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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Efficient QAOA Optimization using Directed Restarts and Graph Lookup

Variational Quantum Algorithms (VQA) aim to enhance the capabilities of Noisy Intermediate-Scale Quantum (NISQ) devices. These algorithms utilize parameterized circuits and classical optimizers to iteratively execute circuits with varying parameters. However, VQA faces computational overheads due to repeated iterations and random restarts. Prior work suggests using basic sub-graphs to transfer parameters for the input graph, reducing optimizer overheads but limiting applicability to structured regular graphs. In real-world applications, random irregular graphs are common, and existing methods are not scalable or practical for such graphs. This paper presents a framework that aims to improve random irregular graphs in VQA. The framework uses graph similarity and important features like total edge counts, average edge counts, and variance. It follows an iterative process to choose basis sub-graphs from a small database and adjust parameters accordingly. Classical optimizers then utilize these parameters to determine when to restart and perform gradient descent. This approach increases the chances of reaching global maximum points.

Wang, Meng↗
DOE OSTI2017

CUDA Enabled Graph Subset Examiner

Finding Godsil-McKay switching sets in graphs is one way to demonstrate that a specific graph is not determined by its spectrum--the eigenvalues of its adjacency matrix. An important area of active research in pure mathematics is determining which graphs are determined by their spectra, i.e. when the spectrum of the adjacency matrix uniquely determines the underlying graph. We are interested in exploring the spectra of graphs in the Johnson scheme and specifically seek to determine which of these graphs are determined by their spectra. Given a graph G, a Godsil-McKay switching set is an induced subgraph H on 2k vertices with the following properties: I) H is regular, ii) every vertex in G/H is adjacent to either 0, k, or 2k vertices of H, and iii) at least one vertex in G/H is adjacent to k vertices in H. The software package examines each subset of a user specified size to determine whether or not it satisfies those 3 conditions. The software makes use of the massive parallel processing power of CUDA enabled GPUs. It also exploits the vertex transitivity of graphs in the Johnson scheme by reasoning that if G has a Godsil-McKay switching set, then it has a switching set which includes vertex 1. While the code (in its current state) is tuned to this specific problem, the method of examining each induced subgraph of G can be easily re-written to check for any user specified conditions on the subgraphs and can therefore be used much more broadly.

Johnston, JeremyT.↗
DOE OSTI2013

Comparing Algorithms for Graph Isomorphism Using Discrete- and Continuous-Time Quantum Random Walks

Berry and Wang [Phys. Rev. A 83, 042317 (2011)] show numerically that a discrete-time quan- tum random walk of two noninteracting particles is able to distinguish some non-isomorphic strongly regular graphs from the same family. Here we analytically demonstrate how it is possible for these walks to distinguish such graphs, while continuous-time quantum walks of two noninteracting parti- cles cannot. We show analytically and numerically that even single-particle discrete-time quantum random walks can distinguish some strongly regular graphs, though not as many as two-particle noninteracting discrete-time walks. Additionally, we demonstrate how, given the same quantum random walk, subtle di erences in the graph certi cate construction algorithm can nontrivially im- pact the walk's distinguishing power. We also show that no continuous-time walk of a xed number of particles can distinguish all strongly regular graphs when used in conjunction with any of the graph certi cates we consider. We extend this constraint to discrete-time walks of xed numbers of noninteracting particles for one kind of graph certi cate; it remains an open question as to whether or not this constraint applies to the other graph certi cates we consider.

97 MATHEMATICS AND COMPUTING↗
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↗
NASA NTRS2006

Using Correlation to Compute Better Probability Estimates in Plan Graphs

Plan graphs are commonly used in planning to help compute heuristic "distance" estimates between states and goals. A few authors have also attempted to use plan graphs in probabilistic planning to compute estimates of the probability that propositions can be achieved and actions can be performed. This is done by propagating probability information forward through the plan graph from the initial conditions through each possible action to the action effects, and hence to the propositions at the next layer of the plan graph. The problem with these calculations is that they make very strong independence assumptions - in particular, they usually assume that the preconditions for each action are independent of each other. This can lead to gross overestimates in probability when the plans for those preconditions interfere with each other. It can also lead to gross underestimates of probability when there is synergy between the plans for two or more preconditions. In this paper we introduce a notion of the binary correlation between two propositions and actions within a plan graph, show how to propagate this information within a plan graph, and show how this improves probability estimates for planning. This notion of correlation can be thought of as a continuous generalization of the notion of mutual exclusion (mutex) often used in plan graphs. At one extreme (correlation=0) two propositions or actions are completely mutex. With correlation = 1, two propositions or actions are independent, and with correlation > 1, two propositions or actions are synergistic. Intermediate values can and do occur indicating different degrees to which propositions and action interfere or are synergistic. We compare this approach with another recent approach by Bryce that computes probability estimates using Monte Carlo simulation of possible worlds in plan graphs.

Bryce, Daniel↗
DOE OSTI2016

CUDA Enabled Graph Subset Examiner

Finding Godsil-McKay switching sets in graphs is one way to demonstrate that a specific graph is not determined by its spectrum--the eigenvalues of its adjacency matrix. An important area of active research in pure mathematics is determining which graphs are determined by their spectra, i.e. when the spectrum of the adjacency matrix uniquely determines the underlying graph. We are interested in exploring the spectra of graphs in the Johnson scheme and specifically seek to determine which of these graphs are determined by their spectra. Given a graph G, a Godsil-McKay switching set is an induced subgraph H on 2k vertices with the following properties: I) H is regular, ii) every vertex in G/H is adjacent to either 0, k, or 2k vertices of H, and iii) at least one vertex in G/H is adjacent to k vertices in H. The software package examines each subset of a user specified size to determine whether or not it satisfies those 3 conditions. The software makes use of the massive parallel processing power of CUDA enabled GPUs. It also exploits the vertex transitivity of graphs in the Johnson scheme by reasoning that if G has a Godsil-McKay switching set, then it has a switching set which includes vertex 1. While the code (in its current state) is tuned to this specific problem, the method of examining each induced subgraph of G can be easily re-written to check for any user specified conditions on the subgraphs and can therefore be used much more broadly.

Johnston, Jeremy T.↗
DOE OSTI2015

On Bipartite Graphs Trees and Their Partial Vertex Covers.

Graphs can be used to model risk management in various systems. Particularly, Caskurlu et al. in [7] have considered a system, which has threats, vulnerabilities and assets, and which essentially represents a tripartite graph. The goal in this model is to reduce the risk in the system below a predefined risk threshold level. One can either restricting the permissions of the users, or encapsulating the system assets. The pointed out two strategies correspond to deleting minimum number of elements corresponding to vulnerabilities and assets, such that the flow between threats and assets is reduced below the predefined threshold level. It can be shown that the main goal in this risk management system can be formulated as a Partial Vertex Cover problem on bipartite graphs. It is well-known that the Vertex Cover problem is in P on bipartite graphs, however; the computational complexity of the Partial Vertex Cover problem on bipartite graphs has remained open. In this paper, we establish that the Partial Vertex Cover problem is NP-hard on bipartite graphs, which was also recently independently demonstrated [N. Apollonio and B. Simeone, Discrete Appl. Math., 165 (2014), pp. 37–48; G. Joret and A. Vetta, preprint, arXiv:1211.4853v1 [cs.DS], 2012]. We then identify interesting special cases of bipartite graphs, for which the Partial Vertex Cover problem, the closely related Budgeted Maximum Coverage problem, and their weighted extensions can be solved in polynomial time. We also present an 8/9-approximation algorithm for the Budgeted Maximum Coverage problem in the class of bipartite graphs. We show that this matches and resolves the integrality gap of the natural LP relaxation of the problem and improves upon a recent 4/5-approximation.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2020

Performance and usability enhancements for continuous subgraph matching queries on graph-structured data

A query graph, which includes vertices and edges, represents a query on graph-structured data. The query graph is decomposed into query subgraphs. A network analysis tool performs continuous subgraph matching queries to facilitate analysis of computer network traffic, social media events, or other streams of data represented as a dynamic data graph (graph-structured data). This can help identify emerging trends in the data. Some features of the network analysis tool enhance performance by effectively utilizing distributed computing resources (including processing cores and memory at different nodes of a cluster) to speed up the process of updating the dynamic data graph and detecting matches of query subgraphs. Features of a query graph building tool enhance usability by providing intuitive ways to specify query graphs and their subgraphs. Features of a results visualization tool enhance usability by providing an intuitive way to present the results of continuous subgraph matching queries.

Choudhury, Sutanay↗
DOE OSTI2020

C-SAW: a framework for graph sampling and random walk on GPUs

Many applications require to learn, mine, analyze and visualize large-scale graphs. These graphs are often too large to be addressed efficiently using conventional graph processing technologies. Fortunately, recent research efforts find out graph sampling and random walk, which significantly reduce the size of original graphs, can benefit the tasks of learning, mining, analyzing and visualizing large graphs by capturing the desirable graph properties. This paper introduces C-SAW, the first framework that accelerates Sampling and Random Walk framework on GPUs. Particularly, C-SAW makes three contributions: First, our framework provides a generic API which allows users to implement a wide range of sampling and random walk algorithms with ease. Second, offloading this framework on GPU, we introduce warp-centric parallel selection, and two novel optimizations for collision migration. Third, towards supporting graphs that exceed the GPU memory capacity, we introduce efficient data transfer optimizations for out-of-memory and multi-GPU sampling, such as workload-aware scheduling and batched multi-instance sampling. Taken together, our framework constantly outperforms the state of the art projects in addition to the capability of supporting a wide range of sampling and random walk algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Explaining Missing Data in Graphs: A Constraint-based Approach

Abstract: This paper introduces a constraint-based approach to clarify missing values in graphs. Our method capitalizes on a set S of graph data constraints. An explanation is a sequence of operational enforcement of S towards the recovery of interested yet missing data (e.g., attribute values, edges). We show that constraint-based approach helps us to understand not only why a value is missing, but also how to recover the missing value. We study S-explanation problem, which is to compute the optimal explanations with guarantees on the informativeness and conciseness. We show the problem is in ?P^2 for established graph data constraints such as graph keys and graph association rules. We develop an efficient bidirectional algorithm to compute optimal explanations, without enforcing S on the entire graph. We also show our algorithm can be easily extended to support graph refinement within limited time, and to explain missing answers. Using real-world graphs, we experimentally verify the effectiveness and efficiency of our algorithms.

Data Analytics↗
DOE OSTI2020

GrAMME: Semisupervised Learning Using Multilayered Graph Attention Models

Modern data analysis pipelines are becoming increasingly complex due to the presence of multiview information sources. While graphs are effective in modeling complex relationships, in many scenarios, a single graph is rarely sufficient to succinctly represent all interactions, and hence, multilayered graphs have become popular. Though this leads to richer representations, extending solutions from the single-graph case is not straightforward. Consequently, there is a strong need for novel solutions to solve classical problems, such as node classification, in the multilayered case. In this article, we consider the problem of semisupervised learning with multilayered graphs. Though deep network embeddings, e.g., DeepWalk, are widely adopted for community discovery, we argue that feature learning with random node attributes, using graph neural networks, can be more effective. To this end, we propose to use attention models for effective feature learning and develop two novel architectures, GrAMME-SG and GrAMME-Fusion, that exploit the interlayer dependences for building multilayered graph embeddings. Using empirical studies on several benchmark data sets, we evaluate the proposed approaches and demonstrate significant performance improvements in comparison with the state-of-the-art network embedding strategies. The results also show that using simple random features is an effective choice, even in cases where explicit node attributes are not available.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Identifying Backbones in Three-Dimensional Discrete Fracture Networks: A Bipartite Graph-Based Approach

In this paper, we present a graph-based method to identify primary flow and transport sub-networks in three-dimensional discrete fracture networks (DFNs). The structure of a DFN lends itself to the use of graphs as a coarse-scale representation that retains the multiscale nature of flow and transport through fracture media. We develop a bipartite graph representation that integrates fracture network topology, fracture geometry, and hydraulic properties. We show that the two most common graph-representations of DFNs, vertices representing intersections and vertices representing fractures, are projections of this bipartite graph thereby providing a generalization of previous DFN-graph frameworks. The primary subnetworks in each DFN are identified by running a heuristic algorithm that determines the edge-disjoint shortest paths through the graph which correspond to the regions where the fastest transport occurs. The method does not have any user-defined parameters and terminates in a finite number of steps. The quality of the method is demonstrated by comparing transport simulations on the identified primary subnetwork and full network, which are in good agreement for early and middle times. In conclusion, these estimates of the first passage times can be achieved with close to an order of magnitude reduction of computational expense using the proposed method.

58 GEOSCIENCES↗
DOE OSTI2018

On the Decomposition of a 3-Connected Graph into Cyclically 4-Edge-Connected Components

A graph is called cyclically 4-edge-connected if removing any three edges from it results in a graph in which at most one connected component contains a cycle. A 3-connected graph is 4-edge-connected if and only if removing any three edges from it results in either a connected graph or a graph with exactly two connected components one of which is a single-vertex one. We show how to associate with any 3-connected graph a tree of components such that every component is a 3-connected and cyclically 4-edge-connected graph.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

An Upper Bound on the Number of Edges of a Graph Whose kth Power Has a Connected Complement

We say that a graph is k-wide if for any partition of its vertex set into two subsets, one can choose vertices at distance at least k in these subsets (i.e., the complement of the kth power of this graph is connected). We say that a graph is k-mono-wide if for any partition of its vertex set into two subsets, one can choose vertices at distance exactly k in these subsets.We prove that the complement of a 3-wide graph on n vertices has at least 3n − 7 edges, and the complement of a 3-mono-wide graph on n vertices has at least 3n − 8 edges. We construct infinite series of graphs for which these bounds are attained.We also prove an asymptotically tight bound for the case k ≥ 4: the complement of a k-wide graph contains at least (n − 2k)(2k − 4[log{sub 2}k] − 1) edges.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Discrete Green’s functions and spectral graph theory for computationally efficient thermal modeling

Here, this work concerns solutions of the heat equation with the spectral graph method, for which the temperature is defined at discrete points in the domain and the spatial relationship among the points is described by a graph. The heat equation on the graph is solved using matrix techniques involving the eigenvectors and eigenvalues of the Laplacian matrix. The spectral graph approach precludes the computationally intensive meshing and numerous time-integration steps of the finite element method. In the present work, the spectral graph method is extended to include heat loss at the boundaries with a generalized boundary condition, and physics-based edge weights are introduced which simplify the calibration process. From this approach a discrete Green’s function is defined which allows for solutions under a variety of heating conditions including: space-varying initial conditions; time-and-space varying internal heating; and, time-and-space-varying heating at boundaries of type 1 (Dirichlet), type 2 (Neumann) and type 3 (Robin). Results are provided for benchmark heat transfer problems in one spatial dimension and in three spatial dimensions, and verification is provided by comparison with exact analytical solutions and finite difference solutions. The spectral graph method converges within 0.4% error of the analytical solution. The practical utility of the approach is demonstrated by thermal simulation of a multilayer additive manufacturing process. The spectral graph results are compared to experimentally-obtained temperature data for two metal parts, with error less than 5% of the experimental measurements, with computation time less than one minute on a desktop computer.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Graphs, matrices, and the GraphBLAS: Seven good reasons

The analysis of graphs has become increasingly important to a wide range of applications. Graph analysis presents a number of unique challenges in the areas of (1) software complexity, (2) data complexity, (3) security, (4) mathematical complexity, (5) theoretical analysis, (6) serial performance, and (7) parallel performance. Implementing graph algorithms using matrix-based approaches provides a number of promising solutions to these challenges. The GraphBLAS standard (istcbigdata.org/GraphBlas) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. The GraphBLAS mathematically defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the GraphBLAS and describes how the GraphBLAS can be used to address many of the challenges associated with analysis of graphs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Acceleration of Graph Neural Network-Based Prediction Models in Chemistry via Co-Design Optimization on Intelligence Processing Units

Atomic structure prediction and associated property calculations are the bedrock of chemical physics. Since high-fidelity ab initio modeling techniques for computing the structure and properties can be prohibitively expensive, this motivates the development of machine-learning (ML) models that make these predictions more efficiently. Training graph neural networks over large atomistic databases introduces unique computational challenges such as the need to process millions of small graphs with variable size and support communication patterns that are distinct from learning over large graphs such as social networks. We demonstrate a novel hardware-software co-design approach to scale up the training of atomistic graph neural networks (GNN) for structure and property prediction. First, to eliminate redundant computation and memory associated with alternative padding techniques and to improve throughput via minimizing communication, we formulate the effective coalescing of the batches of variable-size atomistic graphs as the bin packing problem and introduce a hardware-agnostic algorithm to pack these batches. In addition, we propose hardware-specific optimizations including a planner and vectorization for the gather-scatter operations targeted for Graphcore’s Intelligence Processing Unit (IPU), as well as model-specific optimizations such as merged communication collectives and optimized softplus. Putting these all together, we demonstrate the effectiveness of the proposed co-design approach by providing an implementation of a well-established atomistic GNN on the Graphcore IPUs. We evaluate the training performance on multiple atomistic graph databases with varying degrees of graph counts, sizes and sparsity. Here, we demonstrate that such a co-design approach can reduce the training time of atomistic GNNs and can improve the performance by up to 1.5× compared to the baseline implementation of the model on the IPUs. Additionally, we compare our IPU implementation with a Nvidia GPU-based implementation and show that our atomistic GNN implementation on the IPUs can run 1.8× faster on average compared to the execution time on the GPUs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗