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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 631 records · Page 35
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Sanibel Symposium in the Petascale-Exascale Computational Era

The 56 th Sanibel Symposium was held February 14-19 2016 at the King and Prince Hotel, St. Simons Island, GA. It successfully brought quantum chemists and chemical and condensed matter physicists together in presentations, posters, and informal discussions bridging those two communities. The Symposium has had a significant role in preparing generations of quantum theorists. As computational potency and algorithmic sophistication have grown, the Symposium has evolved to emphasize more heavily computationally oriented method development in chemistry and materials physics, including nanoscience, complex molecular phenomena, and even bio-molecular methods and problems. Given this context, the 56 th Sanibel meeting systematically and deliberately had sessions focused on exascale computation. A selection of outstanding theoretical problems that need serious attention was included. Five invited sessions, two contributed sessions (hot topics), and a poster session were organized with the exascale theme. This was a historic milestone in the evolution of the Symposia. Just as years ago linear algebra, perturbation theory, density matrices, and band-structure methods dominated early Sanibel Symposia, the exascale sessions of the 56 th meeting contributed a transformative influence to add structure and strength to the computational physical science community in an unprecedented way. A copy of the full program of the 56 th Symposium is attached. The exascale sessions were Linear Scaling, Non-Adabatic Dynamics, Interpretive Theory and Models, Computation, Software, and Algorithms, and Quantum Monte Carlo. The Symposium Proceedings will be published in Molecular Physics (2017). Note that the Sanibel proceedings from 2015 and 2014 were published as Molecular Physics vol. 114, issue 3-4 (2016) and vol. 113, issue 3-4 (2015) respectively.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Symmetry reduction of tensor networks in many-body theory: I. Automated symbolic evaluation of SU(2) algebra

Abstract The ongoing progress in (nuclear) many-body theory is accompanied by an ever-rising increase in complexity of the underlying formalisms used to solve the stationary Schrödinger equation. The associated working equations at play in state-of-the-art ab initio nuclear many-body methods can be analytically reduced with respect to angular-momentum, i.e. SU (2), quantum numbers whenever they are effectively employed in a symmetry-restricted context. The corresponding procedure constitutes a tedious and error-prone but yet an integral part of the implementation of those many-body frameworks. Indeed, this symmetry reduction is a key step to advance modern simulations to higher accuracy since the use of symmetry-adapted tensors can decrease the computational complexity by orders of magnitude. While attempts have been made in the past to automate the (anti-) commutation rules linked to Fermionic and Bosonic algebras at play in the derivation of the working equations, there is no systematic account to achieve the same goal for their symmetry reduction. In this work, the first version of an automated tool performing graph-theory-based angular-momentum reduction is presented. Taking the symmetry-unrestricted expressions of a generic tensor network as an input, the code provides their angular-momentum-reduced form in an error-safe way in a matter of seconds. Several state-of-the-art many-body methods serve as examples to demonstrate the generality of the approach and to highlight the potential impact on the many-body community.

Tichai, A.↗
DOE OSTI2014

Space Charge Simulation in COSY using The Fast Multipole Method

A method is implemented in COSY Infinity that allows the computation of space charge effects of arbitrary and large distributions of particles in an efficient and accurate way based on a variant of the Fast Multipole Method (FMM). It relies on an automatic multigrid-based decomposition of charges in near and far regions and the use of high-order differential algebra methods to obtain decompositions of far fields that lead to an error that scales with a high power of the order. Given an ensemble of N particles, the method allows the computation of the self-fields of all particles on each other with a computational expense that scales as O(N). Further- more, the method allows the computation of all high-order multipoles of the space charge fields that are necessary for the computation of high-order transfer maps and all resulting aberrations. Space charge effects are crucial in modeling the latter stages of the six-dimensional (6D) cooling channel for the Muon Collider. Results of simulating the 6D cooling channel for the Muon Collider using the FMM method and other tools and improvements implemented for ionization cooling lattices are presented.

Loseth, B.↗
DOE OSTI2016

A fast band–Krylov eigensolver for macromolecular functional motion simulation on multicore architectures and graphics processors

We introduce a new iterative Krylov subspace-based eigensolver for the simulation of macromolecular motions on desktop multithreaded platforms equipped with multicore processors and, possibly, a graphics accelerator (GPU). The method consists of two stages, with the original problem first reduced into a simpler band-structured form by means of a high-performance compute-intensive procedure. This is followed by a memory-intensive but low-cost Krylov iteration, which is off-loaded to be computed on the GPU by means of an efficient data-parallel kernel. The experimental results reveal the performance of the new eigensolver. Concretely, when applied to the simulation of macromolecules with a few thousands degrees of freedom and the number of eigenpairs to be computed is small to moderate, the new solver outperforms other methods implemented as part of high-performance numerical linear algebra packages for multithreaded architectures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Planetary normal mode computation: Parallel algorithms, performance and reproducibility

This report is an extension of work entitled “Computing planetary interior normal modes with a highly parallel polynomial filtering eigensolver.” by Shi et al., [1] originally presented at the SC18 conference. A highly parallel polynomial filtered eigensolver was developed and exploited to calculate the planetary normal modes. The proposed method is ideally suited for computing interior eigenpairs for large-scale eigenvalue problems as it greatly enhances memory and computational efficiency. In this article, the second-order finite element method is used to further improve the accuracy as only the first-order finite element method was deployed in the previous work. The parallel algorithm, its parallel performance up to 20k processors, and the great computational accuracy are illustrated. The reproducibility of the previous work was successfully performed on the Student Cluster Competition at the SC19 conference by several participant teams using a completely different Mars-model dataset on different clusters. Both weak and strong scaling performances of the reproducibility by the participant teams were impressive and encouraging. The analysis and reflection of their results are demonstrated and future direction is discussed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Randomized Algorithms for Symmetric Nonnegative Matrix Factorization

Symmetric Nonnegative Matrix Factorization (SymNMF) is a technique in data analysis and machine learning that approximates a matrix with a product of a nonnegative, low-rank matrix and it transpose. To design faster and more scalable algorithms for SymNMF we develop two randomized algorithms for its computation. The first method uses randomized matrix sketching to compute an initial low-rank approximation to the input matrix and proceeds to uses this as a low-rank input to rapidly compute a SymNMF. The second methods uses randomized leverage score sampling to approximately solve constrained least squares problems. Many successful methods for SymNMF rely on (approximately) solving sequences of constrained least squares problems. Here, we prove theoretically that leverage score sampling can approximately solve constrained least squares problems to e-accuracy. Finally we demonstrate both methods work in practice by applying them to graph clustering tasks on large real world data sets. These experiments show that our methods approximately maintain solution quality and achieve significant speed ups for both large dense and large sparse problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A Linear-Complexity Tensor Butterfly Algorithm for Compressing High-Dimensional Oscillatory Integral Operators

This paper presents a multilevel tensor compression algorithm called tensor butterfly algorithm for efficiently representing large-scale and high-dimensional oscillatory integral operators, including Green's functions for wave equations and integral transforms such as Radon transforms and Fourier transforms. The proposed algorithm leverages a tensor extension of the so-called complementary low-rank property of existing matrix butterfly algorithms. The algorithm partitions the discretized integral operator tensor into subtensors of multiple levels and factorizes each subtensor at the middle level as a Tucker-type interpolative decomposition, whose factor matrices are formed in a multilevel fashion. For a d-dimensional (d > 1) integral operator discretized into a 2d-mode tensor with n2d entries, the overall CPU time and memory requirement scale as O(nd), in stark contrast to the O(nd log n) complexity of existing matrix algorithms such as matrix butterfly algorithms and fast Fourier transforms (FFTs), where n is the number of points per direction. When comparing with other tensor algorithms such as quantized tensor train (QTT), the proposed algorithm also shows superior CPU and memory performance for tensor contraction. Remarkably, the tensor butterfly algorithm can efficiently model high-frequency Green's function interactions between two unit cubes, each spanning 512 wavelengths per direction, which represents problems of scale over 512× larger than that existing butterfly algorithms can handle, with the same amount of computation resources. On the other hand, for a problem representing 64 wavelengths per direction, which is the largest size existing algebraic matrix algorithms can handle, our tensor butterfly algorithm exhibits 200x speedups and 30× memory reduction compared with existing ones. Moreover, the tensor butterfly algorithm also permits O(nd)-complexity FFTs and Radon transforms up to d = 6 dimensions.

Kielstra, P Michael↗
DOE OSTI2023

High-Performance Electron Sources: Numerical Methods and Beam Dynamics at the Precision Frontier

Electron sources have a wide range of applications and there are many stakeholders that express continuing need for improvements and performance enhancements. Whether we consider ultra-cold, high-brightness, high-charge or high-average current source needs, there are some common themes from the point of view of the beam dynamics involved. These are the following ones: ability to model accurately the emission processes, including the presence of often complicated cathode and other boundary surfaces with a wide range of spatial scales; ability to deal accurately and efficiently with a large number of particles interacting pair-wise, including the stochastic part of these interactions with a wide range of spatial scales; and ability to propagate the particle distributions in time, including collisions with a wide range of temporal scales. These tasks require high precision and accuracy since the goal is usually generation, transport and preservation of very high-quality beams. This grant addressed one of the rem

43 PARTICLE ACCELERATORS↗
DOE OSTI2015

Design Choices for Thermofluid Flow Components and Systems that are Exported as Functional Mockup Units

This paper discusses design decisions for exporting Modelica thermofluid flow components as Functional Mockup Units. The purpose is to provide guidelines that will allow building energy simulation programs and HVAC equipment manufacturers to effectively use FMUs for modeling of HVAC components and systems. We provide an analysis for direct input-output dependencies of such components and discuss how these dependencies can lead to algebraic loops that are formed when connecting thermofluid flow components. Based on this analysis, we provide recommendations that increase the computing efficiency of such components and systems that are formed by connecting multiple components. We explain what code optimizations are lost when providing thermofluid flow components as FMUs rather than Modelica code. We present an implementation of a package for FMU export of such components, explain the rationale for selecting the connector variables of the FMUs and finally provide computing benchmarks for different design choices. It turns out that selecting temperature rather than specific enthalpy as input and output signals does not lead to a measurable increase in computing time, but selecting nine small FMUs rather than a large FMU increases computing time by 70%.

Wetter, Michael↗
DOE OSTI2023

Semantic embedding for quantum algorithms

The study of classical algorithms is supported by an immense understructure, founded in logic, type, and category theory, that allows an algorithmist to reason about the sequential manipulation of data irrespective of a computation’s realizing dynamics. As quantum computing matures, a similar need has developed for an assurance of the correctness of high-level quantum algorithmic reasoning. Parallel to this need, many quantum algorithms have been unified and improved using quantum signal processing (QSP) and quantum singular value transformation (QSVT), which characterize the ability, by alternating circuit ansätze, to transform the singular values of sub-blocks of unitary matrices by polynomial functions. However, while the algebraic manipulation of polynomials is simple (e.g., compositions and products), the QSP/QSVT circuits realizing analogous manipulations of their embedded polynomials are non-obvious. This work constructs and characterizes the runtime and expressivity of QSP/QSVT protocols where circuit manipulation maps naturally to the algebraic manipulation of functional transforms (termed semantic embedding). In this way, QSP/QSVT can be treated and combined modularly, purely in terms of the functional transforms they embed, with key guarantees on the computability and modularity of the realizing circuits. We also identify existing quantum algorithms whose use of semantic embedding is implicit, spanning from distributed search to proofs of soundness in quantum cryptography. The methods used, based in category theory, establish a theory of semantically embeddable quantum algorithms, and provide a new role for QSP/QSVT in reducing sophisticated algorithmic problems to simpler algebraic ones.

Physics↗
DOE OSTI2018

Color Confinement, Hadron Dynamics, and Hadron Spectroscopy from Light-Front Holography and Superconformal Algebra

The QCD light-front Hamiltonian equation H L F Ψ = M 2 Ψ derived from quantization at fixed LF time τ = t + z / c provides a causal, frame-independent method for computing hadron spectroscopy as well as dynamical observables such as structure functions, transverse momentum distributions, and distribution amplitudes. The QCD Lagrangian with zero quark mass has no explicit mass scale. de Alfaro, Fubini, and Furlan (dAFF) have made an important observation that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator. If one applies the dAFF procedure to the QCD light-front Hamiltonian, it leads to a color-confining potential κ 4 ζ 2 for mesons, where ζ 2 is the LF radial variable conjugate to the q q ¯ invariant mass squared. The same result, including spin terms, is obtained using light-front holography, the duality between light-front dynamics and A d S 5 , if one modifies the A d S 5 action by the dilaton e κ 2 z 2 in the fifth dimension z . When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions provide a unified Regge spectroscopy of meson, baryon, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons and baryons and a universal Regge slope. The pion q q ¯ eigenstate has zero mass at m q = 0 . The superconformal relations also can be extended to heavy-light quark mesons and baryons. This approach also leads to insights into the physics underlying hadronization at the amplitude level. I will also discuss the remarkable features of the Poincaré invariant, causal vacuum defined by light-front quantization and its impact on the interpretation of the cosmological constant. AdS/QCD also predicts the analytic form of the nonperturbative running coupling α s ( Q 2 ) ∝ e - Q 2 / 4 κ 2 . The mass scale κ underlying hadron masses can be connected to the parameter Λ M S ¯ in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling α s ( Q 2 ) defined at all momenta. One obtains empirically viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. Finally, I address the interesting question of whether the momentum sum rule is valid for nuclear structure functions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Light-front puzzles

Abstract Light-front formulations of quantum field theories have many advantages for computing electroweak matrix elements of strongly interacting systems and other quantities that are used to study hadronic structure. The theory can be formulated in Hamiltonian form so non-perturbative calculations of the strongly interacting initial and final states are in principle reduced to linear algebra. These states are needed for calculating parton distribution functions and other types of distribution amplitudes that are used to understand the structure of hadrons. Light-front boosts are kinematic transformations so the strongly interacting states can be computed in any frame. This is useful for computing current matrix elements involving electroweak probes where the initial and final hadronic states are in different frames related by the momentum transferred by the probe. Finally in many calculations the vacuum is trivial so the calculations can be formulated in Fock space. The advantages of light front-field theory would not be interesting if the light-front formulation was not equivalent to the covariant or canonical formulations of quantum field theory. Many of the distinguishing properties of light-front quantum field theory are difficult to reconcile with canonical or covariant formulations of quantum field theory. This paper discusses the resolution of some of the apparent inconsistencies in canonical, covariant and light-front formulations of quantum field theory. The puzzles that will be discussed are (1) the problem of inequivalent representations (2) the problem of the trivial vacuum (3) the problem of ill-posed initial value problems (4) the problem of rotational covariance (5) the problem of zero modes and (6) the problem of spontaneously broken symmetries.

Physics↗
DOE OSTI2018

Discrete Hahn polynomials for numerical solution of two-dimensional variable-order fractional Rayleigh–Stokes problem

The main aim of this paper is to find the numerical solutions of 2D Rayleigh–Stokes problem with the variable-order fractional derivatives in the Riemann–Liouville sense. The presented method is based on collocation procedure in combination with the new operational matrix of the variable-order fractional derivatives, in the Caputo sense, for the discrete Hahn polynomials. The main advantage of the proposed method is obtaining a global approximation for spatial and temporal discretizations, and it reduced the problem to an algebraic system, which is easier to solve. Also, the profit of approximating a continuous function by Hahn polynomials is that for computing the coefficients of the expansion, we only have to compute a summation and the calculation of coefficients is exact. The error bound for the approximate solution is estimated. Finally, we evaluate results of the presented method with other numerical methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Spectral partitioning with blends of eigenvectors

We report many common methods for data analysis rely on linear algebra. We provide new results connecting data analysis error to numerical accuracy in the context of spectral graph partitioning. We provide pointwise convergence guarantees so that spectral blends (linear combinations of eigenvectors) can be employed to solve data analysis problems with confidence in their accuracy. We apply this theory to an accessible model problem, the ring of cliques, by deriving the relevant eigenpairs and finding necessary and sufficient solver tolerances. Analysis of the ring of cliques provides an upper bound on eigensolver tolerances for graph partitioning problems. These results bridge the gap between linear algebra based data analysis methods and the convergence theory of iterative approximation methods. These results explain how the combinatorial structure of a problem can be recovered much faster than numerically accurate solutions to the associated linear algebra problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Quantum Time-Space Tradeoffs for Matrix Problems

We consider the time and space required for quantum computers to solve a wide variety of problems involving matrices, many of which have only been analyzed classically in prior work. Our main results show that for a range of linear algebra problems—including matrix-vector product, matrix inversion, matrix multiplication and powering—existing classical time-space tradeoffs, several of which are tight for every space bound, also apply to quantum algorithms with at most a constant factor loss. For example, for almost all fixed matrices 𝐴, including the discrete Fourier transform matrix, we prove that quantum circuits with at most 𝑇 input queries and 𝑆 qubits of memory require 𝑇 = Ω⁢(𝑛 2 /𝑆) to compute matrix-vector product 𝐴⁢𝑥 for 𝑥 ∈{0,1 𝑛 . We similarly prove that matrix multiplication for 𝑛 ×𝑛 binary matrices requires 𝑇 = Ω⁢(𝑛 3 /$\sqrt{𝑆}$). Because many of our lower bounds are matched by deterministic algorithms with the same time and space complexity, our results show that quantum computers cannot provide any asymptotic advantage for these problems with any space bound. We obtain matching lower bounds for the stronger notion of quantum cumulative memory complexity—the sum of the space per layer of a circuit. We also consider Boolean (i.e., AND-OR) matrix multiplication and matrix-vector products, improving the previous quantum time-space tradeoff lower bounds for 𝑛 × 𝑛 Boolean matrix multiplication to 𝑇 = Ω⁢(𝑛 2.5 /𝑆 1/4 ) from 𝑇 = Ω⁢(𝑛 2.5 /𝑆 1/2 ). Our improved lower bound for Boolean matrix multiplication is based on a new coloring argument that extracts more from the strong direct product theorem that was the basis for prior work. To obtain our tight lower bounds for linear algebra problems, we require much stronger bounds than strong direct product theorems. We obtain these bounds by adding a new bucketing method to the quantum recording-query technique of Zhandry that lets us apply classical arguments to upper bound the success probability of quantum circuits.

lower bounds↗