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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Orbital design of flat bands in non-line-graph lattices via line-graph wave functions

Line-graph (LG) lattices are known for having flat bands (FBs) from the destructive interference of Bloch wave functions encoded in only lattice symmetry. In this work, we develop a generic atomic/molecular orbital design principle for FBs in non-LG lattices. Based on linear combination of atomic orbital theory, we demonstrate that the underlying wave-function symmetry of FBs in a LG lattice can be transformed into the atomic/molecular orbital symmetry in a non-LG lattice. We illustrate such orbital-designed topological FBs in three 2D non-LG, square, trigonal, and hexagonal lattices, where the designed orbitals faithfully reproduce the corresponding lattice symmetries of checkerboard, kagome, and diatomic-kagome lattices, respectively. Interestingly, systematic design of FBs with a high Chern number is also achieved based on the same principle. Fundamentally our theory enriches the FB physics; practically, it significantly expands the scope of FB materials, since most materials have multiple atomic/molecular orbitals at each lattice site, rather than a single s orbital mandated in graph theory and generic lattice models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Scalable edge clustering of dynamic graphs via weighted line graphs

Timestamped relational datasets consisting of records (or connections) between pairs of entities are ubiquitous in network science. For applications like peer-to-peer communication, email, various social network interactions, and computer network security, it is useful to organize these records into groups based on how and when they are occurring. Weighted line graphs offer a natural way to model how records are related in such datasets but for large real-world graph topologies, building and utilizing the line graph is prohibitively expensive. Here, we present the framework to cluster the edges of a dynamic graph via the associated line graph that contains two major contributions. The first is a method to work with the line graph implicitly and the second is a distributed scale implementation of an agglomerative hierarchical graph clustering algorithm. We outline a novel hierarchical dynamic graph edge clustering approach that efficiently breaks massive relational datasets into small sets of edges containing events at various timescales. This is in stark contrast to traditional graph clustering algorithms that prioritize highly connected (clique-like) community structures. Our approach relies on constructing a sufficient subgraph of a weighted line graph and applying a hierarchical agglomerative clustering. This approach is related to scalable techniques from spatial clustering, nonlinear-dimension reduction, topological data analysis, and draws particular inspiration from HDBSCAN. As an edge clustering, this method yields an overlapping node clustering. Our algorithm is parallelizable and we demonstrate efficient clustering of a billion-scale, real-world dynamic graph into small edge sets that correlate in topology and time. The entire clustering process for a graph with tens of billions of edges takes just a few minutes of run time on 256 nodes of a distributed compute environment. We argue how the output of the edge clustering is useful for a multitude of data visualization and powerful machine learning tasks, both involving the original massive dynamic graph data and metadata associated with the nodes and edges. Finally, we describe how this approach can be extended to dynamic hypergraphs and dynamic graphs/hypergraphs with unstructured data living on vertices and edges.

Data Analysis↗
DOE OSTI2021

Non-Hermitian topological states in 2D line-graph lattices: evolving triple exceptional points on reciprocal line graphs

Non-Hermitian (NH) topological states, such as the doubly-degenerate nodes dubbed as exceptional points (EPs) in Bloch band structure of 2D lattices driven by gain and loss, have attracted much recent interest. We demonstrate theoretically that in the three-site edge-centered lattices, i.e. the so-called line-graph lattices, such as kagome lattice which is a line graph of hexagonal lattice, there exist three types of triply-degenerate EPs evolving intriguingly on another set of line graphs in the reciprocal space. A single TEP (STEP) with ±1/3 topological charge moves faithfully along the edges of reciprocal line graphs with varying gain and loss, while two STEPs merge distinctively into one unconventional orthogonal double TEP (DTEP) with ±2/3 charge at the vertices, which is characterized with two ordinary self-orthogonal eigenfunctions but one surprising 'orthogonal' eigenfunction. Differently, in a modified line-graph lattice with an off-edge-center site, the ordinary coalesced state of DTEPs emerges with three identical self-orthogonal eigenfunctions. Such NH states and their evolution can be generally realized in various artificial systems, such as photonic and sonic crystals, where light and sonic vortex beams with different fractional twisting can be found. Our findings shed new light on fundamental understanding of gapless topological states in NH systems in terms of creation and evolution of high-order EPs, and open up new research directions to further link line graph and flow network theory coupled with topological physics, especially under non-equilibrium gain/loss conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Parallel Algorithms for Efficient Computation of High-Order Line Graphs of Hypergraphs

This paper considers structures of systems beyond dyadic (pairwise) interactions and investigates mathematical modeling of multi-way interactions and connections as hypergraphs, where captured relationships among system entities are set-valued. To date, in most situations, entities in a hypergraph are considered connected as long as there is at least one common ``neighbor''. However, minimal commonality sometimes discards the ``strength'' of connections and interactions among groups. To this end, considering the ``width'' of a connection, referred to as the \emph{$s$-overlap} of neighbors, provides more meaningful insights into how closely the communities or entities interact with each other. In addition, $s$-overlap computation is the fundamental kernel to construct the line graph of a hypergraph, a low-order approximation of the hypergraph which can carry significant information about the original hypergraph. Subsequent stages of a data analytics pipeline then can apply highly-tuned graph algorithms on the line graph to reveal important features. Given a hypergraph, computing the $s$-overlaps by exhaustively considering all pairwise entities can be computationally prohibitive. To tackle this challenge, we develop efficient algorithms to compute $s$-overlaps and the corresponding line graph of a hypergraph. We propose several heuristics to avoid execution of redundant work and improve performance of the $s$-overlap computation. Our parallel algorithm, combined with these heuristics, is orders of magnitude (more than $10\times$) faster than the naive algorithm in all cases and the SpGEMM algorithm with filtration in most cases (especially with large $s$ value).

hypergraph algorithms, graph algorithms, parallel ↗
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 OSTI2022

pnnl/NWHypergraph

NWHypergraph is a C++ hypergraph processing framework for shared-memory architecture. NWHypergraph provides efficient algorithms to construct s-line graphs, a lower-order approximation of a given hypergraph, and computes different graph metrics of a s-line graph such as s-connected components, s-betweenness centrality, s-closeness centrality, etc. It also provides Python APIs for s-line graph computation. The Python APIs are provided using Pybind11

Lumsdaine, Andrew↗
DOE OSTI2021

Screening two-dimensional materials with topological flat bands

The topological flat band (TFB) has been proposed theoretically in various lattice models, to exhibit a rich spectrum of intriguing physical behaviors. However, the experimental demonstration of flat band (FB) properties has been severely hindered by the lack of materials realization. In this study, by screening materials from a first-principles materials database, we identify a group of two-dimensional materials with TFBs near the Fermi level, covering some simple line-graph and generalized line-graph FB lattice models. These include the kagome sublattice of O in Ti O 2 yielding a spin-unpolarized TFB, and that of V in ferromagnetic V 3 F 8 yielding a spin-polarized TFB. The monolayer Nb 3 Te Cl 7 and its counterparts from element substitution are found to be breathing-kagome-lattice crystals. The family of monolayer II I 2 V I 3 compounds exhibit a TFB representing the coloring-triangle lattice model. Re F 3 , Mn F 3 , and Mn Br 3 are all predicted to be diatomic-kagome-lattice crystals, with TFB transitions induced by atomic substitution. Finally, Hg F 2 , Cd F 2 , and Zn F 2 are discovered to host dual TFBs in the diamond-octagon lattice. Our findings pave the way to further experimental exploration of eluding FB materials and properties.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices

Topological flat bands, such as the band in twisted bilayer graphene, are becoming a promising platform to study topics such as correlation physics, superconductivity, and transport. In this Letter, we introduce a generic approach to construct two-dimensional (2D) topological quasiflat bands from line graphs and split graphs of bipartite lattices. A line graph or split graph of a bipartite lattice exhibits a set of flat bands and a set of dispersive bands. The flat band connects to the dispersive bands through a degenerate state at some momentum. We find that, with spin-orbit coupling (SOC), the flat band becomes quasiflat and gapped from the dispersive bands. By studying a series of specific line graphs and split graphs of bipartite lattices, we find that (i) if the flat band (without SOC) has inversion or C 2 symmetry and is nondegenerate, then the resulting quasiflat band must be topologically nontrivial, and (ii) if the flat band (without SOC) is degenerate, then there exists a SOC potential such that the resulting quasiflat band is topologically nontrivial. This generic mechanism serves as a paradigm for finding topological quasiflat bands in 2D crystalline materials and metamaterials.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Accelerating defect predictions in semiconductors using graph neural networks

First-principles computations reliably predict the energetics of point defects in semiconductors but are constrained by the expense of using large supercells and advanced levels of theory. Machine learning models trained on computational data, especially ones that sufficiently encode defect coordination environments, can be used to accelerate defect predictions. Here, we develop a framework for the prediction and screening of native defects and functional impurities in a chemical space of group IV, III–V, and II–VI zinc blende semiconductors, powered by crystal Graph-based Neural Networks (GNNs) trained on high-throughput density functional theory (DFT) data. Using an innovative approach of sampling partially optimized defect configurations from DFT calculations, we generate one of the largest computational defect datasets to date, containing many types of vacancies, self-interstitials, anti-site substitutions, impurity interstitials and substitutions, as well as some defect complexes. We applied three types of established GNN techniques, namely crystal graph convolutional neural network, materials graph network, and Atomistic Line Graph Neural Network (ALIGNN), to rigorously train models for predicting defect formation energy (DFE) in multiple charge states and chemical potential conditions. We find that ALIGNN yields the best DFE predictions with root mean square errors around 0.3 eV, which represents a prediction accuracy of 98% given the range of values within the dataset, improving significantly on the state-of-the-art. We further show that GNN-based defective structure optimization can take us close to DFT-optimized geometries at a fraction of the cost of full DFT. The current models are based on the semi-local generalized gradient approximation-Perdew–Burke–Ernzerhof (PBE) functional but are highly promising because of the correlation of computed energetics and defect levels with higher levels of theory and experimental data, the accuracy and necessity of discovering novel metastable and low energy defect structures at the PBE level of theory before advanced methods could be applied, and the ability to train multi-fidelity models in the future with new data from non-local functionals. The DFT-GNN models enable prediction and screening across thousands of hypothetical defects based on both unoptimized and partially optimized defective structures, helping identify electronically active defects in technologically important semiconductors.

Rahman, Md Habibur (ORCID:000000027705984X)↗
DOE OSTI2022

Topological Simplifications of Hypergraphs

Here we study hypergraph visualization via its topological simplification. We explore both vertex simplification and hyperedge simplification of hypergraphs using tools from topological data analysis. In particular, we transform a hypergraph into its graph representations, known as the line graph and clique expansion. A topological simplification of such a graph representation induces a simplification of the hypergraph. In simplifying a hypergraph, we allow vertices to be combined if they belong to almost the same set of hyperedges, and hyperedges to be merged if they share almost the same set of vertices. Our proposed approaches are general and mathematically justifiable, and put vertex simplification and hyperedge simplification in a unifying framework.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Harnessing distributed GPU computing for generalizable graph convolutional networks in power grid reliability assessments

Although machine learning (ML) has emerged as a powerful tool for rapidly assessing grid contingencies, prior studies have largely considered a static grid topology in their analyses. This limits their application, since they need to be re-trained for every new topology. Here, this paper explores the development of generalizable graph convolutional network (GCN) models by pre-training them across a range of grid topologies and contingency types. We found that a GCN model with auto-regressive moving average (ARMA) layers with a line graph representation of the grid offered the best predictive performance in predicting voltage magnitudes (VM) and voltage angles (VA). We introduced the concept of phantom nodes to consider disparate grid topologies with a varying number of nodes and lines. For pre-training the GCN ARMA model across a variety of topologies, distributed graphics processing unit (GPU) computing afforded us significant training scalability. The predictive performance of this model on grid topologies that were part of the training data is substantially better than the direct current (DC) approximation. Although direct application of the pre-trained model to topologies that are not part of the grid is not particularly satisfactory, fine-tuning with small amounts of data from a specific topology of interest significantly improves predictive performance. In general, this paper highlights the feasibility of training large-scale GNN models to assess the reliability of power grids by considering a wide variety of grid topologies and contingency types. With the advent of foundational models in ML and the exponential increase in GPU computing clusters, generalizable ML models will significantly enhance how utilities manage power systems and make decisions in real-time or near-real-time.

24 - POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Efficient and interpretable graph network representation for angle-dependent properties applied to optical spectroscopy

Abstract Graph neural networks are attractive for learning properties of atomic structures thanks to their intuitive graph encoding of atoms and bonds. However, conventional encoding does not include angular information, which is critical for describing atomic arrangements in disordered systems. In this work, we extend the recently proposed ALIGNN (Atomistic Line Graph Neural Network) encoding, which incorporates bond angles, to also include dihedral angles (ALIGNN-d). This simple extension leads to a memory-efficient graph representation that captures the complete geometry of atomic structures. ALIGNN-d is applied to predict the infrared optical response of dynamically disordered Cu(II) aqua complexes, leveraging the intrinsic interpretability to elucidate the relative contributions of individual structural components. Bond and dihedral angles are found to be critical contributors to the fine structure of the absorption response, with distortions that represent transitions between more common geometries exhibiting the strongest absorption intensity. Future directions for further development of ALIGNN-d are discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2025

..delta..-Learning of High-Fidelity Electronic Structure Using Graph Neural Networks with Modified Node-Level Features

In this work, we present a ..delta..-learning approach for predicting the eigenvalues calculated with the hybrid functional HSE06 (..epsilon..nkHSE) for a set of metal and nitrogen doped graphene catalysts (MNCs) from Perdew-Burke-Ernzerhof (PBE) inputs. The model presented here incorporates electronic scalar features along with structural information in a graph neural network (GNN). In particular, the PBE eigenvalues for different bands and k-points and orbital-resolved projectors are combined with the applied potential as node-level features along with structural information within the Atomistic Line Graph Neural Network (ALIGNN) architecture. These features enable flexibility for systems with electrified interfaces, such as in electrocatalysts and achieves mean absolute error (MAE) of less than 0.1 eV. The machine learning model reported here achieves a strong generalization to left-out adsorbates (MAE = 0.074 eV) and leave-one-chemical-space-out (MAE = 0.08 eV) and completely left-out metals (MAE = 0.072 eV), confirming the robustness of the machine learning (ML) model in predicting ..epsilon..nkHSE.

36 MATERIALS SCIENCE↗
NASA NTRS1994

A componential model of human interaction with graphs: 1. Linear regression modeling

Task analyses served as the basis for developing the Mixed Arithmetic-Perceptual (MA-P) model, which proposes (1) that people interacting with common graphs to answer common questions apply a set of component processes-searching for indicators, encoding the value of indicators, performing arithmetic operations on the values, making spatial comparisons among indicators, and repsonding; and (2) that the type of graph and user's task determine the combination and order of the components applied (i.e., the processing steps). Two experiments investigated the prediction that response time will be linearly related to the number of processing steps according to the MA-P model. Subjects used line graphs, scatter plots, and stacked bar graphs to answer comparison questions and questions requiring arithmetic calculations. A one-parameter version of the model (with equal weights for all components) and a two-parameter version (with different weights for arithmetic and nonarithmetic processes) accounted for 76%-85% of individual subjects' variance in response time and 61%-68% of the variance taken across all subjects. The discussion addresses possible modifications in the MA-P model, alternative models, and design implications from the MA-P model.

Gillan, Douglas J.↗
DOE OSTI2024

Kondo effect and its destruction in heterobilayer transition metal dichalcogenides

Moiré structures, along with line-graph-based d -electron systems, represent a setting to realize flat bands. One form of the associated strong correlation physics is the Kondo effect. Here, we address the recently observed Kondo-driven heavy fermion state and its destruction in AB-stacked hetero-bilayer transition metal dichalcogenides, which can be controlled by the gate voltages. By studying an effective interacting Hamiltonian using the slave spin approach, we obtained a phase diagram with the total filling factor and the displacement field strength as the tunable parameters. In an extended range of the tunable displacement field, our numerical results show that the relative filling of the d orbital, which is associated with the highest moiré band from the MoTe 2 layer, is enforced to be ν d ≈ 1 by the interaction. This agrees with the experimental observation. We also argue that the observed high coherence temperature scale could be explained by the non-negligible bandwidth of the d orbital. Our results set the stage to address the amplified quantum fluctuations that the Kondo effect may produce in these structures and new regimes that the systems open up for Kondo-destruction quantum criticality. Published by the American Physical Society 2024

Xie, Fang (ORCID:000000021327767X)↗
DOE OSTI2022

EDD Basic Stats and Graphs Notebook analysis (EDD BSG Notebook) v1.0

This jupyter notebook calculates basic statistics (e.g., mean, standard deviation, coefficient of variation) and simple graphs (e.g., bar graphs, line plots) for data from the Experiment Data Depot (EDD) to provide rapid and reproducible assessment of data quality to aid research efforts across the JBEI and ABF projects. It rapidly and reproducibly calculates basic statistical values for data stored in the EDD which aids researchers and strengthens comparisons across different experiments and projects.

Petzold, ChristopherJ↗
DOE OSTI2020

E3SM Water Cycle Visualization Project (Final Report)

Motivated by the need to improve visualizations of Earth's complex water cycle, this team embarked on non-trivial tasks to push from traditional methods of viewing data from simulations as static line graphs and contour plots into new realms with multiple dimensions (three spatial dimensions and the time component) viewable at once. To do this, we chose to feature the extremes in the general circulation of the atmosphere because these Earth system elements are short-lived, but impactful events. We used simulation data produced by the Department of Energy's (DOE) Energy Exascale Earth System Model (E3SM),which is designed to answer DOE science questions using DOE computing facilities. The E3SM project includes three sets of simulation experiments: cryosphere, bio-geochemical cycles, and the water cycle. The water cycle experiment campaign includes a set of simulations designed to understand how the water cycle will change in coming decades under a changing climate.

54 ENVIRONMENTAL SCIENCES↗