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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

ITeM: Independent temporal motifs to summarize and compare temporal networks

We report networks are a fundamental and flexible way of representing various complex systems. Many domains such as communication, citation, procurement, biology, social media, and transportation can be modeled as a set of entities and their relationships. Temporal networks are a specialization of general networks where every relationship occurs at a discrete time. The temporal evolution of such networks is as important to understand as the structure of the entities and relationships. We present the Independent Temporal Motif (ITeM) to characterize temporal graphs from different domains. ITeMs can be used to model the structure and the evolution of the graph. In contrast to existing work, ITeMs are edge-disjoint directed motifs that measure the temporal evolution of ordered edges within the motif. For a given temporal graph, we produce a feature vector of ITeM frequencies and the time it takes to form the ITeM instances. We apply this distribution to measure the similarity of temporal graphs. We show that ITeM has higher accuracy than other motif frequency-based approaches. We define various ITeM-based metrics that reveal salient properties of a temporal network. We also present importance sampling as a method to efficiently estimate the ITeM counts. We present a distributed implementation of the ITeM discovery algorithm using Apache Spark and GraphFrame. We evaluate our approach on both synthetic and real temporal networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Local structure graph models with higher-order dependence

Local structure graph models (LSGMs) describe random graphs and networks as a Markov random field (MRF)—each graph edge has a specified conditional distribution dependent on explicit neighbourhoods of other graph edges. Centered parameterizations of LSGMs allow for direct control and interpretation of parameters for large- and small-scale structures (e.g., marginal means vs. dependence). Here, we extend this parameterization to account for triples of dependent edges and illustrate the importance of centered parameterizations for incorporating covariates and interpreting parameters. Using a MRF framework, common exponential random graph models are also shown to induce conditional distributions without centered parameterizations and thereby have undesirable features. This work attempts to advance graph models through conditional model specifications with modern parameterizations, covariates and higher-order dependencies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Estimating soybean yields from high-temporal-resolution multi-source data using deep learning

Accurate and timely crop yield prediction is crucial for ensuring food security and maintaining stable agricultural markets. In recent years, there has been a surge in interest in leveraging high-temporal-resolution, multi-source data for effective crop growth monitoring and yield estimation. A notable challenge arises from the difficulty in capturing the intricate interactions between variables across different time steps within these high-temporal-resolution time series datasets. This complexity hinders the reliable extraction of yield information from voluminous and often noisy datasets, especially during periods of extreme weather events. Here, in this study, we propose an Attention and Graph Isomorphism Network-enhanced Bi-directional Long Short-Term Memory network (AGB-LSTM) for estimating county-level soybean yield in the United States. This model integrates a diverse set of remote sensing data, including Near-Infrared Reflectance of Vegetation (NIRv), Sun-Induced chlorophyll Fluorescence (SIF), and Gross Primary Productivity (GPP), along with environmental covariates. The AGB-LSTM effectively leverages information related to crop yield from high-temporal-resolution time series data (5-days), achieving an accuracy of R²= 0.67 and rRMSE = 14.46%. This approach significantly outperforms traditional machine learning methods such as Random Forest (RF) (R²= 0.52, rRMSE = 17.36%) and Bi-LSTM (R²= 0.58, rRMSE = 16.17%). Sensitivity experiments with different time steps and ranges demonstrated that our model could accurately and stably predict yields 1 to 2 months before harvest. Moreover, data with a finer temporal resolution consistently improved prediction performance, resulting in an approximately 20% increase in and an approximately 20% decrease in rRMSE compared to using monthly composites. We also evaluated the robustness of the model under extreme climate events and observed strong performance (R²= 0.50, rRMSE = 21.32%). Finally, yield mapping for major soybean-producing regions in North America in 2023 revealed spatial patterns that closely matched USDA yield reports. Our findings suggest that the AGB-LSTM model is a promising and effective method for estimating yield and has notable potential for global crop yield forecasting.

Deep learning↗
DOE OSTI2024

Nonperturbative Zou-Wang-Mandel effect

The Zou-Wang-Mandel (ZWM) effect is a remarkable consequence of photon indistinguishability and continuous-variable entanglement in which an optical phase shift is imprinted on photonic modes associated with optical paths that that do not pass through the phase shift source. By bringing the canonical formalism of continuous-variable Gaussian states to bear on the mode-structure of the ZWM experiment, we show that the physical consequence of implementing optical path identity is a renormalization of quadrature squeezing which governs the entanglement of four effective optical modes. Nonperturbative expressions for the ZWM interference patterns and normalized first-order coherence function are derived. Generalizations to $\mathscr{H}$-graph states with more than four modes directly follow from the general method used to analyze the minimal example. Here, we show that a ZWM interferometer with a laser-seeded signal mode, which estimates an idler phase shift by detecting photons that did not propagate through the phase shift, exhibits an optimal sensitivity comparable to that of a laser-seeded SU(1,1) interferometer if path identity is implemented with high fidelity.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Contributions of vegetation heterogeneity within tower footprint to CO 2 flux estimations through graph neural network modeling

Net ecosystem exchange of CO 2 (Fc) measured directly by eddy covariance towers is based on various assumptions, including large, flat and homogenous land cover type. In reality, often a tower site is not large enough for flux measurements, and landscapes consist of patches of different land cover types within the flux footprint. In addition, some portions of fluxes are contributed by different cover types when a footprint exceeds the size of the target ecosystem. The contributions of non-dominant patches to Fc are often ignored. Here, in this study, we propose a novel integrated modeling framework that combines random forest (RF) and XGBoost with a residual correction module based on a deep graph convolutional network (DeeperGCN) to simulate Fc for seven flux measurement sites in southwest Michigan. High-resolution remote sensing vegetation indices, soil properties, meteorological variables, and footprint-weighted spatial features were used as model inputs at three spatial resolutions (10 m, 20 m, 30 m), and their importance in predicting Fc with DeeperGCN was assessed. We found that residual correction using DeeperGCN significantly improved prediction accuracy, with the R 2 increasing from 0.9098 to 0.9479 for RF and from 0.9235 to 0.9433 for XGBoost. At site level, the maximum improvement in R 2 reached 0.1617. Paired t-tests confirmed that these improvements were statistically significant (p < 0.05). Among all predictors, leaf area index and incoming shortwave radiation emerged as the dominant drivers of spatial residual variation, followed by precipitation, relative humidity, and selected vegetation indices. The 20 m resolution yielded the best balance between model performance and computational efficiency. In conclusion, our modeling framework effectively captures both spatial heterogeneity and nonlinear interactions, offering a robust solution for spatially explicit flux modeling in structurally diverse ecosystems beyond the study sites.

footprint model↗
DOE OSTI2025

Predicting the von Neumann entanglement entropy using a graph neural network

Calculating the von Neumann entanglement entropy from experimental data is challenging due to its dependence on the complete wavefunction, forcing reliance on approximations such as classical mutual information (MI). We propose a machine learning approach using a graph neural network to predict the von Neumann entropy directly from experimentally accessible bitstrings. We test this approach on a Rydberg ladder system and achieve a mean absolute error of $3.6\,\times 10^{-3}$ when evaluating within the training range on a dataset with entropy values ranging from 0 to 1.9. The model achieves a mean absolute percentage error of 1.44% and outperforms MI-based bounds. When tested beyond the training range, the model maintains reasonable accuracy. Furthermore, we demonstrate that fine-tuning the model with small datasets significantly improves performance on data outside the original training range.

graph neural networks↗
DOE OSTI2023

Convoluted filtering for process cycle modeling

Principles of materials science and engineering, physics, mathematics, and information science are used to extract knowledge and insights from the process-structure–property-performance relationships hidden in materials data. The process-structure modeling can be accelerated without loss of interpretability, with artificial intelligence tools that mimic the salient features of the process and process-structure relations. In this work, a novel convoluted model-filtering technique was exploited to build and successfully train the Convoluted Filter (CoFi) artifacts for Fe-based alloy heat treatment cycles. The artifacts were pre-trained to filter out deep models that change the surrogate microstructure state after the heat treatment at ambient conditions. Direct representation of the thermal cycle features within knowledge Graph facilitated development of meaningful data models for microstructure evolution, which reduce overfitting to limited datasets.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Benchmarking machine learning interatomic potentials via phonon anharmonicity

Abstract Machine learning approaches have recently emerged as powerful tools to probe structure-property relationships in crystals and molecules. Specifically, machine learning interatomic potentials (MLIPs) can accurately reproduce first-principles data at a cost similar to that of conventional interatomic potential approaches. While MLIPs have been extensively tested across various classes of materials and molecules, a clear characterization of the anharmonic terms encoded in the MLIPs is lacking. Here, we benchmark popular MLIPs using the anharmonic vibrational Hamiltonian of ThO 2 in the fluorite crystal structure, which was constructed from density functional theory (DFT) using our highly accurate and efficient irreducible derivative methods. The anharmonic Hamiltonian was used to generate molecular dynamics (MD) trajectories, which were used to train three classes of MLIPs: Gaussian approximation potentials, artificial neural networks (ANN), and graph neural networks (GNN). The results were assessed by directly comparing phonons and their interactions, as well as phonon linewidths, phonon lineshifts, and thermal conductivity. The models were also trained on a DFT MD dataset, demonstrating good agreement up to fifth-order for the ANN and GNN. Our analysis demonstrates that MLIPs have great potential for accurately characterizing anharmonicity in materials systems at a fraction of the cost of conventional first principles-based approaches.

interatomic potentials↗
DOE OSTI2020

Determining Compression Characteristics of Honeycomb Material - 19674

The objective is to determine compression test characteristics of stainless steel honeycomb material to be able to represent honeycomb structures accurately in analytical models used to simulate hypothetical accident scenarios of shipping packages. Honeycomb is a material used primary in the aerospace industry due to its high strength-to-weight ratio. Because it doesn't have a shelf life and can withstand high heats, it is an excellent candidate for a structural material in package designs. Honeycomb has orthotropic material properties. The honeycomb currently being evaluated is made of metal ribbons spot welded together to form hexagon pattern between metal plates. The hexagon ribbons are brazed to the metal plates. The complexity of the honeycomb significantly lengthens the simulation time, which is further complicated when the brazing, welding, and imperfections of the material is considered. This means to affectively represent the honeycomb in simulation programs, such as Abaqus, the material needs to be approximated as a uniform orthotropic material. This requires material properties in each of the three directions, T, W, and L. The T direction is defined as the 'strong' direction, perpendicular to the honeycomb sheet. The L direction is parallel the ribbon and the W direction is perpendicular to the ribbon. Honeycomb has 3 different compression stages. Stage 1 is the initial compression where the honeycomb maintains its structural integrity and does not permanently deform from loads from normal operations. Stage 2 is when the initial buckling causes irreversible damage to the honeycomb. Stage 2 is the one we are most interested in because it absorbs the most energy from a hypothetical accident scenario. During Stage 2, the honeycomb fails layer-by-layer, indicating that the more layers, the longer material crushing is sustained, and thus the more energy that is absorbed. Stage 3 is final compression, similar to compressing solid metal. During stage 3 the stress increases with a diminishing rate of elongation and the honeycomb is completely failed where the plates between the honeycomb core sandwich the crushed honeycomb ribbon. The stress-strain graph bellow shows compression test of 3 different samples in the T direction. The red lines divide the three stages. The far left is Stage 1, the middle stage 2, and the right stage 3. The data collected is displayed in the table below. The expressions in the table represent the regression formula that represents each stage of the compression on a stress-strain graph. Stage 1 is assumed to intersect with the origin; data for stage 3 for the crush in W and L directions where unable to be gathered due to the nature of failure for those directions. Stage 1 and 2 are linear regressions while stage 3 is a degree 2, to best match the curve. Linear regression is used on stage 2 because ultimately that represents the energy absorbed. With more data, a degree n x 2 regression would be a more appropriate regression for stage 2, where n is the number of layers. The table below is the approximation of each scenario and stage. Each stage starts and ends at the intersection of the next stage. There where two main objectives for these tests: firstly to understand how honeycomb performs under extreme compression, and secondly to be able to numerically represent the honeycomb structure. Both of these where completed to varying degrees. It is important understood how the honeycomb fails. If it is crushed in the T direction it retains its integrity even after being crushed, however when crushed in the L and W crush direction, if it fails, it disintegrates, and loses all integrity. Also, the more layers the more time the material spends in stage 2. Failure is started by buckling, thus if there is any imperfection, the stress will not spike but transition straight into stage 2. The data collected and aggregated can be used for initial simulation of honeycomb used in packages. The initial testing has set the ground work for more data to be collected in order to verify results and to allow more confidence in the simulation results. This is only the initial data collected. The next steps is to continue to collect more data to verify results and to test more variants of honeycomb, with different brazing, layers, and shape.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Towards Geospatial Knowledge Graph Infused Neuro-Symbolic AI for Remote Sensing Scene Understanding

Deep learning has proven its effectiveness in numerous tasks for remote sensing scene understanding. However there is an increasing interest to explore fusion of domain-specific background information to the deep neural network to further improve its performance. Remote sensing researchers are also working towards developing models that generalize and adapt to multiple applications. Generalization challenges coupled with the scarcity of large corpora of high-quality noise-free labelled data, have together fueled an interest for leveraging background information. Knowledge graphs serve as excellent choice to represent domain-specific information in a structured, standardized and extensible manner. Integrating symbolic knowledge representations in the form of Knowledge Graph Embedding (KGE) to perform neuro-symbolic reasoning is an emerging research direction promising significant impacts. This vision paper seeks to position ideas and provoke early thoughts toward advancing neuro-symbolic artificial intelligence in the context of geospatial challenges. Specifically, it conceptualizes and elaborates on an architecture for infusing geospatial knowledge from knowledge graph in a deep neural network pipeline. As guiding case studies - land-use land-cover classification, object detection and instance segmentation can benefit from infusing spatio-contextual information with remote sensing imagery. The discussion further reflects on and articulates the challenges and explainable AI opportunities anticipated when scaling and maintaining large-scale geospatial knowledge graphs.

Potnis, Abhishek↗
DOE OSTI2023

Refined views of ancient ocean chemistry: Tracking trace element incorporation in pyrite framboids using atom probe tomography

The trace element chemistry of pyrite can be used to determine the origin, timing, and conditions of formation of ore deposits; as a vectoring tool for mineral exploration; and to determine the evolution of the Earth’s oceanic and atmospheric chemistry. However, little is known about whether trace elements are held with the pyrite structure or within nano-inclusions of other phases. This distinction is important for two primary reasons. First, trace element incorporation into the pyrite structure can affect the partitioning of other trace elements. Second, if trace elements are held within nano-inclusions, the partition coefficient of the mineral phases that make up the nano-inclusion, rather than pyrite, are the critical consideration in related interpretations. Previous studies addressing this topic have used laser ablation inductively coupled plasma mass spectrometry; however, the resulting data do not provide sufficient spatial resolution to delineate trace element distributions unless the inclusions are large. Further, they use these flat element profiles in time resolved laser ablation output graphs to argue that pyrite trace element content provides a direct relationship between trace element content of seawater and pyrite trace element content. To improve resolution, we have used atom probe tomography to characterize trace element distributions in pyrite framboids from the Cariaco Basin and Demerara Rise in three-dimensions at sub-nanometer resolution. Manganese was found to be concentrated in the pyrite nanocrystal part of the original framboid structure. In contrast, Ni was mostly found along the grain boundary, though it still appeared to be contained within the pyrite structure. Copper was concentrated in later pyrite overgrowths, and As varied in its location. These observations suggest that some important trace elements are incorporated into pyrite during early diagenesis, even in euxinic settings dominated by water-column pyrite formation. Statistical analysis was used to determine whether trace elements were incorporated in the lattice or within nanoscale inclusions (referred to here are nano-inclusions). We found that As, Ni, Cu, and Mn were commonly held within the pyrite structure, but As, Ni, and Cu can also be held as nano-inclusions or within grain interfaces. Incorporation of As is known to enhance the incorporation of other trace elements and in this case appears to correlated to elevated Ni and Cu concentrations in the Cariaco Basin samples. Furthermore, understanding these relationships strongly impacts our ability to utilize pyrite trace metal concentrations to analyze and quantify early ocean chemistry and its evolution through time.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Tackling the Challenges in Scene Graph Generation With Local-to-Global Interactions

In this work, we seek new insights into the underlying challenges of the scene graph generation (SGG) task. Quantitative and qualitative analysis of the visual genome (VG) dataset implies: 1) ambiguity: even if interobject relationship contains the same object (or predicate), they may not be visually or semantically similar; 2) asymmetry: despite the nature of the relationship that embodied the direction, it was not well addressed in previous studies; and 3) higher-order contexts: leveraging the identities of certain graph elements can help generate accurate scene graphs. Motivated by the analysis, we design a novel SGG framework, Local-to-global interaction networks (LOGINs). Locally, interactions extract the essence between three instances of subject, object, and background, while baking direction awareness into the network by explicitly constraining the input order of subject and object. Globally, interactions encode the contexts between every graph component (i.e., nodes and edges). Finally, Attract and Repel loss is utilized to fine-tune the distribution of predicate embeddings. By design, our framework enables predicting the scene graph in a bottom-up manner, leveraging the possible complementariness. To quantify how much LOGIN is aware of relational direction, a new diagnostic task called Bidirectional Relationship Classification (BRC) is also proposed. Overall, experimental results demonstrate that LOGIN can successfully distinguish relational direction than existing methods (in BRC task), while showing state-of-the-art results on the VG benchmark (in SGG task).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Automated Generation of Weather and Climate Analysis Products

Wind roses are an important part to site operations as they depict the wind speed and direction percentage over a time period. In this project, I automated the production of wind roses for SRS meteorological towers. I developed a script to sequence through the dataset by period and create a wind rose for each of those period sets. Graphics were generated for every 4-hour period of the day, for each of the 4 heights of the instruments, for every half of each month. A 10-year climatological period consisted of wind speed and directions measurements at 15-minute intervals. We used the years 2014-2024 as the wind instruments on the tower were upgraded to sonic anemometers in early 2014. I then compared these wind roses to those from a previous study done in 2003 to analyze the differences and similarities in the wind patterns. The wind roses are also used to understand environmental transport conditions at SRS. When comparing the different heights of the anemometers to the 2003 report, there is a similarity in the fact that the direction is relatively the same across the levels, with the wind speeds increasing as you get higher in the air. When comparing the season of our graphs against the 2003 report, we noticed that the winter and summer months appear to have very similar wind directions. However, in the spring we noticed that there were more southerly winds compared to the 2003 report which had more westerly winds. Finally, in the fall months, we noticed that there was a higher percentage of northeasterly winds, while the 2003 report showed more southeasterly winds. We can use these summaries to estimate the directional dependence of dose that the surrounding areas receive throughout the year according to time of day.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

Capturing Historic Reliability Performance Through Graph Databases: A Model Based System Engineering Approach

With the goal of improving the performance and reliability of high dependable technological systems such as nuclear power plants, advanced monitoring and health management systems are employed to inform system engineers on observed degradation processes and anomalous behaviors of assets and components. This information is captured in the form of large amount of data which can be heterogenous in nature (e.g., numeric, textual). Such large data availability poses challenges when system engineers are required to parse and analyze them in order to track historic reliability performance of assets and components. This paper tackles directly this challenge by providing means to organize data in the form of a graph: a knowledge graph. The presented approach distinguish itself from current knowledge graph-based methods by the fact that model-based system engineering (MBSE) models are used to “put data into context”. In particular, MBSE models are used as skeleton of a knowledge graph; numeric and textual data elements, once processed, are associated to MBSE model elements. Thus, a knowledge graph captures both system architecture (though MBSE models) and health/performance data. Such feature opens the door to new data analytics methods designed to identify causal relations between observed phenomena.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Spectral Clustering-Based Partitioning of Large-Scale Power Electronics-Based Power Systems for Small-Signal Stability Analysis

The nodal admittance matrix (NAM)-based approach is well-suited for small-signal stability analysis of large-scale power electronics-based power systems (PEPSs), as it preserves the system structure through its admittance matrix. Previous studies have explored partitioning such systems into subareas and interconnections to reduce computational burden; however, they lacked a formal algorithmic procedure for determining feasible partitions. While several grid partitioning methods, such as those based on graph theory or machine learning, exist in the literature, they cannot be directly applied to NAM-based analysis due to differing objectives and constraints. Here, this paper addresses this gap by presenting a systematic, step-by-step procedure for applying a spectral partitioning algorithm that yields a division of the system into subareas suitable for NAM-based analysis. The computational complexity of the proposed method is also derived to demonstrate its efficiency and justify the practicality of the resulting subarea decomposition. The performance of the partitioning method is evaluated by applying the spectral clustering-derived subareas and interconnections to the NAM-based partitioning approach on a 140-bus system. Computational times for the full-system and partitioned NAM analyses are compared using MATLAB. Additionally, PSCAD simulations of the complete system and partitioned subareas are carried out to verify the effectiveness of the proposed method.

Nupur [Univ. of Tennessee, Knoxville, TN (United S↗
DOE OSTI2022

GraphAlign: Graph-Enabled Machine Learning for Seismic Event Filtering

This report summarizes results from a 2 year effort to improve the current automated seismic event processing system by leveraging machine learning models that can operated over the inherent graph data structure of a seismic sensor network. Specifically, the GraphAlign project seeks to utilize prior information on which stations are more likely to detect signals originating from particular geographic regions to inform event filtering. To date, the GraphAlign team has developed a Graphical Neural Network (GNN) model to filter out false events generated by the Global Associator (GA) algorithm. The algorithm operates directly on waveform data that has been associated to an event by building a variable sized graph of station waveforms nodes with edge relations to an event location node. This builds off of previous work where random forest models were used to do the same task using hand crafted features. The GNN model performance was analyzed using an 8 week IMS/IDC dataset, and it was demonstrated that the GNN outperforms the random forest baseline. We provide additional error analysis of which events the GNN model performs well and poorly against concluded by future directions for improvements.

58 GEOSCIENCES↗
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

Accelerating network layouts using graph neural networks

Graph layout algorithms used in network visualization represent the first and the most widely used tool to unveil the inner structure and the behavior of complex networks. Current network visualization software relies on the force-directed layout (FDL) algorithm, whose high computational complexity makes the visualization of large real networks computationally prohibitive and traps large graphs into high energy configurations, resulting in hard-to-interpret “hairball” layouts. Here we use Graph Neural Networks (GNN) to accelerate FDL, showing that deep learning can address both limitations of FDL: it offers a 10 to 100 fold improvement in speed while also yielding layouts which are more informative. We analytically derive the speedup offered by GNN, relating it to the number of outliers in the eigenspectrum of the adjacency matrix, predicting that GNNs are particularly effective for networks with communities and local regularities. Finally, we use GNN to generate a three-dimensional layout of the Internet, and introduce additional measures to assess the layout quality and its interpretability, exploring the algorithm’s ability to separate communities and the link-length distribution. The novel use of deep neural networks can help accelerate other network-based optimization problems as well, with applications from reaction-diffusion systems to epidemics.

97 MATHEMATICS AND COMPUTING↗