knowledge of the forward gain of the elements in the array. In general, the forward gain pattern is directionally dependent and varies with time due to a number of reasons. Some factors, such as rotation of the primary beam with Parallactic Angle for Azimuth–Elevation mount antennas are known a priori. Some, such as antenna pointing errors and structural deformation/projection effects for aperture-array elements cannot be measured a priori. Thus, in addition to algorithms to correct for DD effects known a priori, algorithms to solve for DD gains are required for high dynamic range imaging. Here, we discuss a mathematical framework for antenna-based DDE calibration algorithms and show that this framework leads to computationally efficient optimal algorithms that scale well in a parallel computing environment. As an example of an antenna-based DD calibration algorithm, we demonstrate the Pointing SelfCal (PSC) algorithm to solve for the antenna pointing errors. Our analysis show that the sensitivity of modern ASRT is sufficient to solve for antenna pointing errors and other DD effects. We also discuss the use of the PSC algorithm in real-time calibration systems and extensions for antenna Shape SelfCal algorithm for real-time tracking and corrections for pointing offsets and changes in antenna shape.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

GentenMPI: Distributed Memory Sparse Tensor Decomposition

GentenMPl is a toolkit of sparse canonical polyadic (CP) tensor decomposition algorithms that is designed to run effectively on distributed-memory high-performance computers. Its use of distributed-memory parallelism enables it to efficiently decompose tensors that are too large for a single compute node's memory. GentenMPl leverages Sandia's decades-long investment in the Trilinos solver framework for much of its parallel-computation capability. Trilinos contains numerical algorithms and linear algebra classes that have been optimized for parallel simulation of complex physical phenomena. This work applies these tools to the data science problem of sparse tensor decomposition. In this report, we describe the use of Trilinos in GentenMPl, extensions needed for sparse tensor decomposition, and implementations of the CP-ALS (CP via alternating least squares) and GCP-SGD (generalized CP via stochastic gradient descent) sparse tensor decomposition algorithms. We show that GentenMPl can decompose sparse tensors of extreme size, e.g., a 12.6-terabyte tensor on 8192 computer cores. We demonstrate that the Trilinos backbone provides good strong and weak scaling of the tensor decomposition algorithms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Parallel Programming Models and Systems for High Performance Computing. In: Emerging Research in Cloud Distributed Computing Systems

A parallel programming model is an abstraction of a parallel system that allows expression of both algorithms and shared data structures. To accommodate the diversity in parallel system architectures and user requirements, there are a variety of programming models including the models providing a shared memory view or a distributed memory view of the system. The programming models are implemented as libraries, language extensions, or compiler directives. This chapter provides a discussion on programming models and its implementations aimed at application developers, system software researchers, and hardware architects. The first part provides an overview of the programming models. The second part is an in-depth discussion on high-performance networking interface to implement the programming model. The last part of the chapter discusses implementation of a programming model with a case study. Each part of the chapter concludes with a discussion on current research trends and its impact on future architectures.

Venkata, Manjunath Gorentia↗