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At least 1,441 records · Page 80
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Steepest-descent algorithm for simulating plasma-wave caustics via metaplectic geometrical optics

The design and optimization of radiofrequency-wave systems for fusion applications is often performed using ray-tracing codes, which rely on the geometrical-optics (GO) approximation. However, GO fails at wave cutoffs and caustics. To accurately model the wave behavior in these regions, more advanced and computationally expensive “full-wave” simulations are typically used, but this is not strictly necessary. A new generalized formulation called metaplectic geometrical optics (MGO) has been proposed that reinstates GO near caustics. The MGO framework yields an integral representation of the wavefield that must be evaluated numerically in general. We present an algorithm for computing these integrals using Gauss-Freud quadrature along the steepest-descent contours. Benchmarking is performed on the standard Airy problem, for which the exact solution is known analytically. Furthermore, the numerical MGO solution provided by the new algorithm agrees remarkably well with the exact solution and significantly improves on previously derived analytical approximations of the MGO integral.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Modeling electrokinetic flows with the discrete ion stochastic continuum overdamped solvent algorithm

In this article we develop an algorithm for the efficient simulation of electrolytes in the presence of physical boundaries. In previous work the discrete ion stochastic continuum overdamped solvent (DISCOS) algorithm was derived for triply periodic domains, and was validated through ion-ion pair correlation functions and Debye-Hückel-Onsager theory for conductivity, including the Wien effect for strong electric fields. In extending this approach to include an accurate treatment of physical boundaries we must address several important issues. First, the modifications to the spreading and interpolation operators necessary to incorporate interactions of the ions with the boundary are described. Next we discuss the modifications to the electrostatic solver to handle the influence of charges near either a fixed potential or dielectric boundary. An additional short-ranged potential is also introduced to represent interaction of the ions with a solid wall. Finally, the dry diffusion term is modified to account for the reduced mobility of ions near a boundary, which introduces an additional stochastic drift correction. Herein, several validation tests are presented confirming the correct equilibrium distribution of ions in a channel. Additionally, the methodology is demonstrated using electro-osmosis and induced-charge electro-osmosis, with comparison made to theory and other numerical methods. Notably, the DISCOS approach achieves greater accuracy than a continuum electrostatic simulation method. We also examine the effect of under-resolving hydrodynamic effects using a “dry diffusion” approach, and find that considerable computational speedup can be achieved with a negligible impact on accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Precise algorithm to generate random sequential adsorption of hard polygons at saturation

Random sequential adsorption (RSA) is a time-dependent packing process, in which particles of certain shapes are randomly and sequentially placed into an empty space without overlap. In the infinite-time limit, the density approaches a "saturation'' limit. Although this limit has attracted particular research interest, the majority of past studies could only probe this limit by extrapolation. We have previously found an algorithm to reach this limit using finite computational time for spherical particles, and could thus determine the saturation density of spheres with high accuracy. Here in this paper, we generalize this algorithm to generate saturated RSA packings of two-dimensional polygons. We also calculate the saturation density for regular polygons of three to ten sides, and obtain results that are consistent with previous, extrapolation-based studies.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Accurate and Scalable O(N) Algorithm for First-Principles Molecular-Dynamics Computations on Large Parallel Computers

We present the first truly scalable first-principles molecular dynamics algorithm with O(N) complexity and controllable accuracy, capable of simulating systems with finite band gaps of sizes that were previously impossible with this degree of accuracy. By avoiding global communications, we provide a practical computational scheme capable of extreme scalability. Accuracy is controlled by the mesh spacing of the finite difference discretization, the size of the localization regions in which the electronic wave functions are confined, and a cutoff beyond which the components of the overlap matrix can be omitted when computing selected elements of its inverse. We demonstrate the algorithm's excellent parallel scaling for up to 101 952 atoms on 23 328 processors, with a wall-clock time of the order of 1 min per molecular dynamics time step and numerical error on the forces of less than 7x10 -4 Ha/Bohr.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Optimal Protocols in Quantum Annealing and Quantum Approximate Optimization Algorithm Problems

Quantum annealing (QA) and the quantum approximate optimization algorithm (QAOA) are two special cases of the following control problem: apply a combination of two Hamiltonians to minimize the energy of a quantum state. Which is more effective has remained unclear. Here we analytically apply the framework of optimal control theory to show that generically, given a fixed amount of time, the optimal procedure has the pulsed (or “bang-bang”) structure of QAOA at the beginning and end but can have a smooth annealing structure in between. This is in contrast to previous works which have suggested that bang-bang (i.e., QAOA) protocols are ideal. To support this theoretical work, we carry out simulations of various transverse field Ising models, demonstrating that bang-anneal-bang protocols are more common. Futher, the general features identified here provide guideposts for the nascent experimental implementations of quantum optimization algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Demonstration of Algorithmic Quantum Speedup

Despite the development of increasingly capable quantum computers, an experimental demonstration of a provable algorithmic quantum speedup employing today’s non-fault-tolerant devices has remained elusive. Here, in this study, we unequivocally demonstrate such a speedup within the oracular model, quantified in terms of the scaling with the problem size of the time-to-solution metric. We implement the single-shot Bernstein-Vazirani algorithm, which solves the problem of identifying a hidden bitstring that changes after every oracle query, using two different 27-qubit IBM Quantum superconducting processors. The speedup is observed on only one of the two processors when the quantum computation is protected by dynamical decoupling but not without it. The quantum speedup reported here does not rely on any additional assumptions or complexity-theoretic conjectures and solves a bona fide computational problem in the setting of a game with an oracle and a verifier.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Solving reaction dynamics with quantum computing algorithms

The description of quantum many-body dynamics is extremely challenging on classical computers, as it can involve many degrees of freedom. However, the time evolution of quantum states is a natural application for quantum computers that are designed to efficiently perform unitary transformations. Here, in this paper, we study quantum algorithms for response functions, relevant for describing different reactions governed by linear response. We focus on nuclear-physics applications and consider a qubit-efficient mapping on the lattice, which can efficiently represent the large volumes required for realistic scattering simulations. For the case of a contact interaction, we develop an algorithm for time evolution based on the Trotter approximation that scales logarithmically with the lattice size and is combined with quantum phase estimation. We eventually focus on the nuclear two-body system and a typical response function relevant for electron scattering as an example. We also investigate ground-state preparation and examine the total circuit depth required for a realistic calculation and the hardware noise level required to interpret the signal.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Inference of response functions with the help of machine-learning algorithms

Response functions are a key quantity to describe the near-equilibrium dynamics of strongly interacting many-body systems. Recent techniques that attempt to overcome the challenges of calculating these ab initio have employed expansions in terms of orthogonal polynomials. We employ a neural network prediction algorithm to reconstruct a response function 𝑆⁡(𝜔) defined over a range in frequencies 𝜔. Here, we represent the calculated response function as a truncated Chebyshev series whose coefficients can be optimized to reduce the representation error. We compare the quality of response functions obtained using coefficients calculated using a neural network (NN) algorithm with those computed using the Gaussian integral transform (GIT) method. In the regime where only a small number of terms in the Chebyshev series are retained, we find that the NN scheme outperforms the GIT method.

Kurkcuoglu, Doga Murat [Fermi National Accelerator↗
DOE OSTI2025

Analyzing the Quantum Approximate Optimization Algorithm: Ansätze, Symmetries, and Lie Algebras

The quantum approximate optimization algorithm (QAOA) has been proposed as a method to obtain approximate solutions for combinatorial optimization tasks. In this work, we study the underlying algebraic properties of three QAOA ansätze for the maximum-cut problem on connected graphs, while focusing on the generated Lie algebras as well as their invariant subspaces. Specifically, we analyze the standard QAOA ansatz as well as the orbit and multiangle ansätze. We are able to fully characterize the Lie algebras of the multiangle ansatz across arbitrary connected graphs, finding that they only fall into one of just six families. Aside from the cycle and path graphs, the Lie dimensions for every graph are exponentially large in the system size, meaning that multiangle ansätze are extremely prone to exhibiting barren plateaus. Then, a similar quasi-graph-independent Lie-algebraic characterization beyond the multiangle ansatz is impeded as the circuit exhibits additional “hidden” symmetries besides those naturally arising from a certain parity-superselection operator and all automorphisms of the considered graph. Disregarding the “hidden” symmetries, we can upper bound the dimensions of the orbit and the standard Lie algebras, and the dimensions of the associated invariant subspaces are determined via explicit character formulas. To finish, we conjecture that (for most graphs) the standard Lie algebras have only components that are either exponential or that grow, at most, polynomially with the system size. This would imply that the QAOA is either prone to barren plateaus or classically simulable. More generally, our work provides a symmetry framework and tools to analyze any desired variational quantum algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Insight into 3D micro-CT data: exploring segmentation algorithms through performance metrics

Three-dimensional (3D) micro-tomography (µ-CT) has proven to be an important imaging modality in industry and scientific domains. Understanding the properties of material structure and behavior has produced many scientific advances. An important component of the 3D µ-CT pipeline is image partitioning (or image segmentation), a step that is used to separate various phases or components in an image. Image partitioning schemes require specific rules for different scientific fields, but a common strategy consists of devising metrics to quantify performance and accuracy. The present article proposes a set of protocols to systematically analyze and compare the results of unsupervised classification methods used for segmentation of synchrotron-based data. Additionally, the proposed dataflow for Materials Segmentation and Metrics (MSM) provides 3D micro-tomography image segmentation algorithms, such as statistical region merging (SRM), k-means algorithm and parallel Markov random field (PMRF), while offering different metrics to evaluate segmentation quality, confidence and conformity with standards. Both experimental and synthetic data are assessed, illustrating quantitative results through the MSM dashboard, which can return sample information such as media porosity and permeability. The main contributions of this work are: (i) to deliver tools to improve material design and quality control; (ii) to provide datasets for benchmarking and reproducibility; (iii) to yield good practices in the absence of standards or ground-truth for ceramic composite analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

SHAD: the Scalable High-performance Algorithms and Data-structures Library

The unprecedented amount of data that needs to be processed in emerging data analytics applications poses novel challenges to industry and academia. Scalability and high performance become more than a desirable feature because, due to the scale and the nature of the problems, they draw the line between what is achievable and what is unfeasible. In this paper, we propose SHAD, the Scalable High-performance Algorithms and Data-structures library. SHAD adopts a modular design that confines low level details and promotes reuse. SHAD's core is built on an Abstract Runtime Interface which enhances portability and identifies the minimal set of features of the underlying system required by the framework. The core library includes common data-structures such as: Array, Vector, Map and Set. These are designed to accommodate significant amount of data which can be accessed in massively parallel environments, and used as building blocks for SHAD extensions, i.e. higher level software libraries. We have validated and evaluated our design with a performance and scalability study of the core components of the library. We have validated the design flexibility by proposing a Graph Library as an example of SHAD extension, which implements two different graph data-structures; we evaluate their performance with a set of graph applications. Experimental results show that the approach is promising in terms of both performance and scalability. On a distributed system with 320 cores, SHAD Arrays are able to sustain a throughput of 65 billion operations per second, while SHAD Maps sustain 1 billion of operations per second. Algorithms implemented using the Graph Library exhibit performance and scalability comparable to a custom solution, but with smaller development effort.

Castellana, Vito G.↗
DOE OSTI2019

Multi-physics simulations of particle tracking in arterial geometries with a scalable moving window algorithm

In arterial systems, cancer cell trajectories determine metastatic cancer locations; similarly, particle trajectories determine drug delivery distribution. Predicting trajectories is challenging, as the dynamics are affected by local interactions with red blood cells, complex hemodynamic flow structure, and downstream factors such as stenoses or blockages. Direct simulation is not possible, as a single simulation of a large arterial domain with explicit red blood cells is currently intractable on even the largest supercomputers. To overcome this limitation, we present a multi-physics adaptive window algorithm, in which individual red blood cells are explicitly modeled in a small region of interest moving through a coupled arterial fluid domain. We describe the coupling between the window and fluid domains, including automatic insertion and deletion of explicit cells and dynamic tracking of cells of interest by the window. We show that this algorithm scales efficiently on heterogeneous architectures and enables us to perform large, highly-resolved particle-tracking simulations that would otherwise be intractable.

Herschlag, Gregory↗
DOE OSTI2022

GCoD: Graph Convolutional Network Acceleration via Dedicated Algorithm and Accelerator Co-Design

Graph Convolutional Networks (GCNs) have emerged as the state-of-the-art graph learning model. However, it remains notoriously challenging to inference GCNs over large graph datasets, limiting their application to large real-world graphs and hindering the exploration of deeper and more sophisticated GCN graphs. This is because real-world graphs can be extremely large and sparse. Furthermore, the node degree of GCNs tends to follow the power-law distribution and therefore have highly irregular adjacency matrices, resulting in prohibitive inefficiencies in both data processing and movement and thus substantially limiting the achievable GCN acceleration efficiency. To this end, this paper proposes the first GCN algorithm and accelerator Co-Design framework dubbed GCoD which can largely alleviate the aforementioned GCN irregularity and boost GCNs' inference efficiency. Specifically, on the algorithm level, GCoD integrates a divide and conquer GCN training strategy that polarizes the graphs to be either denser or sparser in local neighborhoods without compromising the model accuracy, resulting in graph adjacency matrices that (mostly) have merely two levels of workload and enjoys largely enhanced regularity and thus ease of acceleration. On the hardware level, we further develop a dedicated two-pronged accelerator with a separated engine to process each of the aforementioned workloads, further boosting the overall utilization and acceleration efficiency. Extensive experiments and ablation studies validate that our GCoD consistently outperforms state-of-the-art designs in terms of accelerator efficiency while maintaining or even improving the task accuracy. Additionally, we visualize GCoD trained graph adjacency matrices to better understand its advantages. All codes and pre-trained models will be released upon acceptance.

You, Haoran↗
DOE OSTI2022

SparseLU, A Novel Algorithm and Math Library for Sparse LU Factorization

Decomposing sparse matrices into lower and upper triangular matrices (sparse LU factorization) is a key operation in many computational scientific applications. We developed SparseLU, a sparse linear algebra library that implements a new algorithm for LU factorization on general sparse matrices. The new algorithm divides the input matrix into tiles to which OpenMP tasks are created for factorization computation, where only tiles that contain nonzero elements are computed. For comparative performance analysis, we used the reference library SuperLU. Testing was performed on synthetically generated matrices which replicate the conditions of the real-world matrices. SparseLU is able to reach a mean speedup of ~29× compared to SuperLU.

Valero Lara, Pedro↗
DOE OSTI2013

An Efficient Deterministic Parallel Algorithm for Adaptive Multidimensional Numerical Integration on GPUs

Recent development in Graphics Processing Units (GPUs) has enabled a new possibility for highly efficient parallel computing in science and engineering. Their massively parallel architecture makes GPUs very effective for algorithms where processing of large blocks of data can be executed in parallel. Multidimensional integration has important applications in areas like computational physics, plasma physics, computational fluid dynamics, quantum chemistry, molecular dynamics and signal processing. The computationally intensive nature of multidimensional integration requires a high-performance implementation. In this study, we present an efficient deterministic parallel algorithm for adaptive multidimensional numerical integration on GPUs. Various optimization techniques are applied to maximize the utilization of the GPU. GPU-based implementation outperforms the best known sequential methods and achieves a speed-up of up to 100. It also shows good scalability with the increase in dimensionality.

Arumugam, Kamesh↗
DOE OSTI2014

CAST: Contraction Algorithm for Symmetric Tensors

Tensor contractions represent the most compute-intensive core kernels in ab initio computational quantum chemistry and nuclear physics. Symmetries in these tensor contractions makes them difficult to load balance and scale to large distributed systems. In this paper, we develop an efficient and scalable algorithm to contract symmetric tensors. We introduce a novel approach that avoids data redistribution in contracting symmetric tensors while also avoiding redundant storage and maintaining load balance. We present experimental results on two parallel supercomputers for several symmetric contractions that appear in the CCSD quantum chemistry method. We also present a novel approach to tensor redistribution that can take advantage of parallel hyperplanes when the initial distribution has replicated dimensions, and use collective broadcast when the final distribution has replicated dimensions, making the algorithm very efficient.

distributed memory↗
DOE OSTI2013

Design of Fair Charging Algorithm for Smart Electrical Vehicle Charging Infrastructure

Smart charging infrastructure is required to meet the growing demand for Electrical Vehicle (EV) charging from ever more abundant EV owners. WINSmartEV™ is a software based smart charging infrastructure that can monitor, control and manage EV charging. It also can use multiplexing to share scarce charging resources among different EVs plugged in simultaneously. By default WINSmartEV™ uses a round-robin algorithm to schedule charging time between EVs charging on the 120V level one charging device. In order to enhance user acceptance of this technology, charge time allocation fairness is defined and an algorithm to enhance this fairness is proposed.

Chung, Ching-Yen↗
DOE OSTI2016

The Reverse Cuthill-McKee Algorithm in Distributed-Memory

Ordering vertices of a graph is key to minimize fill-in and data structure size in sparse direct solvers, maximize locality in iterative solvers, and improve performance in graph algorithms. Except for naturally parallelizable ordering methods such as nested dissection, many important ordering methods have not been efficiently mapped to distributed-memory architectures. In this paper, we present the first-ever distributed-memory implementation of the reverse Cuthill-McKee (RCM) algorithm for reducing the profile of a sparse matrix. Our parallelization uses a two-dimensional sparse matrix decomposition. We achieve high performance by decomposing the problem into a small number of primitives and utilizing optimized implementations of these primitives. Our implementation shows strong scaling up to 1024 cores for smaller matrices and up to 4096 cores for larger matrices.

97 MATHEMATICS AND COMPUTING↗