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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 OSTI2022

Projecting the Thermal Response in a HTGR-Type System during Conduction Cooldown Using Graph-Laplacian Based Machine Learning

Accurate prediction of an off-normal event in a nuclear reactor is dependent upon the availability of sensory data, reactor core physical condition, and understanding of the underlying phenomenon. This work presents a method to project the data from some discrete sensory locations to the overall reactor domain during conduction cooldown scenarios similar to High Temperature Gas-cooled Reactors (HTGRs). The existing models for conductive cooldown in a heterogeneous multi-body system, such as an assembly of prismatic blocks or pebble beds relies on knowledge of the thermal contact conductance, requiring significant knowledge of local thermal contacts and heat transport possibilities across those contacts. With a priori knowledge of bulk geometry features and some discrete sensors, a machine learning approach was devised. The presented work uses an experimental facility to mimic conduction cooldown with an assembly of 68 cylindrical rods initially heated to 1200 K. High-fidelity temperature data were collected using an infrared (IR) camera to provide training data to the model and validate the predicted temperature data. The machine learning approach used here first converts the macroscopic bulk geometry information into Graph-Laplacian, and then uses the eigenvectors of the Graph-Laplacian to develop Kernel functions. Support vector regression (SVR) was implemented on the obtained Kernels and used to predict the thermal response in a packed rod assembly during a conduction cooldown experiment. The usage of SVR modeling differs from most models today because of its representation of thermal coupling between rods in the core. When trained with thermographic data, the average normalized error is less than 2% over 400 s, during which temperatures of the assembly have dropped by more than 500 K. The rod temperature prediction performance was significantly better for rods in the interior of the assembly compared to those near the exterior, likely due to the model simplification of the surroundings.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

Multilevel Spectral Coarsening for Graph Laplacian Problems with Application to Reservoir Simulation

We extend previously developed two-level coarsening procedures for graph Laplacian problems written in a mixed saddle point form to the fully recursive multilevel case. The resulting hierarchy of discretizations gives rise to a hierarchy of upscaled models, in the sense that they provide approximation in the natural norms (in the mixed setting). This property enables us to utilize them in three applications: (i) as an accurate reduced model, (ii) as a tool in multilevel Monte Carlo simulations (in application to finite volume discretizations), and (iii) for providing a sequence of nonlinear operators in a full approximation scheme for solving nonlinear pressure equations discretized by the conservative two-point flux approximation. Finally, we illustrate the potential of the proposed multilevel technique in all three applications on a number of popular benchmark problems used in reservoir simulation.

multilevel Monte Carlo↗
DOE OSTI2023

Protection Against Graph-Based False Data Injection Attacks on Power Systems

Graph signal processing (GSP) has emerged as a powerful tool for practical network applications, including power system monitoring. By representing power system voltages as smooth graph signals, recent research has focused on developing GSP-based methods for state estimation, attack detection, and topology identification. Included, efficient methods have been developed for detecting false data injection (FDI) attacks, which until now were perceived as non-smooth with respect to the graph Laplacian matrix. Consequently, these methods may not be effective against smooth FDI attacks. In this paper, we propose a graph FDI (GFDI) attack that minimizes the Laplacian-based graph total variation (TV) under practical constraints. In addition, we develop a low-complexity algorithm that solves the non-convex GDFI attack optimization problem using ell_1-norm relaxation, the projected gradient descent (PGD) algorithm, and the alternating direction method of multipliers (ADMM). We then propose a protection scheme that identifies the minimal set of measurements necessary to constrain the GFDI output to high graph TV, thereby enabling its detection by existing GSP-based detectors. Our numerical simulations on the IEEE-57 bus test case reveal the potential threat posed by well-designed GSP-based FDI attacks. Moreover, we demonstrate that integrating the proposed protection design with GSP-based detection can lead to significant hardware cost savings compared to previous designs of protection methods against FDI attacks.

Morgenstern, Gal↗
DOE OSTI2023

Gaps labeling theorem for the bubble-diamond self-similar graphs

Abstract Motivated by the appearance of fractals in several areas of physics, especially in solid state physics and the physics of aperiodic order, and in other sciences, including the quantum information theory, we present a detailed spectral analysis for a new class of fractal-type diamond graphs, referred to as bubble-diamond graphs, and provide a gap-labeling theorem in the sense of Bellissard for the corresponding probabilistic graph Laplacians using the technique of spectral decimation. Labeling the gaps in the Cantor set by the normalized eigenvalue counting function, also known as the integrated density of states, we describe the gap labels as orbits of a second dynamical system that reflects the branching parameter of the bubble construction and the decimation structure. The spectrum of the natural Laplacian on limit graphs is shown generically to be pure point supported on a Cantor set, though one particular graph has a mixture of pure point and singularly continuous components.

Physics↗
DOE OSTI2020

Online Event Detection in Synchrophasor Data with Graph Signal Processing

Online detection of anomalies is crucial to enhancing the reliability and resiliency of power systems. We propose a novel data-driven online event detection algorithm with synchrophasor data using graph signal processing. In addition to being extremely scalable, our proposed algorithm can accurately capture and leverage the spatio-temporal correlations of the streaming PMU data. This paper also develops a general technique to decouple spatial and temporal correlations in multiple time series. Finally, we develop a unique framework to construct a weighted adjacency matrix and graph Laplacian for product graph. Case studies with real-world, large-scale synchrophasor data demonstrate the scalability and accuracy of our proposed event detection algorithm. Compared to the state-of-the-art benchmark, the proposed method not only achieves higher detection accuracy but also yields higher computational efficiency.

Event detection↗
DOE OSTI2020

Online Event Detection in Synchrophasor Data with Graph Signal Processing

Online detection of anomalies is crucial to enhancing the reliability and resiliency of power systems. We propose a novel data-driven online event detection algorithm with synchrophasor data using graph signal processing. In addition to being extremely scalable, our proposed algorithm can accurately capture and leverage the spatio-temporal correlations of the streaming PMU data. This paper also develops a general technique to decouple spatial and temporal correlations in multiple time series. Finally, we develop a unique framework to construct a weighted adjacency matrix and graph Laplacian for product graph. Case studies with real-world, large-scale synchrophasor data demonstrate the scalability and accuracy of our proposed event detection algorithm. Compared to the state-of-the-art benchmark, the proposed method not only achieves higher detection accuracy but also yields higher computational efficiency.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Reduced-Order Models of Static Power Grids based on Spectral Clustering

For large-scale interconnected power systems that cover large geographical areas, certain electrical studies are required so that appropriate decisions ensure system reliability and low cost. For such studies, it is often neither practical nor necessary to model in detail the entire power system, which is increasingly complex due to a more diverse range of grid assets to choose from in both short and long-term planning. The goal of this paper is to present a methodology to reduce the order of large-scale power networks based on spectral graph theory given that current methods for static network reduction are not scalable. A brief analysis of some spectral clustering properties to determine which graph Laplacian matrix should be used and why is included. The analysis shows that the utilization of the normalized graph Laplacian is more advantageous for clustering purposes. Techniques are proposed to approximate cost functions for the aggregated generators. This is done via linear regression. The reduced-order model obtained with the proposed methodology has an accuracy above 94% and solves the scalability issue commonly present in other reduction methods. If the utilization of the reduced-order model is either constrained to load levels above mid-peak demand, or cost functions of aggregated units are approximated via a piecewise quadratic approach, then the error distribution is in the order of 10^-3. .

Baquedano-Aguilar, Mario D.↗
DOE OSTI2024

A Performance and Energy Study of GPU-Resident Preconditioners for Conjugate Gradient Solvers: In the Context of Existing and Novel Approaches

Optimizing a particular subprogram out of the set of Basic (sparse) Linear Algebra Subprograms (BLAS) for a given architecture is a common topic of research. In applications, however, these BLAS functions rarely appear in isolation; usually, many of them are used together, in various combinations and with varying inputs. As the need to solve a large, sparse linear system is ubiquitous throughout HPC applications, linear solvers constitute a realistic, sufficiently complex and well-defined representative use case for composite BLAS routines. To this end, based on a representative set of matrices drawn from a diverse set of fields, we present a framework to study, from the performance and energy perspective, the efficacy of GPU- resident parallel Conjugate Gradient (CG) linear solver with different preconditioner options, including Gauss-Seidel, Jacobi, and incomplete Cholesky. We also propose a novel GPU-based preconditioner, in which the triangular solves are approximated by an iterative process. The development of this preconditioner was motivated by solving large graph Laplacian linear systems, for which the existing preconditioners either perform slow on GPU-based platforms or are not applicable. We compare the performance of these preconditioners on different hardware accelerator architectures, i.e., AMD MI250X, MI100, Nvidia A100, V100, and Jetson. Our experiments reveal performance trade-offs and provide information on how to select the best strategy for the given linear system, dictated by its properties, and the platform of interest. We demonstrate the application of our novel preconditioner for solving CG and graph Laplacian systems. Overall, the framework can be utilized as a benchmark to guide informed decisions in choosing a specific preconditioner, i.e., whether it is better to rely on the performance of a triangular solver or on the performance of sparse matrix-vector product. Finally, by considering power consumption to solve the linear systems, we report the energy footprint for the solvers.

Preconditioned Conjugate Gradient, GPUs, iterative↗
DOE OSTI2026

Polynomial-time preparation of low-temperature Gibbs states for two-dimensional toric code

In this work, we propose a polynomial-time algorithm for preparing the Gibbs state of the two-dimensional toric code Hamiltonian at any temperature, starting from any initial state, significantly improving upon prior estimates that suggested exponential scaling with inverse temperature. We prove that fast mixing at low temperature for the two-dimensional toric code can be achieved by augmenting local jump operators with simple global jump operators, which enable efficient transitions between logical sectors. To establish tight lower bounds on the spectral gap, we introduce a new reduction method that eventually maps the problem to estimating the spectral gap of a perturbed graph Laplacian on a stair graph. Our proof also shows that the Lindblad dynamics with a digitally implemented low-temperature local Davies generator is able to efficiently drive the quantum state toward the ground state manifold.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Flexible Machine Learning-Based Cyberattack Detection Using Spatiotemporal Patterns for Distribution Systems

This letter develops a flexible machine learning detection method for cyberattacks in distribution systems considering spatiotemporal patterns. Spatiotemporal patterns are recognized by the graph Laplacian based on system-wide measurements. A flexible Bayes classifier (BC) is used to train spatiotemporal patterns which could be violated when cyberattacks occur. Cyberattacks are detected by using flexible BCs online. The effectiveness of the developed method is demonstrated through standard IEEE 13- and 123-node test feeders.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

The concept of spin ice graphs and a field theory for their charges

Originally detected in rare earth pyrochlores, spin ice physics is now being artificially extended to a variety of geometries that control collective behavior and exotic properties, making graph theory their proper framework. We relate spin ice notions, such as ice rule, ice manifold, Coulomb phases, charges, and monopoles, to graph-theoretical notions, such as balance, in/out-degrees, and Euler paths. We then propose a field-theoretical treatment in which topological charges and monopoles are the degrees of freedom, while the binary spins are subsumed in an entropic interaction among charges. We show that for a spin ice on a graph in a Gaussian approximation, the kernel of the entropic interaction is the inverse of the graph Laplacian, and we compute screening functions from the graph spectra as Green operators for the screened Poisson problem on a graph. We then apply the treatment to star graphs, tournaments, cycles, and regular spin ice in different dimensions. Our aim is twofold: to set spin ice physics in a proper graph setting, where only topological rather than geometrical notions hold, and to invite graph theorists to contribute their powerful tools to the field of spin ice.

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

Directional Laplacian Centrality for Cyber Situational Awareness

Cyber operations is drowning in diverse, high-volume, multi-source data. To get a full picture of current operations and identify malicious events and actors, analysts must see through data generated by a mix of human activity and benign automated processes. Although many monitoring and alert systems exist, they typically use signature-based detection methods. We introduce a general method rooted in spectral graph theory to discover patterns and anomalies without a priori knowledge of signatures. We derive and propose a new graph-theoretic centrality measure based on the derivative of the graph Laplacian matrix in the direction of a vertex. To build intuition about our measure, we show how it identifies the most central vertices in standard network datasets and compare to other graph centrality measures. Finally, we focus our attention on studying its effectiveness in identifying important IP addresses in network flow data. Using both real and synthetic network flow data, we conduct several experiments to test our measure’s sensitivity to two types of injected attack profiles and show that vertices participating in injected attack profiles exhibit noticeable changes in our centrality measures, even when the injected anomalies are relatively small, and in the presence of simulated network dynamics.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2022

Randomized Cholesky Preconditioning for Graph Partitioning Applications

A graph is a mathematical representation of a network; we say it consists of a set of vertices, which are connected by edges. Graphs have numerous applications in various fields, as they can model all sorts of connections, processes, or relations. For example, graphs can model intricate transit systems or the human nervous system. However, graphs that are large or complicated become difficult to analyze. This is why there is an increased interest in the area of graph partitioning, reducing the size of the graph into multiple partitions. For example, partitions of a graph representing a social network might help identify clusters of friends or colleagues. Graph partitioning is also a widely used approach to load balancing in parallel computing. The partitioning of a graph is extremely useful to decompose the graph into smaller parts and allow for easier analysis. There are different ways to solve graph partitioning problems. For this work, we focus on a spectral partitioning method which forms a partition based upon the eigenvectors of the graph Laplacian (details presented in Acer, et. al.). This method uses the LOBPCG algorithm to compute these eigenvectors. LOBPCG can be accelerated by an operator called a preconditioner. For this internship, we evaluate a randomized Cholesky (rchol) preconditioner for its effectiveness on graph partitioning problems with LOBPCG. We compare it with two standard preconditioners: Jacobi and Incomplete Cholesky (ichol). This research was conducted from August to December 2021 in conjunction with Sandia National Laboratories.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Monitoring and flaw detection during wire-based directed energy deposition using in-situ acoustic sensing and wavelet graph signal analysis

The goal of this work is to detect flaw formation in the wire-based directed energy deposition (W-DED) process using in-situ sensor data. The W-DED studied in this work is analogous to metal inert gas electric arc welding. The adoption of W-DED in industry is limited because the process is susceptible to stochastic and environmental disturbances that cause instabilities in the electric arc, eventually leading to flaw formation, such as porosity and suboptimal geometric integrity. Moreover, due to the large size of W-DED parts, it is difficult to detect flaws post-process using non-destructive techniques, such as X-ray computed tomography. Accordingly, the objective of this work is to detect flaw formation in W-DED parts using data acquired from an acoustic (sound) sensor installed near the electric arc. To realize this objective, we develop and apply a novel wavelet integrated graph theory approach. The approach extracts a single feature called graph Laplacian Fiedler number from the noise-contaminated acoustic sensor data, which is subsequently tracked in a statistical control chart. Using this approach, the onset of various types of flaws are detected with a false alarm rate less-than 2%. This work demonstrates the potential of using advanced data analytics for in-situ monitoring of W-DED.

42 ENGINEERING↗
DOE OSTI2026

Soft factorisation and exponentiation from Schwinger-space geometry

Infrared divergences in Quantum Field Theory govern the low-energy dynamics of many physical theories, and their understanding is a crucial ingredient in predicting the outcomes of collider experiments. We present a novel approach to deriving the structure of these divergences by employing the Schwinger parametrization of Feynman integrals. After using tropical geometry to identify divergent limits, we study the all-orders asymptotic properties of Feynman diagrams via matrix manipulations of graph Laplacians, which allows us to analyse their IR behaviour systematically. We explicitly demonstrate the soft-hard factorization of the integrand for a broad class of diagrams, and reveal that when written in terms of worldline distances, topologically distinct diagrams asymptote to the same integrand at leading order in the soft limit. In particular, for the case of Quantum Electrodynamics (with massive fermions), we use this fact to show how ladder-type diagrams combine in Schwinger-parameter space to yield the correct exponentiated soft anomalous dimension. This framework provides a foundation for extending these methods to more complex theories like Quantum Chromodynamics and offers a pathway towards a systematic understanding of infrared divergences in perturbative amplitudes.

Factorization↗
DOE OSTI2025

Physics-based stabilized finite element approximations of the Poisson–Nernst–Planck equations

We present and analyze two stabilized finite element methods for solving numerically the Poisson–Nernst–Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for the ion equations, whereas the discrete equation for the electric potential need not be stabilized. Discrete solutions stemmed from the first algorithm preserve both maximum and minimum discrete principles. For the second algorithm, its discrete solutions are conceived so that they hold discrete principles and obey an entropy law provided that an acuteness condition is imposed for meshes. Remarkably the latter is found to be unconditionally stable. We validate our methodology through transient numerical experiments that show convergence toward steady-state solutions.

97 MATHEMATICS AND COMPUTING↗