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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

ConnectIt: a framework for static and incremental parallel graph connectivity algorithms

Connected components is a fundamental kernel in graph applications. The fastest existing multicore algorithms for solving graph connectivity are based on some form of edge sampling and/or linking and compressing trees. However, many combinations of these design choices have been left unexplored. In this paper, we design the ConnectIt framework, which provides different sampling strategies as well as various tree linking and compression schemes. ConnectIt enables us to obtain several hundred new variants of connectivity algorithms, most of which extend to computing spanning forest. In addition to static graphs, we also extend ConnectIt to support mixes of insertions and connectivity queries in the concurrent setting. We present an experimental evaluation of ConnectIt on a 72-core machine, which we believe is the most comprehensive evaluation of parallel connectivity algorithms to date. Compared to a collection of state-of-the-art static multicore algorithms, we obtain an average speedup of 12.4x (2.36x average speedup over the fastest existing implementation for each graph). Using ConnectIt, we are able to compute connectivity on the largest publicly-available graph (with over 3.5 billion vertices and 128 billion edges) in under 10 seconds using a 72-core machine, providing a 3.1x speedup over the fastest existing connectivity result for this graph, in any computational setting. For our incremental algorithms, we show that our algorithms can ingest graph updates at up to several billion edges per second. To guide the user in selecting the best variants in ConnectIt for different situations, we provide a detailed analysis of the different strategies. Finally, we show how the techniques in ConnectIt can be used to speed up two important graph applications: approximate minimum spanning forest and SCAN clustering.

Computer Science↗
DOE OSTI2021

A Parallel Cut-Cell Algorithm for the Free-Boundary Grad--Shafranov Problem

A parallel cut-cell algorithm is described to solve the free-boundary problem of the Grad--Shafranov equation. The algorithm reformulates the free-boundary problem in an irregular bounded domain and its important aspects include a searching algorithm for the magnetic axis and separatrix, a surface integral along the irregular boundary to determine the boundary values, an approach to optimize the coil current based on a targeting plasma shape, Picard iterations with Aitken's acceleration for the resulting nonlinear problem, and a Cartesian grid embedded boundary method to handle the complex geometry. Here the algorithm is implemented in parallel using a standard domain-decomposition approach and a good parallel scaling is observed. Numerical results verify the accuracy and efficiency of the free-boundary Grad--Shafranov solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Novel Geometric Operations for Linear Programming

This report summarizes the work performed under the project "Linear Programming in Strongly Polynomial Time." Linear programming (LP) is a classic combinatorial optimization problem heavily used directly and as an enabling subroutine in integer programming (IP). Specifically IP is the same as LP except that some solution variables must take integer values (e.g. to represent yes/no decisions). Together LP and IP have many applications in resource allocation including general logistics, and infrastructure design and vulnerability analysis. The project was motivated by the PI's recent success developing methods to efficiently sample Voronoi vertices (essentially finding nearest neighbors in high-dimensional point sets) in arbitrary dimension. His method seems applicable to exploring the high-dimensional convex feasible space of an LP problem. Although the project did not provably find a strongly-polynomial algorithm, it explored multiple algorithm classes. The new medial simplex algorithms may still lead to solvers with improved provable complexity. We describe medial simplex algorithms and some relevant structural/complexity results. We also designed a novel parallel LP algorithm based on our geometric insights and implemented it in the Spoke-LP code. A major part of the computational step is many independent vector dot products. Our parallel algorithm distributes the problem constraints across processors. Current commercial and high-quality free LP solvers require all problem details to fit onto a single processor or multicore. Our new algorithm might enable the solution of problems too large for any current LP solvers. We describe our new algorithm, give preliminary proof-of-concept experiments, and describe a new generator for arbitrarily large LP instances.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Designing a parallel Feel-the-Way clustering algorithm on HPC systems

This paper introduces a new parallel clustering algorithm, named Feel-the-Way clustering algorithm, that provides better or equivalent convergence rate than the traditional clustering methods by optimizing the synchronization and communication costs. Our algorithm design centers on how to optimize three factors simultaneously: reduced synchronizations, improved convergence rate, and retained same or comparable optimization cost. To compare the optimization cost, we use the Sum of Square Error (SSE) cost as the metric, which is the sum of the square distance between each data point and its assigned clusters. Compared with the traditional MPI k-means algorithm, the new Feel-the-Way algorithm requires less communications among participating processes. As for the convergence rate, the new algorithm requires fewer number of iterations to converge. As for the optimization cost, it obtains the SSE costs that are close to the k-means algorithm. In the paper, we first design the full-step Feel-the-Way k-means clustering algorithm that can significantly reduce the number of iterations that are required by the original k-means clustering method. Next, we improve the performance of the full-step algorithm by adopting an optimized sampling-based approach, named reassignment-history-aware sampling. Our experimental results show that the optimized sampling-based Feel-the-Way method is significantly faster than the widely used k-means clustering method, and can provide comparable optimization costs. More extensive experiments with several synthetic datasets and real-world datasets (e.g., MNIST, CIFAR-10, ENRON, and PLACES-2) show that the new parallel algorithm can outperform the open source MPI k-means library by up to 110% on a high-performance computing system using 4,096 CPU cores. In addition, the new algorithm can take up to 51% fewer iterations to converge than the k-means clustering algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A scalable multidimensional fully implicit solver for Hall magnetohydrodynamics

We propose an optimally performant fully implicit algorithm for the Hall magnetohydrodynamics (HMHD) equations based on multigrid-preconditioned Jacobian-free Newton-Krylov methods. HMHD is a challenging system to solve numerically because it supports stiff fast dispersive waves. The preconditioner is formulated using an operator-split approximate block factorization (Schur complement), informed by physics insight. We use a vector-potential formulation (instead of a magnetic field one) to allow a clean segregation of the problematic $\nabla$ x $\nabla$ x operator in the electron Ohm's law subsystem. This segregation allows the formulation of an effective damped block-Jacobi smoother for multigrid. We demonstrate by analysis that our proposed block-Jacobi iteration is convergent and has the smoothing property. The resulting HMHD solver is verified linearly with wave propagation examples, and nonlinearly with the GEM challenge reconnection problem by comparison against another HMHD code. We demonstrate the excellent algorithmic and parallel performance of the algorithm up to 16384 MPI tasks in two dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Massively-parallel Lagrangian particle code and applications

Massively-parallel, distributed-memory algorithms for the Lagrangian particle hydrodynamic method (Samulyak et al., 2018) have been developed, verified, and implemented. The key component of parallel algorithms is a particle management module that includes a parallel construction of octree databases, dynamic adaptation and refinement of octrees, and particle migration between parallel subdomains. The particle management module is based on the p4est (parallel forest of k-trees) library. The massively-parallel Lagrangian particle code has been applied to a variety of fundamental science and applied problems. A summary of Lagrangian particle code applications to the injection of impurities into thermonuclear fusion devices and to the simulation of supersonic hydrogen jets in support of laser-plasma wakefield acceleration research has also been presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

ParChain: a framework for parallel hierarchical agglomerative clustering using nearest-neighbor chain

This paper studies the hierarchical clustering problem, where the goal is to produce a dendrogram that represents clusters at varying scales of a data set. We propose the ParChain framework for designing parallel hierarchical agglomerative clustering (HAC) algorithms, and using the framework we obtain novel parallel algorithms for the complete linkage, average linkage, and Ward's linkage criteria. Compared to most previous parallel HAC algorithms, which require quadratic memory, our new algorithms require only linear memory, and are scalable to large data sets. ParChain is based on our parallelization of the nearest-neighbor chain algorithm, and enables multiple clusters to be merged on every round. We introduce two key optimizations that are critical for efficiency: a range query optimization that reduces the number of distance computations required when finding nearest neighbors of clusters, and a caching optimization that stores a subset of previously computed distances, which are likely to be reused. Experimentally, we show that our highly-optimized implementations using 48 cores with two-way hyper-threading achieve 5.8--110.1x speedup over state-of-the-art parallel HAC algorithms and achieve 13.75--54.23x self-relative speedup. Compared to state-of-the-art algorithms, our algorithms require up to 237.3x less space. Our algorithms are able to scale to data set sizes with tens of millions of points, which existing algorithms are not able to handle.

Computer Science↗
DOE OSTI2025

A GPU‐Accelerated Generative Adversarial Model for Causal Inference

We develop a GPU-accelerated machine learning generative adversarial model designed to facilitate causal inferences from observational data. Our model's theoretical framework is conceptualized in a manner that is amenable to being operable and scalable for high-performance computing platforms. We leverage GPU acceleration to develop a parallel evolutionary algorithm to achieve large-scale parallel computation of the model within a now widely accessible computing platform. This capability both enhances computational speedup and efficiency and also extends the use of the model to a broader range of substantive research domains while maintaining the underlying theoretical properties of the model.

GPU↗
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 OSTI2024

Single-Shot Decoding of Good Quantum LDPC Codes

Abstract Quantum Tanner codes constitute a family of quantum low-density parity-check codes with good parameters, i.e., constant encoding rate and relative distance. In this article, we prove that quantum Tanner codes also facilitate single-shot quantum error correction (QEC) of adversarial noise, where one measurement round (consisting of constant-weight parity checks) suffices to perform reliable QEC even in the presence of measurement errors. We establish this result for both the sequential and parallel decoding algorithms introduced by Leverrier and Zémor. Furthermore, we show that in order to suppress errors over multiple repeated rounds of QEC, it suffices to run the parallel decoding algorithm for constant time in each round. Combined with good code parameters, the resulting constant-time overhead of QEC and robustness to (possibly time-correlated) adversarial noise make quantum Tanner codes alluring from the perspective of quantum fault-tolerant protocols.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Performance Analysis of Speculative Parallel Adaptive Local Timestepping for Conservation Laws

Stable simulation of conservation laws, such as those used to model fluid dynamics and plasma physics applications, requires the satisfaction of the so-called Courant-Friedrichs-Lewy condition. By allowing regions of the mesh to advance with different timesteps that locally satisfy this stability constraint, significant work reduction can be attained when compared to a time integration scheme using a single timestep size. However, parallelizing this algorithm presents considerable difficulty. Since the stability condition depends on the state of the system, dependencies become dynamic and potentially non-local. In this article, we present an adaptive local timestepping algorithm using an optimistic (Timewarp-based) parallel discrete event simulation. We introduce waiting heuristics to limit misspeculation and a semi-static load balancing scheme to eliminate load imbalance as parts of the mesh require finer or coarser timesteps. Last, we outline an interface for separating the physics of the specific conservation law from the temporal integration allowing for productive adoption of our proposed algorithm. We present a misspeculation study for three conservation laws, demonstrating both the productivity of the local timestepping API, for which 74% of the lines of code are reused across different conservation laws, and the robustness of the waiting heuristics—at most 1.5% of element updates are rolled back. Our performance studies demonstrate up to a 2.8× speedup versus a baseline unoptimized local timestepping approach, a 4x improvement in per-node throughput compared to an MPI parallelization of synchronous timestepping, and scalability up to 3,072 cores on NERSC’s Cori Haswell partition.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Triangle Counting with Cyclic Distributions

Triangles are the simplest non-trivial subgraphs and triangle counting is used in a number of different applications. The order in which vertices are processed in triangle counting strongly effects the amount of work that needs to be done (and thus the overall performance). Ordering vertices by degree has been shown to be one particularly effective ordering approach. However, for graphs with skewed degree distributions (such as power-law graphs), ordering by degree effects the distribution of work; parallelization must account for this distribution in order to balance work among workers. In this paper we provide an in- depth analysis of the ramifications of degree-based ordering on parallel triangle counting. We present approach for partitioning work in triangle counting, based on cyclic distribution and some surprisingly simple C++ implementations. Experimental results demonstrate the effectiveness of our approach, particularly for power-law (and social network) graphs.

Graph algorithms, parallel algorithms↗
DOE OSTI2020

TriC: Distributed-memory Triangle Counting by Exploiting the Graph Structure

Graph analytics has emerged as an important tool in the analysis of large scale data from diverse application domains such as social networks, cyber security and bioinformatics. Counting the number of triangles in a graph is a fundamental kernel with several applications such as detecting the community structure of a graph or in identifying important vertices in a graph. The ubiquity of massive datasets is driving the need to scale graph analytics on parallel systems. However, numerous challenges exist in efficiently parallelizing graph algorithms, especially on distributed-memory systems. Irregular memory accesses and communication patterns, low computation to communication ratios, and the need for frequent synchronization are some of the leading challenges. In this paper, we present TriC, our distributed-memory implementation of triangle counting in graphs using the Message Passing Interface (MPI), as a submission to the 2020 GraphChallenge competition. Using a set of synthetic and real-world inputs from the challenge, we demonstrate a speedup of up to 90x relative to previous work on 32 processor-cores of a NERSC Cori node. We also provide details from distributed runs with up to8192 processes along with strong scaling results. The observations presented in this work provide an understanding of the system-level bottlenecks at scale that specifically impact sparse-irregular workloads and will therefore benefit other efforts to parallelize graph algorithms.

Halappanavar, Mahantesh↗
DOE OSTI2024

Non-Intrusive Parallel-in-Time Solvers for Partial Differential Equations (Final Report)

Many time-dependent problems and simulations are often modeled using Partial Differential Equations. Traditional modeling approaches that use sequential time-stepping are reaching a bottleneck in optimizing efficiency. The Center of Applied Science and Computing at Lawrence Livermore National Laboratory extensively works on parallelizing these algorithms to leverage the increasing computational power from the growing number of processors in computer hardware. In particular, they aim to design non-intrusive algorithms that can generalize to a variety of problems and sizes without requiring additional information from or modifications on the original problems. Multigrid Reduction in Time (MGRIT) is a parallel-in-time algorithm that is designed to be non-intrusive. This project focuses on increasing the efficiency of MGRIT by approximating the coarse-grid operator using machine learning approaches as a means to find the most non-intrusive, or general, solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Virtual Time III, Part 1: Unified Virtual Time Synchronization for Parallel Discrete Event Simulation

Algorithms for synchronization of parallel discrete event simulation have historically been divided between conservative methods that require lookahead but not rollback, and optimistic methods that require rollback but not lookahead. In this paper we present a new approach in the form of a framework called Unified Virtual Time (UVT) that unifies the two approaches, combining the advantages of both within a single synchronization theory. Whenever timely lookahead information is available, a logical process (LP) executes conservatively using an irreversible event handler. When lookahead information is not available the LP does not block, as it would in a classical conservative execution, but instead executes optimistically using a reversible event handler. The switch from conservative to optimistic synchronization and back is decided on an event-by-event basis by the simulator, transparently to the model code. UVT treats conservative synchronization algorithms as optional accelerators for an underlying optimistic synchronization algorithm, enabling the speed of conservative execution whenever it is applicable, but otherwise falling back on the generality of optimistic execution. We describe UVT in a novel way, based on fundamental invariants, monotonicity requirements, and synchronization rules. UVT permits zero-delay messages and pays careful attention to tie-handling using superposition. We prove that under fairly general conditions a UVT simulation always makes progress in virtual time. This is Part 1 of a trio of papers describing the UVT framework for PDES, mixing conservative and optimistic synchronization and integrating throttling control.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Optimization and Augmentation for Data Parallel Contour Trees

Contour trees are used for topological data analysis in scientific visualization. While originally computed with serial algorithms, recent work has introduced a vector-parallel algorithm. Furthermore, this algorithm is relatively slow for fully augmented contour trees which are needed for many practical data analysis tasks. We therefore introduce a representation called the hyperstructure that enables efficient searches through the contour tree and use it to construct a fully augmented contour tree in data parallel, with performance on average 6 times faster than the state-of-the-art parallel algorithm in the TTK topological toolkit.

97 MATHEMATICS AND COMPUTING↗