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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 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Classical eikonal from Magnus expansion

In a classical scattering problem, the classical eikonal is defined as the generator of the canonical transformation that maps in-states to out-states. It can be regarded as the classical limit of the log of the quantum S-matrix. In a classical analog of the Born approximation in quantum mechanics, the classical eikonal admits an expansion in oriented tree graphs, where oriented edges denote retarded/advanced worldline propagators. The Magnus expansion, which takes the log of a time-ordered exponential integral, offers an efficient method to compute the coefficients of the tree graphs to all orders. We exploit a Hopf algebra structure behind the Magnus expansion to develop a fast algorithm which can compute the tree coefficients up to the 12th order (over half a million trees) in less than an hour. In a relativistic setting, our methods can be applied to the post-Minkowskian (PM) expansion for gravitational binaries in the worldline formalism. We demonstrate the methods by computing the 3PM eikonal and find agreement with previous results based on amplitude methods. Importantly, the Magnus expansion yields a finite eikonal, while the naïve eikonal based on the time-symmetric propagator is infrared-divergent from 3PM on.

Black Holes↗
DOE OSTI2024

Sachdev-Ye-Kitaev model on a noisy quantum computer

Here we study the SYK model -- an important toy model for quantum gravity on IBM's superconducting qubit quantum computers. By using a graph-coloring algorithm to minimize the number of commuting clusters of terms in the qubitized Hamiltonian, we find the gate complexity of the time evolution using the first-order product formula for N Majorana fermions is $\mathscr{O}$(N 5 J 2 t 2 /ε) where J is the dimensionful coupling parameter, t is the evolution time, and ε is the desired precision. With this improved resource requirement, we perform the time evolution for N=6,8 with maximum two-qubit circuit depth of 343. We perform different error mitigation schemes on the noisy hardware results and find good agreement with the exact diagonalization results on classical computers and noiseless simulators. In particular, we compute return probability after time t and out-of-time order correlators (OTOC) which is a standard observable of quantifying the chaotic nature of quantum systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Unifying Combinatorial and Graphical Methods in Artificial Intelligence

Recently, a new graph Laplacian, called the inner product Laplacian, was introduced which generalizes many existing Laplacians, including the normalized and combinatorial Laplacian and their weighted variants. The key observation behind the inner product Laplacian is that by defining appropriate inner product spaces on the vertices and edges, the standard Laplacians can be recovered as Hodge Laplacians over the simplicial complex formed by the edges and vertices. These inner product spaces form a natural way to incorporate non-combinatorial information into the definition of a domain-specific Laplacian. In particular, in contrast to current domain-specific weighting schemes which rely solely on edge weights, information regarding the similarity of non-adjacent vertices and arbitrary pairs of edges can be effectively incorporated into the Laplacian. In order to illustrate this approach we consider the problem of calculating the potential energy of an atomistic configuration using Graph Neural Networks. In comparison with start-of-the-art approaches, such as SchNet, our approach replaces a learned (via auto-encoder) representation of the atom types with an inner product space on atoms based on scientific knowledge (e.g., electronegativity). We will illustrate how this approach captures key chemical properties of the molecules and compare the energy calculations with state-of-the-art neural network approaches. However, to compute the resulting Laplacian involves a mixture of sparse and dense matrix computation and yields a dense matrix as the basis for the graph convolution. This dense convolutional kernel necessitates moving away from the standard message passing framework for graph neural networks and increases the computational cost of applying the kernel. In order to mitigate these costs we investigate means of leveraging the mixed sparse and dense computations to reduce the overall computational cost and how these approaches can be automatically transferred to energy efficient hardware (e.g., field programmable gate arrays (FPGAs)).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Understanding Discrete Fracture Networks Through Spectral Graph Theory

Discrete Fracture Network models (DFNs) are used to simulate fluid flow and particle transport through fracture networks in low permeability rock. Understanding these processes are essential in many subsurface applications, such as environmental restoration of contaminated fractured media, CO 2 sequestration, detection of low-level nuclear tests, and hydrocarbon extraction. Compared with other models, DFNs allow for incorporation of a wider range of network characteristics but have substantially greater computation cost. These networks can be represented with graphs, allowing the use of graph theory tools to study the networks. I used Python to simulate flow and transport on a range of DFNs and analyzed these networks using methods from network analysis and spectral graph theory. My purpose was to find ways to gain insight about flow and transport on DFNs using these graph representations, bypassing the computationally intensive meshing typically required. My work is still in progress, but I have discovered several interesting trends and patterns that I believe could be useful towards my goal. If I am able to bring these results to fruition, they will aid subsurface geologists in extracting flow and transport information about fracture networks more efficiently.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Efficient Topology Assessment for Integrated Transmission and Distribution Network with 10,000+ Inverter-based Resources

The renewable energy proliferation calls upon the grid operators and planners to systematically evaluate the potential impacts of distributed energy resources (DERs). Considering the significant differences between various inverter-based resources (IBRs), especially the different capabilities between grid-forming inverters and grid-following inverters, it is crucial to develop an efficient and effective assessment procedure besides available co-simulation framework with high computation burdens. This paper presents a streamlined graph-based topology assessment for the integrated power system transmission and distribution networks. Graph analyses were performed based on the integrated graph of modified miniWECC grid model and IEEE 8500-node test feeder model, high performance computing platform with 40 nodes and total 2400 CPUs has been utilized to process this integrated graph, which has 100,000+ nodes and 10,000+ IBRs. The node ranking results not only verified the applicability of the proposed method, but also revealed the potential of distributed grid forming (GFM) and grid following (GFL) inverters interacting with the centralized power plants.

Graph Analysis, Topology evaluation, Infrastructur↗
DOE OSTI2021

Preventing Failures By Dataset Shift Detection in Safety-Critical Graph Applications

Dataset shift refers to the problem where the input data distribution may change over time (e.g., between training and test stages). Since this can be a critical bottleneck in several safety-critical applications such as healthcare, drug-discovery, etc., dataset shift detection has become an important research issue in machine learning. Though several existing efforts have focused on image/video data, applications with graph-structured data have not received sufficient attention. Therefore, in this paper, we investigate the problem of detecting shifts in graph structured data through the lens of statistical hypothesis testing. Specifically, we propose a practical two-sample test based approach for shift detection in large-scale graph structured data. Our approach is very flexible in that it is suitable for both undirected and directed graphs, and eliminates the need for equal sample sizes. Using empirical studies, we demonstrate the effectiveness of the proposed test in detecting dataset shifts. We also corroborate these findings using real-world datasets, characterized by directed graphs and a large number of nodes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A Block-Based Triangle Counting Algorithm on Heterogeneous Environments

Triangle counting is a fundamental building block in graph algorithms. In this article, we propose a block-based triangle counting algorithm to reduce data movement during both sequential and parallel execution. Our block-based formulation makes the algorithm naturally suitable for heterogeneous architectures. The problem of partitioning the adjacency matrix of a graph is well-studied. Our task decomposition goes one step further: it partitions the set of triangles in the graph. By streaming these small tasks to compute resources, we can solve problems that do not fit on a device. We demonstrate the effectiveness of our approach by providing an implementation on a compute node with multiple sockets, cores and GPUs. The current state-of-the-art in triangle enumeration processes the Friendster graph in 2.1 seconds, not including data copy time between CPU and GPU. Using that metric, our approach is 20 percent faster. When copy times are included, our algorithm takes 3.2 seconds. This is 5.6 times faster than the fastest published CPU-only time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A Block-Based Triangle Counting Algorithm on Heterogeneous Environments

Triangle counting is a fundamental building block in graph algorithms. In this paper, we propose a block-based triangle counting algorithm to reduce data movement during both sequential and parallel execution. Our block-based formulation makes the algorithm naturally suitable for heterogeneous architectures. The problem of partitioning the adjacency matrix of a graph is well-studied. Our task decomposition goes one step further: it partitions the set of triangles in the graph. By streaming these small tasks to compute resources, we can solve problems that do not fit on a device. We demonstrate the effectiveness of our approach by providing an implementation on a compute node with multiple sockets, cores and GPUs. The current state-of-the-art in triangle enumeration processes the Friendster graph in 2.1 seconds, not including data copy time between CPU and GPU. Using that metric, our approach is 20 percent faster. When copy times are included, our algorithm takes 3.2 seconds. This is 5.6 times faster than the fastest published CPU-only time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Randomized Cholesky Preconditioning for Graph Partitioning Applications

Graph partitioning has emerged as an area of interest due to its use in various applications in computational research. One way to partition a graph is to solve for the eigenvectors of the corresponding graph Laplacian matrix. This project focuses on the eigensolver LOBPCG and the evaluation of a new preconditioner: Randomized Cholesky Factorization (rchol). This proconditioner was tested for its speed and accuracy against other well-known preconditioners for the method. After experiments were run on several known test matrices, rchol appears to be a better preconditioner for structured matrices. This research was sponsored by National Nuclear Security Administration Minority Serving Institutions Internship Program (NNSA-MSIIP) and completed at host facility Sandia National Laboratories. As such, after discussion of the research project itself, this report contains a brief reflection on experience gained as a result of participating in the NNSA-MSIIP.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Fixed-angle conjectures for the quantum approximate optimization algorithm on regular MaxCut graphs

The quantum approximate optimization algorithm (QAOA) is a near-term combinatorial optimization algorithm suitable for noisy quantum devices. However, little is known about performance guarantees for p > 2. A recent work computing MaxCut performance guarantees for 3-regular graphs conjectures that any d-regular graph evaluated at particular fixed angles has an approximation ratio greater than some worst-case guarantee. In this work, we provide numerical evidence for this fixed angle conjecture for p < 12. We compute and provide these angles via numerical optimization and tensor networks. These fixed angles serve for an optimization-free version of QAOA and have universally good performance on any 3-regular graph. Heuristic evidence is presented for the fixed angle conjecture on graph ensembles, which suggests that these fixed angles are "close" to global optimum. Under the fixed angle conjecture, QAOA has a larger performance guarantee than the Goemans Williamson algorithm on 3-regular graphs for p >= 11.

Wurtz, Jonathan↗
DOE OSTI2020

GPU-Based Static Data-Flow Analysis for Fast and Scalable Android App Vetting

Many popular vetting tools for Android applications use static code analysis techniques. In particular, Interprocedural Data-Flow Graph (IDFG) construction is the computation at the core of Android static data-flow analysis and consumes most of the analysis time. Many analysis tools use a worklist algorithm, an iterative fixed-point approach, to construct the IDFG. In this paper, we observe that a straightforward GPU parallelization of the worklist algorithm leads to significant underutilization of the GPU resources. We identify four performance bottlenecks, namely, frequent dynamic memory allocations, high branch divergence, workload imbalance, and irregular memory access patterns. Accordingly, we propose GDroid, a GPU-based worklist algorithm implementation with multiple fine-grained optimizations tailored to common characteristics of Android applications. The optimizations considered are: matrix-based data structure, memory access-based node grouping, and worklist merging. Our experimental evaluation, performed on 1000 Android applications, shows that the proposed optimizations are beneficial to performance, and GDroid can achieve up to 128X speedups against a plain GPU implementation.

Android security↗
DOE OSTI2021

HAM: Hotspot-Aware Manager for Improving Communications with 3D-Stacked Memory

merging High-Performance Computing (HPC) workloads, such as graph analytics, machine learning, and big data science, are data-intensive. Data-intensive workloads usually present fine-grained memory accesses with limited or no data locality, and thus incur frequent cache misses and low utilization of memory bandwidth. 3D-stacked memory devices such as Hybrid Memory Cube (HMC) and High Bandwidth Memory (HBM) can provide significantly higher bandwidth than conventional memory modules. However, the traditional interfaces and optimization methods for JEDEC DDR devices do not allow to fully exploit the potential performance of 3D-stacked memory with the massive amount of irregular memory accesses of data-intensive applications. In this paper, we propose a novel Hotspot-Aware Manager (HAM) infrastructure for 3D-stacked memory devices capable of optimizing memory access streams via request aggregation, hotspot detection, and in-memory prefetching. %and an associated hotspot-aware page policy. We present the HAM design and implementation, and simulate it on a system using RISC-V embedded cores with attached HMC devices. We extensively evaluate HAM with over 12 benchmarks and applications representing diverse irregular memory access patterns. The results show that, on average, HAM reduces redundant requests by 37.51\% and increases the prefetch buffer hit rate by 4.2 times, compared to a baseline streaming prefetcher. On the selected benchmark set, HAM provides performance gains of 21.81\% in average (up to 34.28\%) and power savings of 35.07\% over a standard 3D-stacked memory.

Wang, Xi↗
DOE OSTI2021

Single-node Partitioned-Memory for Huge Graph Analytics: Cost and Performance Trade-offs

Nonvolatile memory NVDIMMs, available as Intel Optane, are less expensive than DRAM and bring large byte-addressable storage within reach to many applications. Evaluations on graph analytics have shown promising performance only when DRAM is used as a hardware cache (Memory mode). An open question is whether graph applications can exploit Optane and DRAM directly (AppDirect mode) and achieving better-than-DRAM average bandwidth and run times. We evaluate Optane as a volatile pool on two large-scale graph applications with very different computational patterns, Grappolo and Ripples. We show that AppDirect mode can deliver better-than-DRAM performance, by allocating data structures to Optane and DRAM according to their access characteristics, resulting in higher average memory bandwidth and lower average latency. Memory mode provides DRAM-competitive performance with capacity equal to persistent memory. We demonstrate occasional 4x improvement using the latest AppDirect option and frequently observe competitive performance between Optane AppDirect Memory modes and DRAM.

Ghosh, Sayan↗
NASA NTRS1971

A study of the Nordsieck-type predictor-corrector methods

Predictor-corrector schemes are discussed for the numerical integration of initial value problems by computer. Descloux formulas, which are considered modified Nordsieck formulas are studied because of their desirable stability and truncation properties along with the standard Nordsieck formulas. The stability of Nordsieck and modified Nordsieck algorithms are computed, and the results are graphed. Test problems are included as examples for comparing the efficiency of the algorithms.

Eiserike, H. M.↗
NASA NTRS1972

Application of numerical methods to extend capabilities for optimal rocket guidance: report on reentry guidance of shuttle orbiter

Analytical models are presented for optimal trajectories and reentry guidance of the space shuttle orbiter. Major emphasis is placed on the development of a "footprint', which refers to a set of reachable destination positions attainable by the shuttle at a specified terminal altitude. An unconstrained reentry footprint was calculated for a shuttle vehicle which enters the earth's atmosphere at 93 km initial altitude after a deboost from a near earth orbit. The method of computation is briefly described, and graphs are presented which illustrate the footprint and the variation of state and control variables along it. The effects of constraints and of variations in initial state upon the footprint are discussed.

Source record↗
NASA NTRS1986

Modeling of multi-rotor torsional vibrations in rotating machinery using substructuring

The application of FEM modeling techniques to the analysis of torsional vibrations in complex rotating systems is described and demonstrated, summarizing results reported by Soares (1985). A substructuring approach is used for determination of torsional natural frequencies and resonant-mode shapes, steady-state frequency-sweep analysis, identification of dynamically unstable speed ranges, and characterization of transient linear and nonlinear systems. Results for several sample problems are presented in diagrams, graphs, and tables. STORV, a computer code based on this approach, is in use as a preliminary design tool for drive-train torsional analysis in the High Altitude Wind Tunnel at NASA Lewis.

Soares, Fola R.↗
NASA NTRS1989

A model for the distribution of dark matter, galaxies, and the intergalactic medium in a cold dark matter-dominated universe

The spatial distribution of the cold-dark-matter (CDM) and baryonic components of CDM-dominated cosmological models are characterized, summarizing the results of recent theoretical investigations. The evolution and distribution of matter in an Einstein-de Sitter universe on length scales small enough so that the Newtonian approximation is valid is followed chronologically, assuming (1) that the galaxies, CDM, and the intergalactic medium (IGM) are coupled by gravity, (2) that galaxies form by taking mass and momentum from the IGM, and (3) that the IGM responds to the energy input from the galaxies. The results of the numerical computations are presented in extensive graphs and discussed in detail.

Ryu, Dongsu↗