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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Incremental nonnegative matrix factorization based on correlation and graph regularization for matrix completion

Matrix factorization is widely used in recommendation systems, text mining, face recognition and computer vision. As one of the most popular methods, nonnegative matrix factorization and its incremental variants have attracted much attention. The existing incremental algorithms are established based on the assumption of samples are independent and only update the new latent variable of weighting coefficient matrix when the new sample comes, which may lead to inferior solutions. To address this issue, we investigate a novel incremental nonnegative matrix factorization algorithm based on correlation and graph regularizer (ICGNMF). The correlation is mainly used for finding out those correlated rows to be updated, that is, we assume that samples are dependent on each other. We derive the updating rules for ICGNMF by considering the correlation. We also present tests on widely used image datasets, and show ICGNMF reduces the error by comparing other methods.

Zhang, Xiaoxia↗
DOE OSTI2018

BootCMatch: A Software Package for Bootstrap AMG Based on GraphWeighted Matching

This article has two main objectives: one is to describe some extensions of an adaptive Algebraic Multigrid (AMG) method of the form previously proposed by the first and third authors, and a second one is to present a new software framework, named BootCMatch, which implements all the components needed to build and apply the described adaptive AMG both as a stand-alone solver and as a preconditioner in a Krylov method. The adaptive AMG presented is meant to handle general symmetric and positive definite (SPD) sparse linear systems, without assuming any a priori information of the problem and its origin; the goal of adaptivity is to achieve a method with a prescribed convergence rate. The presented method exploits a general coarsening process based on aggregation of unknowns, obtained by a maximum weight matching in the adjacency graph of the system matrix. More specifically, a maximum product matching is employed to define an effective smoother subspace (complementary to the coarse space), a process referred to as compatible relaxation, at every level of the recursive two-level hierarchical AMG process. Results on a large variety of test cases and comparisons with related work demonstrate the reliability and efficiency of the method and of the software.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Scalable Approaches to Selecting Key Entities in Large Networked Infrastructure Systems

This work aims at bringing advances in discrete optimization algorithms to solving practical engineering problems at scale. Often times, in many engineering design problems, there is a need to select a small set of influential or representative elements from a large ground set of entities in an optimal fashion. Submodular optimization provides for a formal way to solve such problems. Common examples with infrastructure systems involve sensor placement and identification of key entities with certain objectives. However, scaling these approaches to large infrastructure systems can be challenging because of the high computational complexity of the overall framework that include the optimization algorithms as well as high-complexity compute-oracles that provide the necessary objective function values. In this work, we explore a well-studied and widely-applicable paradigm, namely leader-selection in a multi-agent networked setting in the context of scalable methodologies. We demonstrate novel frameworks that utilize variations of accelerated submodular optimization algorithms along with linear-algebraic methods that can help accelerate the oracle computations. We further explore this combination in conjunction with graph partitioning paradigms to take advantage of the accelerated algorithms in a distributed setting. Finally we demonstrate the key findings on a practical problem in an operational setting. For this, we leverage an example road network with approximately 18k nodes and 27k edges in a traffic control application, where we seek a limited number of k=200 key intersections. This problem can be solved in a serial setting in just under 5 hours providing more than 2 orders of magnitude speed-up over methods that do not consider acceleration techniques.

Visweswara Sathanur, Arun↗
NASA NTRS1990

Mapping unstructured grid problems to the connection machine

We present a highly parallel graph mapping technique that enables one to solve unstructured grid problems on massively parallel computers. Many implicit and explicit methods for solving discretizated partial differential equations require each point in the discretization to exchange data with its neighboring points every time step or iteration. The time spent communicating can limit the high performance promised by massively parallel computing. To eliminate this bottleneck, we map the graph of the irregular problem to the graph representing the interconnection topology of the computer such that the sum of the distances that the messages travel is minimized. We show that, in comparison to a naive assignment of processors, our heuristic mapping algorithm significantly reduces the communication time on the Connection Machine, CM-2.

Hammond, Steven W.↗
DOE OSTI2024

Using Convex Optimization to Efficiently Apportion Tracer and Pollutant Sources From Point Concentration Observations

Abstract Rivers transport elements, minerals, chemicals, and pollutants produced in their upstream basins. A sample from a river is a mixture of all of its upstream sources, making it challenging to pinpoint the contribution from each individual source. Here, we show how a nested sample design and convex optimization can be used to efficiently unmix downstream samples of a well‐mixed, conservative tracer in a steady state system into the contributions of their upstream sources. Our approach is significantly faster than previous methods. We represent the river's sub‐catchments, defined by sampling sites, using a directed acyclic graph. This graph is used to build a convex optimization problem which, thanks to its convexity, can be quickly solved to global optimality—in under a second on desktop hardware for data sets of ∼100 samples or fewer. Uncertainties in the upstream predictions can be generated using Monte Carlo resampling. We provide an open‐source implementation of this approach in Python. The inputs required are straightforward: a table containing sample locations and observed tracer concentrations, along with a D8 flow‐direction raster map. As a case study, we use this method to map the elemental geochemistry of sediment sources for rivers draining the Cairngorms mountains, UK. This method could be extended to non‐conservative and non‐steady state tracers. We also show, theoretically, how multiple tracers could be simultaneously inverted to recover upstream run‐off or erosion rates as well as source concentrations. Overall, this approach can provide valuable insights to researchers in various fields, including water quality, geochemical exploration, geochemistry, hydrology, and wastewater epidemiology.

Barnes, Richard↗
DOE OSTI2017

APT malware static trace analysis through bigrams and graph edit distance

Research and business organizations are vulnerable to attack by malware, particularly advanced persistent threat malware tailored for a specific target. Malware identification is made more difficult because samples can be subtly altered to avoid detection by methods that check for an identical match to known code. Different versions of an original piece of malware form a malware family. And when new malicious software is identified, reverse engineers seek to identify its origin and purpose. Knowing whether new malware is from a known family or a previously unobserved family aids the efficiency of reverse engineers. Furthermore, this article presents a three-stage method to classify new malware into a family by comparing its similarity to existing static traces, and assigning it to the most similar family. First, a fast filtering method creates a shortlist of samples with some similarity to the new malware, using a simple bigram comparison of the instructions. The second stage takes the call graph view of the shortlisted static traces and uses simulated annealing to estimate the graph edit distance, a measure of dissimilarity between graphs. Finally, a random forest classifier combines the previous two results to predict the family to which a new sample belongs. Our paper also considers how to detect when malware is from a new family.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2019

Using Graph Coloring to Compute Total Derivatives More Efficiently in OpenMDAO

When they are applicable, gradient based optimization algorithms are the most efficient way to solve design optimization problems. Although gradient based methods are generally efficient, they can be made significantly more so through the usage of analytic techniques to compute the necessary total derivatives. The traditional forward (direct) and reverse (adjoint) analytic techniques have computational costs that scale linearly with the number of design variables and the number of constraints, respectively. In this work, we present an application of a graph coloring algorithm to the analytic techniques for computing total derivative Jacobians in order to achieve much better computational scaling than the pure analytic methods can provide alone. A detailed theoretical explanation of how coloring algorithms interact with analytic derivative methods is presented that illustrates specific types of sparsity patterns that must be present in total derivative Jacobians in order for this coloring technique to be effective. The new technique has been implemented as a feature in the OpenMDAO framework and the implementation is demonstrated on two example problems. The performance on the example problems up to 50% reduction in compute cost for optimizations with bi-directional coloring compared to traditional constraint aggregation. Additionally, the results show how coloring technique alleviates some of the numerical difficulties that constraint aggregation can cause, leading to the ability to solve larger problems. It is expected that the new method will have wide applicability to multidisciplinary optimization problems, and that its availability in OpenMDAO will offer significant computational savings for users without the need for them to implement the coloring algorithm themselves.

Trajectory↗
DOE OSTI2018

Optimal structure and parameter learning of Ising models

Reconstruction of the structure and parameters of an Ising model from binary samples is a problem of practical importance in a variety of disciplines, ranging from statistical physics and computational biology to image processing and machine learning. The focus of the research community shifted toward developing universal reconstruction algorithms that are both computationally efficient and require the minimal amount of expensive data. Here, we introduce a new method, interaction screening, which accurately estimates model parameters using local optimization problems. The algorithm provably achieves perfect graph structure recovery with an information-theoretically optimal number of samples, notably in the low-temperature regime, which is known to be the hardest for learning. Here, the efficacy of interaction screening is assessed through extensive numerical tests on synthetic Ising models of various topologies with different types of interactions, as well as on real data produced by a D-Wave quantum computer. Finally, this study shows that the interaction screening method is an exact, tractable, and optimal technique that universally solves the inverse Ising problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Network-Level Traffic Signal Cooperation: A Higher-Order Conflict Graph Approach

Traffic signal control and cooperation are extremely important to alleviate traffic congestion in a large traffic network. This study develops a higher-order conflict graph approach for network-wide traffic signal control and cooperation. A conflict graph is applied to model the traffic signal configurations, which identifies the conflict and unconflicted movements for each intersection. In conflict graph, the node represents each movement. The weight of each node can be defined as traffic volume, queue length, fuel consumption, or any weighted combinations of these measurements. The calculation of the optimal green light duration and green light sequence (for different movements) is equivalent to sequentially finding the maximum weight independent set (MWIS) in the conflict graph. The conflict graph also provides a uniform and efficient way to connect traffic signal operations among nearby intersections spatially. Then, we introduced the concept of the k -th order neighborhood to model the degree of connectivity between each movement to the movements at upstream or downstream intersections. The weight of each node in the higher-order conflict graph not only represents its own congestion level, but also relates to the traffic conditions of nearby intersections. Through this approach, the cooperation of multiple intersections can be realized by incorporating their spatial connectivity into conflict graph and solving the MWIS problem. A simulation network is built in SUMO to test the effectiveness of the proposed method. Results suggested that the proposed model outperformed other state-of-the-art signal control methods. Also, the scheme maintains good performance under varying traffic demands.

42 ENGINEERING↗
DOE OSTI2024

Addressing GPU memory limitations for Graph Neural Networks in High-Energy Physics applications

Introduction Reconstructing low-level particle tracks in neutrino physics can address some of the most fundamental questions about the universe. However, processing petabytes of raw data using deep learning techniques poses a challenging problem in the field of High Energy Physics (HEP). In the Exa.TrkX Project, an illustrative HEP application, preprocessed simulation data is fed into a state-of-art Graph Neural Network (GNN) model, accelerated by GPUs. However, limited GPU memory often leads to Out-of-Memory (OOM) exceptions during training, due to the large size of models and datasets. This problem is exacerbated when deploying models on High-Performance Computing (HPC) systems designed for large-scale applications. Methods We observe a high workload imbalance issue during GNN model training caused by the irregular sizes of input graph samples in HEP datasets, contributing to OOM exceptions. We aim to scale GNNs on HPC systems, by prioritizing workload balance in graph inputs while maintaining model accuracy. Our paper introduces diverse balancing strategies aimed at decreasing the maximum GPU memory footprint and avoiding the OOM exception, across various datasets. Results Our experiments showcase memory reduction of up to 32.14% compared to the baseline. We also demonstrate the proposed strategies can avoid OOM in application. Additionally, we create a distributed multi-GPU implementation using these samplers to demonstrate the scalability of these techniques on the HEP dataset. Discussion By assessing the performance of these strategies as data loading samplers across multiple datasets, we can gauge their effectiveness in both single-GPU and distributed environments. Our experiments, conducted on datasets of varying sizes and across multiple GPUs, broaden the applicability of our work to various GNN applications that handle input datasets with irregular graph sizes.

Lee, Claire Songhyun↗
DOE OSTI2016

Post-processing interstitialcy diffusion from molecular dynamics simulations

An algorithm to rigorously trace the interstitialcy diffusion trajectory in crystals is developed. The algorithm incorporates unsupervised learning and graph optimization which obviate the need to input extra domain specific information depending on crystal or temperature of the simulation. The algorithm is implemented in a flexible framework as a post-processor to molecular dynamics (MD) simulations. We describe in detail the reduction of interstitialcy diffusion into known computational problems of unsupervised clustering and graph optimization. We also discuss the steps, computational efficiency and key components of the algorithm. Using the algorithm, thermal interstitialcy diffusion from low to near-melting point temperatures is studied. We encapsulate the algorithms in a modular framework with functionality to calculate diffusion coefficients, migration energies and other trajectory properties. The study validates the algorithm by establishing the conformity of output parameters with experimental values and provides detailed insights for the interstitialcy diffusion mechanism. The algorithm along with the help of supporting visualizations and analysis gives convincing details and a new approach to quantifying diffusion jumps, jump-lengths, time between jumps and to identify interstitials from lattice atoms. -- Graphical abstract:.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Uncertainty quantification for molecular property predictions with graph neural architecture search

Graph Neural Networks (GNNs) have emerged as a prominent class of data-driven methods for molecular property prediction. However, a key limitation of typical GNN models is their inability to quantify uncertainties in the predictions. This capability is crucial for ensuring the trustworthy use and deployment of models in downstream tasks. To that end, we introduce AutoGNNUQ, an automated uncertainty quantification (UQ) approach for molecular property prediction. AutoGNNUQ leverages architecture search to generate an ensemble of high-performing GNNs, enabling the estimation of predictive uncertainties. Our approach employs variance decomposition to separate data (aleatoric) and model (epistemic) uncertainties, providing valuable insights for reducing them. In our computational experiments, we demonstrate that AutoGNNUQ outperforms existing UQ methods in terms of both prediction accuracy and UQ performance on multiple benchmark datasets, and generalizes well to out-of-distribution datasets. Additionally, we utilize t-SNE visualization to explore correlations between molecular features and uncertainty, offering insight for dataset improvement. AutoGNNUQ has broad applicability in domains such as drug discovery and materials science, where accurate uncertainty quantification is crucial for decision-making.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

RANDOM WALKS AND EFFECTIVE OPTICAL DEPTH IN RELATIVISTIC FLOW

We investigate the random walk process in relativistic flow. In the relativistic flow, photon propagation is concentrated in the direction of the flow velocity due to the relativistic beaming effect. We show that in the pure scattering case, the number of scatterings is proportional to the size parameter ξ ≡ L/l {sub 0} if the flow velocity β ≡ v/c satisfies β/Γ >> ξ{sup –1}, while it is proportional to ξ{sup 2} if β/Γ << ξ{sup –1}, where L and l {sub 0} are the size of the system in the observer frame and the mean free path in the comoving frame, respectively. We also examine the photon propagation in the scattering and absorptive medium. We find that if the optical depth for absorption τ{sub a} is considerably smaller than the optical depth for scattering τ{sub s} (τ{sub a}/τ{sub s} << 1) and the flow velocity satisfies β≫√(2τ{sub a}/τ{sub s}), then the effective optical depth is approximated by τ{sub *} ≅ τ{sub a}(1 + β)/β. Furthermore, we perform Monte Carlo simulations of radiative transfer and compare the results with the analytic expression for the number of scatterings. The analytic expression is consistent with the results of the numerical simulations. The expression derived in this study can be used to estimate the photon production site in relativistic phenomena, e.g., gamma-ray burst and active galactic nuclei.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Line-Graph Approach to Spiral Spin Liquids

Competition among exchange interactions is able to induce novel spin correlations on a bipartite lattice without geometrical frustration. A prototype example is the spiral spin liquid, which is a correlated paramagnetic state characterized by subdimensional degenerate propagation vectors. Here, using spectral graph theory, we show that spiral spin liquids on a bipartite lattice can be approximated by a further-neighbor model on the corresponding line-graph lattice that is nonbipartite, thus broadening the space of candidate materials that may support the spiral spin liquid phases. As examples, we examine neutron scattering experiments performed on two spinel compounds, ZnCr 2 Se 4 and CuInCr 4 Se 8 , to demonstrate the feasibility of this new approach and expose its possible limitations in experimental realizations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Matrix-Free High-Performance Saddle-Point Solvers for High-Order Problems in \(\boldsymbol{H}(\operatorname{\textbf{div}})\)

Here, this work describes the development of matrix-free GPU-accelerated solvers for high-order finite element problems in H(div). The solvers are applicable to grad-div and Darcy problems in saddle-point formulation, and have applications in radiation diffusion and porous media flow problems, among others. Using the interpolation–histopolation basis, efficient matrix-free preconditioners can be constructed for the (1, 1)-block and Schur complement of the block system. With these approximations, block-preconditioned MINRES converges in a number of iterations that is independent of the mesh size and polynomial degree. The approximate Schur complement takes the form of an M-matrix graph Laplacian and therefore can be well-preconditioned by highly scalable algebraic multigrid methods. High-performance GPU-accelerated algorithms for all components of the solution algorithm are developed, discussed, and benchmarked. Numerical results are presented on a number of challenging test cases, including the “crooked pipe” grad-div problem, the SPE10 reservoir modeling benchmark problem, and a nonlinear radiation diffusion test case.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1984

Generalized serial search code acquisition - The equivalent circular state diagram approach

A transform-domain method for deriving the generating function of the acquisition process resulting from an arbitrary serial search strategy is presented. The method relies on equivalent circular state diagrams, uses Mason's formula from flow-graph theory, and employs a minimum number of required parameters. The transform-domain approach is briefly described and the concept of equivalent circular state diagrams is introduced and exploited to derive the generating function and resulting mean acquisition time for three particular cases of interest, the continuous/center Z search, the broken/center Z search, and the expanding window search. An optimization of the latter technique is performed whereby the number of partial windows which minimizes the mean acquisition time is determined. The numerical results satisfy certain intuitive predictions and provide useful design guidelines for such systems.

Polydoros, A.↗
NASA NTRS1986

Elimination sequence optimization for SPAR

SPAR is a large-scale computer program for finite element structural analysis. The program allows user specification of the order in which the joints of a structure are to be eliminated since this order can have significant influence over solution performance, in terms of both storage requirements and computer time. An efficient elimination sequence can improve performance by over 50% for some problems. Obtaining such sequences, however, requires the expertise of an experienced user and can take hours of tedious effort to affect. Thus, an automatic elimination sequence optimizer would enhance productivity by reducing the analysts' problem definition time and by lowering computer costs. Two possible methods for automating the elimination sequence specifications were examined. Several algorithms based on the graph theory representations of sparse matrices were studied with mixed results. Significant improvement in the program performance was achieved, but sequencing by an experienced user still yields substantially better results. The initial results provide encouraging evidence that the potential benefits of such an automatic sequencer would be well worth the effort.

Hogan, Harry A.↗