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At least 1,567 records · Page 87

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DOE OSTI2025

Parallel-in-time quantum simulation via Page and Wootters quantum time

In the past few decades, researchers have created a veritable zoo of quantum algorithms by drawing inspiration from classical computing, information theory, and even from physical phenomena. Here, we present quantum algorithms for parallel-in-time simulations that are inspired by the Page and Wootters formalism. In this framework, and thus in our algorithms, the classical time variable of quantum mechanics is promoted to the quantum realm by introducing a Hilbert space of “clock” qubits that are then entangled with the “system” qubits. We show that our algorithms can compute temporal properties over 𝑁 different times of many-body systems by only using log⁡(𝑁) clock qubits. As such, we achieve an exponential trade-off between time and spatial complexities. In addition, we rigorously prove that the entanglement created between the system qubits and the clock qubits has operational meaning, as it encodes valuable information about the system’s dynamics. We also provide a circuit depth estimation of all the protocols, showing a running time advantage in computation times over traditional sequential-in-time algorithms. In particular, for the case when the dynamics are determined by the Aubry-Andre model, we present a hybrid method for which our algorithms have a depth that only scales as 𝒪⁡(log⁡(𝑁)⁢𝑛). As a by-product, we can relate the previous schemes to the problem of equilibration of an isolated quantum system, thus indicating that our framework enables a new dimension for studying dynamical properties of many-body systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1984

Structural dynamic analysis on a parallel computer - The finite element machine

Recent and prospective advances in parallel multiple introduction multiple data (MIMD) computers offer significant improvements in the range of structural problems that can be solved, as well as the speed of solutions. These improvements have their basis in the effective selection and implementation of algorithms exploiting parallel computation. Attention is presently given to the solution of the transient response calculations of an experimental MIMD computer designated the 'Finite Element Machine', including its algorithm and its results for representative one- and two-dimensional dynamic response test problems. A factor of 6.5 is noted for the computational speed improvement.

Storaasli, O.↗

DOE OSTI2020

Algorithms in Diffraction Profile Analysis

This chapter introduces several approaches to crystallographic structure refinement from diffraction profile data including the Rietveld method, global optimization methods, and Bayesian modeling. First, the Rietveld method and related nonlinear least squares approaches to analyzing diffraction profiles are briefly discussed. We then review the most common algorithms within global optimization as alternative methods of structure solution: grid search, simulated annealing, and genetic algorithms. As the Rietveld method is the standard tool for analyzing diffraction profile data, we catalogue its challenges and limitations. A Bayesian approach to diffraction profile analysis is presented as an alternative, along with several sampling algorithms including Gibbs sampling, variants of Metropolis sampling, Hamiltonian Monte Carlo, and approximate Bayesian computing. These sampling algorithms are applied to the fitting of a neutron diffraction profile from a National Institute of Standards and Technology silicon standard reference material, and their results are compared.

Singh, Susheela↗

NASA NTRS1987

Large aperture high accuracy satellite laser tracking

A satellite laser ranging station has been established in order to range both low and high earth-orbiting satellites with a few-mm accuracy; this entails precision pointing of a 15-ton, azimuth-elevation-mounted coude telescope. Because tracking is performed under open loop computer control with no feedback from laser returns, the initial acquisition data and the algorithms for orbit computation must be accurate enough to maintain the satellite within the narrow laser beam width. The system is currently being used to track the LAGEOS and STARLETTE satellites.

Mcgarry, Jan L. F.↗

NASA NTRS1992

Content addressable memory project

A parameterized version of the tree processor was designed and tested (by simulation). The leaf processor design is 90 percent complete. We expect to complete and test a combination of tree and leaf cell designs in the next period. Work is proceeding on algorithms for the computer aided manufacturing (CAM), and once the design is complete we will begin simulating algorithms for large problems. The following topics are covered: (1) the practical implementation of content addressable memory; (2) design of a LEAF cell for the Rutgers CAM architecture; (3) a circuit design tool user's manual; and (4) design and analysis of efficient hierarchical interconnection networks.

Hall, J. Storrs↗

NASA NTRS1992

Parallel implementation of an algorithm for Delaunay triangulation

This work concerns the theory and practice of implementing Tanemura's algorithm for 3D Delaunay triangulation on Intel's Gamma prototype, a 128 processor MIMD computer. Tanemura's algorithm does not vectorize to any significant degree and requires indirect addressing. Efficient implementation on a conventional, vector processing, supercomputer is problematic. Efficient implementation on a parallel architecture is possible, however. In this work, speeds in excess of 8 times a single processor Cray Y-mp are realized on 128 processors of the Intel Gamma prototype.

Merriam, Marshall L.↗

NASA NTRS2005

At-Least Version of the Generalized Minimum Spanning Tree Problem: Optimization Through Ant Colony System and Genetic Algorithms

The At-Least version of the Generalized Minimum Spanning Tree Problem (L-GMST) is a problem in which the optimal solution connects all defined clusters of nodes in a given network at a minimum cost. The L-GMST is NPHard; therefore, metaheuristic algorithms have been used to find reasonable solutions to the problem as opposed to computationally feasible exact algorithms, which many believe do not exist for such a problem. One such metaheuristic uses a swarm-intelligent Ant Colony System (ACS) algorithm, in which agents converge on a solution through the weighing of local heuristics, such as the shortest available path and the number of agents that recently used a given path. However, in a network using a solution derived from the ACS algorithm, some nodes may move around to different clusters and cause small changes in the network makeup. Rerunning the algorithm from the start would be somewhat inefficient due to the significance of the changes, so a genetic algorithm based on the top few solutions found in the ACS algorithm is proposed to quickly and efficiently adapt the network to these small changes.

Janich, Karl W.↗

DOE OSTI2020

Practical quantum computation of chemical and nuclear energy levels using quantum imaginary time evolution and Lanczos algorithms

Various methods have been developed for the quantum computation of the ground and excited states of physical and chemical systems, but many of them require either large numbers of ancilla qubits or high-dimensional optimization in the presence of noise. The quantum imaginary-time evolution (QITE) and quantum Lanczos (QLanczos) methods proposed in Motta et al. (2020) eschew the aforementioned issues. In this study, we demonstrate the practical application of these algorithms to challenging quantum computations of relevance for chemistry and nuclear physics, using the deuteron-binding energy and molecular hydrogen binding and excited state energies as examples. With the correct choice of initial and final states, we show that the number of timesteps in QITE and QLanczos can be reduced significantly, which commensurately simplifies the required quantum circuit and improves compatibility with NISQ devices. We have performed these calculations on cloud-accessible IBM Q quantum computers. With the application of readout-error mitigation and Richardson error extrapolation, we have obtained ground and excited state energies that agree well with exact results obtained from diagonalization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2017

Linear Subpixel Learning Algorithm for Land Cover Classification from WELD using High Performance Computing

In this work, we use a Fully Constrained Least Squares Subpixel Learning Algorithm to unmix global WELD (Web Enabled Landsat Data) to obtain fractions or abundances of substrate (S), vegetation (V) and dark objects (D) classes. Because of the sheer nature of data and compute needs, we leveraged the NASA Earth Exchange (NEX) high performance computing architecture to optimize and scale our algorithm for large-scale processing. Subsequently, the S-V-D abundance maps were characterized into 4 classes namely, forest, farmland, water and urban areas (with NPP-VIIRS-national polar orbiting partnership visible infrared imaging radiometer suite nighttime lights data) over California, USA using Random Forest classifier. Validation of these land cover maps with NLCD (National Land Cover Database) 2011 products and NAFD (North American Forest Dynamics) static forest cover maps showed that an overall classification accuracy of over 91 percent was achieved, which is a 6 percent improvement in unmixing based classification relative to per-pixel-based classification. As such, abundance maps continue to offer an useful alternative to high-spatial resolution data derived classification maps for forest inventory analysis, multi-class mapping for eco-climatic models and applications, fast multi-temporal trend analysis and for societal and policy-relevant applications needed at the watershed scale.

Subpixel↗

NASA NTRS1978

A fast D.F.T. algorithm using complex integer transforms

Winograd (1976) has developed a new class of algorithms which depend heavily on the computation of a cyclic convolution for computing the conventional DFT (discrete Fourier transform); this new algorithm, for a few hundred transform points, requires substantially fewer multiplications than the conventional FFT algorithm. Reed and Truong have defined a special class of finite Fourier-like transforms over GF(q squared), where q = 2 to the p power minus 1 is a Mersenne prime for p = 2, 3, 5, 7, 13, 17, 19, 31, 61. In the present paper it is shown that Winograd's algorithm can be combined with the aforementioned Fourier-like transform to yield a new algorithm for computing the DFT. A fast method for accurately computing the DFT of a sequence of complex numbers of very long transform-lengths is thus obtained.

Reed, I. S.↗

NASA NTRS1990

Computational enhancement of an unsymmetric block Lanczos algorithm

An unsymmetric block Lanczos algorithm has been employed for the dynamic analysis of a large system which has arbitrary damping and/or repeated (or closely spaced) eigenvalues. In the algorithm development, the right and left Lanczos vectors are all theoretically biorthogonal to each other. However, these vectors may lose the biorthogonality owing to cancellation and roundoff errors. For the unsymmetric case there can be a breakdown, even without numerical errors. This paper describes computational techniques which have led to a robust unsymmetric block Lanczos algorithm.

Kim, Hyoung M.↗

DOE OSTI2023

ExTreeM: Scalable Augmented Merge Tree Computation via Extremum Graphs

Over the last decade merge trees have been proven to support a plethora of visualization and analysis tasks since they effectively abstract complex datasets. Here, this paper describes the ExTreeM-Algorithm: A scalable algorithm for the computation of merge trees via extremum graphs. The core idea of ExTreeM is to first derive the extremum graph G of an input scalar field f defined on a cell complex K, and subsequently compute the unaugmented merge tree of f on G instead of K; which are equivalent. Any merge tree algorithm can be carried out significantly faster on G, since K in general contains substantially more cells than G. To further speed up computation, ExTreeM includes a tailored procedure to derive merge trees of extremum graphs. The computation of the fully augmented merge tree, i.e., a merge tree domain segmentation of K, can then be performed in an optional post-processing step. All steps of ExTreeM consist of procedures with high parallel efficiency, and we provide a formal proof of its correctness. Our experiments, performed on publicly available datasets, report a speedup of up to one order of magnitude over the state-of-the-art algorithms included in the TTK and VTK-m software libraries, while also requiring significantly less memory and exhibiting excellent scaling behavior.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

An efficient reconstruction algorithm for diffusion on triangular grids using the nodal discontinuous Galerkin method

High-energy-density (HED) hydrodynamics studies such as those relevant to inertial confinement fusion and astrophysics require highly disparate densities, temperatures, viscosities, and other diffusion parameters over relatively short spatial scales. This presents a challenge for high-order accurate methods to effectively resolve the hydrodynamics at these scales, particularly in the presence of highly disparate diffusion. A significant volume of engineering and physics applications use an unstructured discontinuous Galerkin (DG) method developed based on the finite element mesh generation and algorithmic framework. This work discusses the application of an affine reconstructed nodal DG method for unstructured grids of triangles. Solving the diffusion terms in the DG method is non-trivial due to the solution representations being piecewise continuous. Hence, the diffusive flux is not defined on the interface of elements. The proposed numerical approach reconstructs a smooth solution in a parallelogram that is enclosed by the quadrilateral formed by two adjacent triangle elements. The interface between these two triangles is the diagonal of the enclosed parallelogram. Similar to triangles, the mapping of parallelograms from a physical domain to a reference domain is an affine mapping, which is necessary for an accurate and efficient implementation of the numerical algorithm. Thus, all computations can still be performed on the reference domain, which promotes efficiency in computation and storage. This reconstruction does not make assumptions on choice of polynomial basis. Reconstructed DG algorithms have previously been developed for modal implementations of the convection–diffusion equations. However, to the best of the authors’ knowledge, this is the first practical guideline that has been proposed for applying the reconstructed algorithm on a nodal discontinuous Galerkin method with a focus on accuracy and efficiency. As a result, the algorithm is demonstrated on a number of benchmark cases as well as a challenging substantive problem in HED hydrodynamics with highly disparate diffusion parameters.

Computational efficiency↗

DOE OSTI2026

Scalable quantum computational science: A perspective from block-encodings and polynomial transformations

Significant developments made in quantum hardware and error correction recently have been driving quantum computing toward practical utility. However, gaps remain between abstract quantum algorithmic development and practical applications in computational sciences. In this perspective article, we propose several properties that scalable quantum computational science methods should possess. We further discuss how block-encodings and polynomial transformations can potentially serve as a unified framework with the desired properties. Recent advancements on these topics are presented, including the construction and assembly of block-encodings, and various generalizations of quantum signal processing (QSP) algorithms to perform polynomial transformations. The scalability of QSP methods on parallel and distributed quantum architectures is also highlighted. Promising applications in simulation and observable estimation in chemistry, physics, and optimization problems are presented. We hope this perspective serves as a gentle introduction to state-of-the-art quantum algorithms for the computational science community and inspires future development of scalable quantum computational science methodologies that bridge theory and practice.

Bayesian inference↗

DOE OSTI2024

Performance Analysis of an Optimization Algorithm for Metamaterial Design on the Integrated High-Performance Computing and Quantum Systems

Optimizing metamaterials with complex geometries is a big challenge. Although an active learning algorithm, combining machine learning (ML), quantum computing, and optical simulation, has emerged as an efficient optimization tool, it still faces difficulties in optimizing complex structures that have potentially high performance. In this work, we comprehensively analyze the performance of an optimization algorithm for metamaterial design on the integrated HPC and quantum systems. We demonstrate significant time advantages through message-passing interface (MPI) parallelization on the high-performance computing (HPC) system showing approximately 54% faster ML tasks and 67 times faster optical simulation against serial workloads. Furthermore, we analyze the performance of a quantum algorithm designed for optimization, which runs with various quantum simulators on a local computer or HPC-quantum system. Results showcase ~24 times speedup when executing the optimization algorithm on the HPC-quantum hybrid system. This study paves a way to optimize complex metamaterials using the integrated HPC-quantum system.

Kim, Seongmin↗

DOE OSTI2023

Optimal sensor placement for reconstructing wind pressure field around buildings using compressed sensing

Deciding how to optimally deploy sensors in a large, complex, and spatially extended structure is critical to ensure that the surface pressure field is accurately captured for subsequent analysis and design. In some cases, reconstruction of missing data is required in downstream tasks such as the development of digital twins. Here, this paper presents a data-driven sparse sensor selection algorithm, aiming to provide the most information contents for reconstructing aerodynamic characteristics of wind pressures over tall building structures parsimoniously. The algorithm first fits a set of basis functions to the training data, then applies a computationally efficient QR algorithm that ranks existing pressure sensors in order of importance based on the state reconstruction to this tailored basis. The findings of this study show that the proposed algorithm successfully re- constructs the aerodynamic characteristics of tall buildings from sparse measurement locations, generating stable and optimal solutions across a range of conditions. As a result, this study serves as a promising first step toward leveraging the success of data-driven and machine learning algorithms to supplement traditional genetic algorithms currently used in wind engineering.

42 ENGINEERING↗

DOE OSTI2022

Machine learning on FPGA for event selection

Real-time data processing is a frontier field in experimental particle physics. The application of FPGAs at the trigger level is used by many current and planned experiments (CMS, LHCb, Belle2, PANDA). Usually they use conventional processing algorithms. LHCb has implemented Machine Learning (ML) elements for real-time data processing with a triggered readout system that runs most of the ML algorithms on a computer farm. The work described in this article aims to test the ML-FPGA algorithms for streaming data acquisition. Herein, there are many experiments working in this area and they have a lot in common, but there are many specific solutions for detector and accelerator parameters that are worth exploring further. This report describes the purpose of the work and progress in evaluating the ML-FPGA application.

47 OTHER INSTRUMENTATION↗

DOE OSTI2020

Trabecula: A Random Generator of Computational Phantoms for Bone Marrow Dosimetry

This study was motivated by the efforts on evaluation of radiation risk for leukemia incidence in the Techa River Cohort, where the main bone marrow dose contributors were 89,90Sr (bone-seeking beta emitters). Energy deposition in bone marrow targets was evaluated by simulating radiation particle transport using computational phantoms. The present paper describes the computer program “Trabecula” implementing an algorithm for parametric generation of computational phantoms, which serve as the basis for calculating bone marrow doses. “Trabecula” is a user-friendly tool that automatically converts analytical models into voxelized representations that are directly compatible as input to MCNP.

Shishkina, Elena A.↗