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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Discovery of correlated electron molecular orbital materials using graph representations

Correlated electron molecular orbital (CEMO) materials host emergent electronic states built from molecular orbitals localized over clusters of transition metal ions yet have historically been discovered sporadically and generally been treated as isolated case studies. Here we establish CEMO materials as a systematically discoverable class and introduce a graph-based framework to identify, classify, and organize transition-metal cluster motifs in inorganic solids. Starting from crystal structures in the Materials Project, we construct transition metal connectivity graphs, extract cluster motifs using a bond-cutting algorithm, and determine cluster point groups, effective cluster sublattice dimensionality, and translational symmetry. Applying this approach in a high-throughput screen of 34,548 compounds yields 5,306 cluster-containing materials, including 2,627 stable or metastable compounds with isolated clusters and 984 materials featuring mixed-metal clusters. The resulting dataset reveals symmetry and element dependent trends in cluster formation. By integrating cluster classification with flat band lattice topology and battery-relevant information, we provide further relevant information to multiple scientific communities. The accompanying open dataset, Cluster Finder software, and interactive web platform enable systematic exploration of cluster driven electronic phenomena and establish a general pathway for discovering correlated quantum materials and functional materials with cluster-based or extended metal-metal bonding in inorganic solids.

Akhond, Md. Rajbanul [Department of Chemistry, 800↗
DOE OSTI2026

When does global attention help: a unified empirical study on atomistic graph learning

Graph neural networks (GNNs) are widely used as surrogates for costly experiments and first-principles simulations to study the behavior of compounds at atomistic scale, and their architectural complexity is constantly increasing to enable the modeling of complex physics. While most recent GNNs combine more traditional message passing neural networks (MPNNs) layers to model short-range interactions with more advanced graph transformers (GTs) with global attention mechanisms to model long-range interactions, it is still unclear when global attention mechanisms provide real benefits over well-tuned MPNN layers due to inconsistent implementations, features, or hyperparameter tuning. We introduce the first unified, reproducible benchmarking framework–built on HydraGNN–that enables seamless switching among four controlled model classes: MPNN, MPNN with chemistry/topology encoders, GPS-style hybrids of MPNN with global attention, and fully fused localglobal models with encoders. Using seven diverse open-source datasets for benchmarking across regression and classification tasks, we systematically isolate the contributions of message passing, global attention, and encoder-based feature augmentation. Our study shows that encoder-augmented MPNNs form a robust baseline, while fused localglobal models yield the clearest benefits for properties governed by long-range interaction effects. We further quantify the accuracycompute trade-offs of attention, reporting its overhead in memory. Together, these results establish the first controlled evaluation of global attention in atomistic graph learning and provide a reproducible testbed for future model development.

Equivariant graph neural networks↗
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 NTRS1989

Generation of precedence relations for mechanical assemblies

Planning of assembly sequences is essential to the manufacturing system design process. Several methodologies have been proposed to represent all the feasible assembly sequences. In this thesis, three algorithms are presented to generate three sets of precedence relations based on all the infeasible assembly tasks, all the infeasible assembly states, and all the feasible assembly sequences, respectively. The equivalence of the resulting sets of precedence relations to the AND/OR graph is established. A new property, the real time property, of a representation of assembly sequences is defined and discussed. A representation of assembly sequences is said to have the real time property, if it is possible to generate the next assembly task by testing locally in the representation, and it will guarantee that the generated assembly task will not lead the assembly sequence to a dead end situation, in which no feasible assembly task can be performed any more. It is shown that the correctness and completeness of one representation can not guarantee the real time property of the representation. It is proven that the directed graph representation and the set of precedence relations based on all the infeasible assembly states have the real time property, while the AND/OR graph representation and the set of precedence relations based on all the infeasible assembly tasks do not have the real time property. Finally in the thesis, the PLEIDEAS system, a PLanning Environment for Integrated DEsign of Assembly Systems, is described and illustrated by an example.

Zhang, Hui↗
DOE OSTI2025

Ca X ML: Chemistry‐informed machine learning explains mutual changes between protein conformations and calcium ions in calcium‐binding proteins using structural and topological features

Proteins' flexibility is a feature in communicating changes in cell signaling instigated by binding with secondary messengers, such as calcium ions, associated with the coordination of muscle contraction, neurotransmitter release, and gene expression. When binding with the disordered parts of a protein, calcium ions must balance their charge states with the shape of calcium-binding proteins and their versatile pool of partners depending on the circumstances they transmit. Accurately determining the ionic charges of those ions is essential for understanding their role in such processes. However, it is unclear whether the limited experimental data available can be effectively used to train models to accurately predict the charges of calcium-binding protein variants. Here, we developed a chemistry-informed, machine-learning algorithm that implements a game theoretic approach to explain the output of a machine-learning model without the prerequisite of an excessively large database for high-performance prediction of atomic charges. We used the ab initio electronic structure data representing calcium ions and the structures of the disordered segments of calcium-binding peptides with surrounding water molecules to train several explainable models. Network theory was used to extract the topological features of atomic interactions in the structurally complex data dictated by the coordination chemistry of a calcium ion, a potent indicator of its charge state in protein. Our design created a computational tool of Ca X ML, which provided a framework of explainable machine learning model to annotate ionic charges of calcium ions in calcium-binding proteins in response to the chemical changes in an environment. Our framework will provide new insights into protein design for engineering functionality based on the limited size of scientific data in a genome space.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Scaling Laws of Graph Neural Networks for Atomistic Materials Modeling

Atomistic materials modeling is a critical task with wide-ranging applications, from drug discovery to materials science, where accurate predictions of the target material property can lead to significant advancements in scientific discovery. Graph Neural Networks (GNNs) represent the state-of-the-art approach for modeling atomistic material data thanks to their capacity to capture complex relational structures. While machine learning performance has historically improved with larger models and datasets, GNNs for atomistic materials modeling remain relatively small compared to large language models (LLMs), which leverage billions of parameters and terabyte-scale datasets to achieve remarkable performance in their respective domains. To address this gap, we explore the scaling limits of GNNs for atomistic materials modeling by developing a foundational model with billions of parameters, trained on extensive datasets in terabytescale. Our approach incorporates techniques from LLM libraries to efficiently manage large-scale data and models, enabling both effective training and deployment of these large-scale GNN models. This work addresses three fundamental questions in scaling GNNs: the potential for scaling GNN model architectures, the effect of dataset size on model accuracy, and the applicability of LLM-inspired techniques to GNN architectures. Specifically, the outcomes of this study include (1) insights into the scaling laws for GNNs, highlighting the relationship between model size, dataset volume, and accuracy, (2) a foundational GNN model optimized for atomistic materials modeling, and (3) a GNN codebase enhanced with advanced LLM-based training techniques. Our findings lay the groundwork for large-scale GNNs with billions of parameters and terabyte-scale datasets, establishing a scalable pathway for future advancements in atomistic materials modeling.

Li, Chaojian [ORNL] (ORCID:0000000340309777)↗
DOE OSTI2025

COMPASS-FME Synoptic Sites Level 1 Sensor Data v2-1

This is the version 2-1 Level 1 (L1) data release for COMPASS-FME environmental sensors located at our synoptic field sites. COMPASS-FME is studying sites in two distinct regions, the Chesapeake Bay and the Western Lake Erie Basin. We established the network at seven "synoptic" (observational) sites along the Chesapeake Bay and Lake Erie coastlines, collectively generating over three million observations per month, to track and comprehend environmental changes where land and water intersect. Additionally, the two regions provide an interesting contrast of saltwater and freshwater coasts that allow us to differentiate the impacts of inundation and coastal water chemistries in two nationally important coastal systems. L1 data are close to raw, but are units-transformed and have out-of-instrument-bounds, out-of-service, and outlier flags added. Duplicates and missing data are removed but otherwise these data are not filtered, and have not been subject to any additional algorithmic or human QA/QC. Any scientific analyses of L1 data should be performed with care. **This dataset will be updated quarterly with new data for the duration of the project** This dataset includes: - An overall dataset README file that describes the current version, gives citation and contact information, etc. - Site- and year-specific folders, each holding up to 12 CSV (comma separated value) data files for each site and plot in that year. - Metadata files within each site-year folder provide full information on data units, expected ranges, contact information, as well as a general description of the site. - Environmental sensor types that appear in the data files include weather (ClimaVUE50, CS, RM Young, and LI instruments in the graphs below); soil conditions (TEROS12); soil redox state (Redox); groundwater variables (AquaTROLL200 and AquaTROLL600); open water sondes (Exo); tree sap velocity (Sapflow); and system voltage and state (Datalogger). Data are normally logged every 15 minutes. Please see v2-0 Synoptic L1 Sensor Package Quick Start.pdf for detailed information on data package structure, temporal coverage, and versioning. This dataset was updated 2026-03-12: (i) data now go through 2025-12-31 (previous end was 2025-06-30) and (ii) dataset and file names updated to “…v2-1” (previously was “v2-0”).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

COMPASS-FME Terrestrial Ecosystem Manipulation to Probe the Effects of Storm Treatments (TEMPEST) Experiment Level 1 Sensor Data v2-1

This is the version 2-1 Level 1 (L1) data release for COMPASS-FME environmental sensors located at our Terrestrial Ecosystem Manipulation to Probe the Effects of Storm Treatments (TEMPEST) experimental site. This manipulative, ecosystem-scale TEMPEST experiment addresses the potential for freshwater and estuarine-water disturbance events to alter tree function, species composition, and ecosystem processes in a deciduous coastal forest in MD, USA. The experiment uses a large-unit (2000 m2), un-replicated experimental design, with three 50 m × 40 m plots serving as control, freshwater, and estuarine-water treatments. L1 data are close to raw, but are units-transformed and have out-of-instrument-bounds, out-of-service, and outlier flags added. Duplicates and missing data are removed but otherwise these data are not filtered, and have not been subject to any additional algorithmic or human QA/QC. Any scientific analyses of L1 data should be performed with care. **This dataset will be updated quarterly with new data for the duration of the project** This dataset includes: - An overall dataset README file that describes the current version, gives citation and contact information, etc. - Site- and year-specific folders, each holding variable-specific CSV (comma separated value) data files for each site and plot in that year. - Metadata files within each site-year folder provide full information on data units, expected ranges, contact information, detailed flood times, as well as a general description of the site. - Environmental sensor types that appear in the data files include weather (ClimaVUE50, CS, RM Young, and LI instruments in the graphs below); soil conditions (TEROS12); soil redox state (Redox); groundwater variables (AquaTROLL200 and AquaTROLL600); open water sondes (Exo); tree sap velocity (Sapflow); and system voltage and state (Datalogger). Data are normally logged every 15 minutes. Please see v2-1 TEMPEST L1 Sensor Package Quick Start.pdf for detailed information on data package structure, temporal coverage, and versioning. The TEMPEST flood events occurred on the following dates. They lasted for ~10 hours each day and delivered ~80,000 gallons to each plot; many data streams are available at 1 or 5 minute frequency during these periods. * Tests: Aug 25 (fresh plot) and Sep 9 (salt plot), 2021 * TEMPEST 1: June 22, 2022 * TEMPEST 2: June 6-7, 2023 * TEMPEST 3: June 11-13, 2024 This dataset was updated 2026-03-12: (i) data now go through 2025-12-31 (previous end was 2025-06-30) and (ii) dataset and file names updated to “…v2-1” (previously was “v2-0”).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

COMPASS-FME Terrestrial Ecosystem Manipulation to Probe the Effects of Storm Treatments (TEMPEST) Experiment Level 2 Sensor Data v2-1

This is the version v2-1 Level 2 (L2) data release for COMPASS-FME environmental sensors located at our Terrestrial Ecosystem Manipulation to Probe the Effects of Storm Treatments (TEMPEST) experimental site. This manipulative, ecosystem-scale TEMPEST experiment addresses the potential for freshwater and estuarine-water disturbance events to alter tree function, species composition, and ecosystem processes in a deciduous coastal forest in MD, USA. The experiment uses a large-unit (2000 m2), un-replicated experimental design, with three 50 m × 40 m plots serving as control, freshwater, and estuarine-water treatments. Level 2 (L2) data consist of sensor observations from the COMPASS-FME synoptic sites, TEMPEST, and DELUGE. Compared to the L1 data, these are more consistent (always 15-minute timestamps for the entire year); better QA/QC’d (out of bounds, out of service, and extreme outlier values are removed); and more complete, with a gap-filled time series available alongside the main observations, and additional derived (calculated) variables. L2 data are intended to be rapidly and easily usable in analyses and simulations. However, algorithmic outlier identification always carries the risk of removing valid data, and Level 1 data may be more suitable for analyses that focus on variability or extreme events. This dataset includes: - An overall dataset README file that describes the current version, gives citation and contact information, etc. - Site- and year-specific folders, each holding variable-specific Parquet (a high performance, space efficient format; see https://parquet.apache.org) data files for each site and plot in that year. - Metadata files within each site-year folder provide full information on data units, expected ranges, contact information, detailed flood times, as well as a general description of the site. - Environmental sensor types that appear in the data files include weather (ClimaVUE50, CS, RM Young, and LI instruments in the graphs below); soil conditions (TEROS12); soil redox state (Redox); groundwater variables (AquaTROLL200 and AquaTROLL600); open water sondes (Exo); tree sap velocity (Sapflow); and system voltage and state (Datalogger). Data are reported every 15 minutes. Please see v2-1 TEMPEST L2 Sensor Package Quick Start.pdf for detailed information on data package structure, temporal coverage, and versioning. Data files are in Apache Parquet, a high performance, space efficient format for tabular data. These files can be read using R's `arrow` package (https://arrow.apache.org/docs/r/), with similar tools available in other languages. The TEMPEST flood events occurred on the following dates. They lasted for ~10 hours each day and delivered ~80,000 gallons to each plot; many data streams are available at 1 or 5 minute frequency during these periods. * Tests: Aug 25 (fresh plot) and Sep 9 (salt plot), 2021 * TEMPEST 1: June 22, 2022 * TEMPEST 2: June 6-7, 2023 * TEMPEST 3: June 11-13, 2024

EARTH SCIENCE > ATMOSPHERE > ATMOSPHERIC TEMPERATU↗
DOE OSTI2026

COMPASS-FME Synoptic Sites Level 2 Sensor Data v2-1

This is the version 2-1 Level 2 (L2) data release for COMPASS-FME environmental sensors located at our synoptic field sites. COMPASS-FME is studying sites in two distinct regions, the Chesapeake Bay and the Western Lake Erie Basin. We established the network at seven "synoptic" (observational) sites along the Chesapeake Bay and Lake Erie coastlines, collectively generating over three million observations per month, to track and comprehend environmental changes where land and water intersect. Additionally, the two regions provide an interesting contrast of saltwater and freshwater coasts that allow us to differentiate the impacts of inundation and coastal water chemistries in two nationally important coastal systems. Level 2 (L2) data consist of sensor observations from the COMPASS-FME synoptic sites, TEMPEST, and DELUGE. Compared to the L1 data, these are more consistent (always 15-minute timestamps for the entire year); better QA/QC’d (out of bounds, out of service, and extreme outlier values are removed); and more complete, with a gap-filled time series available alongside the main observations, and additional derived (calculated) variables. L2 data are intended to be rapidly and easily usable in analyses and simulations. However, algorithmic outlier identification always carries the risk of removing valid data, and Level 1 data may be more suitable for analyses that focus on variability or extreme events. This dataset includes: - An overall dataset README file that describes the current version, gives citation and contact information, etc. - Site- and year-specific folders, each holding variable-specific Parquet (a high performance, space efficient format; see https://parquet.apache.org) data files for each site and plot in that year. - Metadata files within each site-year folder provide full information on data units, expected ranges, contact information, detailed flood times, as well as a general description of the site. - Environmental sensor types that appear in the data files include weather (ClimaVUE50, CS, RM Young, and LI instruments in the graphs below); soil conditions (TEROS12); soil redox state (Redox); groundwater variables (AquaTROLL200 and AquaTROLL600); open water sondes (Exo); tree sap velocity (Sapflow); and system voltage and state (Datalogger). Data are reported every 15 minutes. Data files are in Apache Parquet, a high performance, space efficient format for tabular data. These files can be read using R's `arrow` package (https://arrow.apache.org/docs/r/), with similar tools available in other languages. Please see v2-1 L2 Sensor Package QStart.pdf for detailed information on data package structure, temporal coverage, and versioning.

EARTH SCIENCE > ATMOSPHERE > ATMOSPHERIC TEMPERATU↗
NASA NTRS1988

Theoretical study of the first and second negative systems of N2(+)

Extended Gaussian basis sets and large CASSCF/multireference CI wave functions are used in theoretical determination of the potential curves for the X 2Sigma(+)g, B 2Sigma(+)g, C 2Sigma(+)u, (1) 2Delta(u), (2) 2Delta(u), 4Pi(u), and 2Sigma(-)u states of N2(+). The results, including the radial dependence of the electronic transition moments, the Einstein coefficients, the radiative lifetimes, and the crossing points between selected states, are presented in extensive tables and graphs and discussed in detail.

Langhoff, Stephen R.↗
NASA NTRS1987

Structure of the geomagnetic tail

Observational data on the structure of the earth magnetotail are summarized and discussed, with reference to theoretical models. Particular attention is given to the interplanetary control of the tail, the magnetic-field structure, the plasma-sheet boundary layer, the magnetotail plasma parameters, the chemical composition of the tail, and the evidence indicating that a steady-state magnetotail cannot exist. Extensive diagrams and graphs are provided.

Fairfield, D. H.↗
NASA NTRS1989

A real-time expert system for self-repairing flight control

An integrated environment for specifying, prototyping, and implementing a self-repairing flight-control (SRFC) strategy is described. At an interactive workstation, the user can select paradigms such as rule-based expert systems, state-transition diagrams, and signal-flow graphs and hierarchically nest them, assign timing and priority attributes, establish blackboard-type communication, and specify concurrent execution on single or multiple processors. High-fidelity nonlinear simulations of aircraft and SRFC systems can be performed off-line, with the possibility of changing SRFC rules, inference strategies, and other heuristics to correct for control deficiencies. Finally, the off-line-generated SRFC can be transformed into highly optimized application-specific real-time C-language code. An application of this environment to the design of aircraft fault detection, isolation, and accommodation algorithms is presented in detail.

Gaither, S. A.↗
NASA NTRS1992

Decision analysis with approximate probabilities

This paper concerns decisions under uncertainty in which the probabilities of the states of nature are only approximately known. Decision problems involving three states of nature are studied. This is due to the fact that some key issues do not arise in two-state problems, while probability spaces with more than three states of nature are essentially impossible to graph. The primary focus is on two levels of probabilistic information. In one level, the three probabilities are separately rounded to the nearest tenth. This can lead to sets of rounded probabilities which add up to 0.9, 1.0, or 1.1. In the other level, probabilities are rounded to the nearest tenth in such a way that the rounded probabilities are forced to sum to 1.0. For comparison, six additional levels of probabilistic information, previously analyzed, were also included in the present analysis. A simulation experiment compared four criteria for decisionmaking using linearly constrained probabilities (Maximin, Midpoint, Standard Laplace, and Extended Laplace) under the eight different levels of information about probability. The Extended Laplace criterion, which uses a second order maximum entropy principle, performed best overall.

Whalen, Thomas↗
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 OSTI2026

Scalable Computation of Topological Abstractions for Scalar Data

Topological data analysis has become an important tool for large scale scalar data analysis and visualization, efficiently extracting the inherent structure and features of interest of the data. However, with growing dataset sizes and complexity, it is increasingly becoming infeasible to compute topological abstractions of interest in serial and on single machines. This paper presents the state of the art in the scalable computation of topological abstractions on scalar data, in shared memory parallel on single machines, and in distributed memory parallel on multiple machines. We highlight results for set‐based, graph‐based and complex‐based abstractions and organize the state of the art based on this taxonomy. The paper identifies parallelization and distribution techniques common in topological algorithms and highlights further areas of interest with underdeveloped efforts.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

AGFormer: Adaptive Spatiotemporal graph informed transformer for multi-reservoir inflow forecasting

Accurate reservoir inflow forecasting is crucial for effective water resource management, yet most machine learning models focus on single-reservoir prediction and overlook spatial dependencies among hydrologically connected reservoirs. Here, we propose AGFormer (Adaptive Graph-Informed Transformer), an end-to-end framework that integrates adaptive graph learning with temporal sequence modeling for multi-reservoir inflow forecasting. A shared encoder and graph attention mechanism generate reservoir-specific embeddings, which are then processed by the Transformer-based encoder–decoder for multi-step inflow forecasting. We also introduce a pretraining paradigm to learn robust temporal embeddings from misaligned historical records. Evaluated on 30 reservoirs in the Upper Colorado River Basin, AGFormer achieves superior seven-day-ahead forecasts, with NSE > 0.75 for 20 reservoirs—outperforming Encoder–Decoder LSTM, GCN+LSTM, and Transformer baselines. Adaptive graph learning captures dynamic inter-reservoir dependencies, and feature attribution aligns with snowmelt-driven hydrology. Incorporating forecasted meteorological inputs further enhances accuracy, demonstrating AGFormer’s potential to support reservoir management under dynamic hydrological conditions.

Adaptive graph learning↗
DOE OSTI2026

Powers of magnetic graph matrix: Fourier spectrum, walk compression, and applications

Magnetic graphs, originally developed to model quantum systems under magnetic fields, have recently emerged as a powerful framework for analyzing complex directed networks. Existing research has primarily used the spectral properties of the magnetic graph matrix to study global and stationary network features. However, their capacity to model local, nonequilibrium behaviors, often described by matrix powers, remains largely unexplored. We present a combinatorial interpretation of the magnetic graph matrix powers through directed walk profiles—counts of graph walks indexed by the number of edge reversals. Crucially, we establish that walk profiles correspond to a Fourier transform of magnetic matrix powers. The connection allows exact reconstruction of walk profiles from magnetic matrix powers at multiple discrete potentials, and more importantly, an even smaller number of potentials often suffices for accurate approximate reconstruction in real networks. This shows the empirical compressibility of the information captured by the magnetic matrix. This fresh perspective suggests further applications; for example, we illustrate how powers of the magnetic matrix can identify frustrated directed cycles (e.g., feedforward loops) and can be effectively employed for link prediction by encoding local structural details in directed graphs.

complex networks↗