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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 OSTI2020

Learning to Count Grave Sites for Cemetery Observation Models With Satellite Imagery

Understanding how people occupy open spaces is important for research in support of population modeling, policy, national security, emergency response, and sustainability. For the past decade, there has been an increase in research toward capturing and reporting population dynamics and patterns of life at the building level and in some open public spaces such as cemeteries and parks. This is done through observation models developed from local sociocultural information acquired at various spatiotemporal scales to inform night, day, and episodic population occupancy estimates (people/1000 sq ft). Sociocultural information for cemeteries and parks is scarcely available and often collected manually. The process is not only marred by inconsistencies but is laborious and time consuming. In this study, we leverage convolutional neural networks (CNNs) and satellite imagery to derive grave site counts as proxy variables to support scalable and accurate sociocultural data required in a population observation model. Through a hybrid workflow (weak localization plus regression model), we characterize a large scale automation process to counting of grave sites. We evaluate and demonstrate the efficacy of proposed workflow using out-of-data set large satellite imagery and establish its broader impact on cemetery observation models.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2025

Hybrid learning techniques for scientific data reduction with performance guarantees

The research initiatives supported by the U.S. Department of Energy (DOE) Grant DE-SC0022265 are fundamentally aimed at pioneering advanced machine learning (ML) techniques for scientific data compression within high-performance computing (HPC) environments. This comprehensive body of work addresses the critical challenge posed by the exponential growth of data generated by scientific simulations in domains such as fusion energy, climate modeling, and computational fluid dynamics (CFD). A core objective is to develop compression algorithms that achieve substantial data reduction—often by orders of magnitude—while rigorously ensuring the fidelity of both the primary data (PD) and scientifically crucial derived quantities of interest (QoI). The methodologies deployed under this grant integrate sophisticated deep learning architectures, prominently featuring autoencoders, advanced generative models like conditional diffusion, and hybrid learning techniques. Key innovations include the development of Guaranteed Autoencoders (GAE) and the Guaranteed Conditional Diffusion with Tensor Correction (GCDTC) framework, which provide explicit, instance-level error bounds on reconstructed data. Furthermore, specialized strategies such as nonlinear constraint satisfaction are employed to preserve the integrity of QoI, a vital requirement for the trustworthiness of downstream scientific analyses. This research also focuses on the design and implementation of scalable, GPU-accelerated software pipelines that seamlessly integrate into existing HPC workflows, ensuring both computational efficiency and practical applicability. The CAESAR framework, for example, unifies foundation and generative models to create an adaptive and efficient compression solution for spatio-temporal scientific data. Collectively, these efforts represent a significant advancement in mitigating the scientific data deluge, enabling more effective data management, accelerated scientific discovery, and optimized utilization of HPC resources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Final report- UFL - RAPIDS2: A SciDAC Institute for Computer Science, Data, and Artificial Intelligence

The research initiatives supported by the U.S. Department of Energy (DOE) Grant DE-SC0022265 are fundamentally aimed at pioneering advanced machine learning (ML) techniques for scientific data compression within high-performance computing (HPC) environments. This comprehensive body of work addresses the critical challenge posed by the exponential growth of data generated by scientific simulations in domains such as fusion energy, climate modeling, and computational fluid dynamics (CFD). A core objective is to develop compression algorithms that achieve substantial data reduction—often by orders of magnitude—while rigorously ensuring the fidelity of both the primary data (PD) and scientifically crucial derived quantities of interest (QoI). The methodologies deployed under this grant integrate sophisticated deep learning architectures, prominently featuring autoencoders, advanced generative models like conditional diffusion, and hybrid learning techniques. Key innovations include the development of Guaranteed Autoencoders (GAE) and the Guaranteed Conditional Diffusion with Tensor Correction (GCDTC) framework, which provide explicit, instance-level error bounds on reconstructed data. Furthermore, specialized strategies such as nonlinear constraint satisfaction are employed to preserve the integrity of QoI, a vital requirement for the trustworthiness of downstream scientific analyses. This research also focuses on the design and implementation of scalable, GPU-accelerated software pipelines that seamlessly integrate into existing HPC workflows, ensuring both computational efficiency and practical applicability. The CAESAR framework, for example, unifies foundation and generative models to create an adaptive and efficient compression solution for spatio-temporal scientific data. Collectively, these efforts represent a significant advancement in mitigating the scientific data deluge, enabling more effective data management, accelerated scientific discovery, and optimized utilization of HPC resources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Enhancing Cluster Identification in Atom Probe Tomography Data Using Transfer Learning

Atom Probe Tomography (APT) is a powerful technique for visualizing the atomic-scale distribution of solutes in materials, but quantitative cluster analysis of APT datasets remains a challenge due to the need for subjective parameter selection in clustering algorithms. While distance-based and density-based methods such as HDBSCAN are widely used, their performance is highly sensitive to user-defined parameters, which undermines reproducibility and accuracy. This study proposes an image-based, deep learning-aided workflow for automating parameter selection and cluster detection in APT data analysis. By projecting 3D APT point clouds onto 2D planes, we leverage pretrained convolutional neural networks (ConvNeXt-Tiny and ResNet-50) through transfer learning to predict the number of clusters present in synthetic datasets. The output is used to guide K-means clustering and estimate HDBSCAN parameters, specifically minimum cluster size and minimum sample points. This approach reduces reliance on manual parameter tuning, improving consistency and scalability. The methodology demonstrates the feasibility of using image-based deep learning for interpreting complex spatial patterns in APT data, enabling faster and more objective analysis. The complete workflow and code are made publicly available to support reproducibility and future research.

Density-based clustering↗
DOE OSTI2022

Fully self-consistent finite-temperature $GW$ in Gaussian Bloch orbitals for solids

In this work, we present algorithmic and implementation details for the fully self-consistent finite-temperature $GW$ method in Gaussian Bloch orbitals for solids. Our implementation is based on the finite-temperature Green's function formalism in which all equations are solved on the imaginary axis, without resorting to analytical continuation during the self-consistency. No quasiparticle approximation is employed and all matrix elements of the self-energy are explicitly evaluated. The method is tested by evaluating the band gaps of selected semiconductors and insulators. We show agreement with other, differently formulated, finite-temperature sc ⁢$GW$ implementations when finite-size corrections and basis-set errors are taken into account. By migrating computationally intensive calculations to graphics processing units, we obtain scalable results on large supercomputers with nearly optimal performance. Our work demonstrates the applicability of Gaussian orbital based sc⁢ $GW$ for ab initio correlated material simulations and provides a sound starting point for embedding methods built on top of $GW$.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

A comparative study of shear band tracking strategies in three-dimensional finite elements with embedded weak discontinuities

We present a computational framework for the treatment of shear localization in metallic materials under dynamic loading, based on the integration of a shear band tracking strategy into an explicit 3D finite element formulation with embedded weak discontinuities. Within this computational framework, an embedded shear band’s mid-surface is represented by an iso-surface of a level set function, which is obtained by solving a heatconduction type boundary value problem (BVP). The solution of this BVP is carried out either globally over the entire problem domain, or locally at the level of individual elements in the mesh. In this paper, we present a detailed comparison of these global and local algorithmic implementations of the shear band tracking strategy. Numerical results obtained using these two implementations, and using a simplified formulation without shear band tracking, are presented and compared. Moreover, we compare the computational efficiency and parallel scaling performance of the local and global implementations. This comparative study shows that both implementations can simulate the initiation of two independent shear bands and their propagation past each other without merging, whereas only the global implementation can successfully simulate the merging of two branches of a single shear band. This study also confirms that the global implementation is more computationally intensive, since it requires a global system of linear equations associated with the level set BVP to be solved at each time step. Both implementations exhibit very good scalability in domain decomposition-based parallel simulations.

36 MATERIALS SCIENCE↗
NASA NTRS2012

SpaceCube Mini

This version of the SpaceCube will be a full-fledged, onboard space processing system capable of 2500+ MIPS, and featuring a number of plug-andplay gigabit and standard interfaces, all in a condensed 3x3x3 form factor [less than 10 watts and less than 3 lb (approximately equal to 1.4 kg)]. The main processing engine is the Xilinx SIRF radiation- hardened-by-design Virtex-5 FX-130T field-programmable gate array (FPGA). Even as the SpaceCube 2.0 version (currently under test) is being targeted as the platform of choice for a number of the upcoming Earth Science Decadal Survey missions, GSFC has been contacted by customers who wish to see a system that incorporates key features of the version 2.0 architecture in an even smaller form factor. In order to fulfill that need, the SpaceCube Mini is being designed, and will be a very compact and low-power system. A similar flight system with this combination of small size, low power, low cost, adaptability, and extremely high processing power does not otherwise exist, and the SpaceCube Mini will be of tremendous benefit to GSFC and its partners. The SpaceCube Mini will utilize space-grade components. The primary processing engine of the Mini is the Xilinx Virtex-5 SIRF FX-130T radiation-hardened-by-design FPGA for critical flight applications in high-radiation environments. The Mini can also be equipped with a commercial Xilinx Virtex-5 FPGA with integrated PowerPCs for a low-cost, high-power computing platform for use in the relatively radiation- benign LEOs (low-Earth orbits). In either case, this version of the Space-Cube will weigh less than 3 pounds (.1.4 kg), conform to the CubeSat form-factor (10x10x10 cm), and will be low power (less than 10 watts for typical applications). The SpaceCube Mini will have a radiation-hardened Aeroflex FPGA for configuring and scrubbing the Xilinx FPGA by utilizing the onboard FLASH memory to store the configuration files. The FLASH memory will also be used for storing algorithm and application code for the PowerPCs and the Xilinx FPGA. In addition, it will feature highspeed DDR SDRAM (double data rate synchronous dynamic random-access memory) to store the instructions and data of active applications. This version will also feature SATA-II and Gigabit Ethernet interfaces. Furthermore, there will also be general-purpose, multi-gigabit interfaces. In addition, the system will have dozens of transceivers that can support LVDS (low-voltage differential signaling), RS-422, or SpaceWire. The SpaceCube Mini includes an I/O card that can be customized to meet the needs of each mission. This version of the SpaceCube will be designed so that multiple Minis can be networked together using SpaceWire, Ethernet, or even a custom protocol. Scalability can be provided by networking multiple SpaceCube Minis together. Rigid-Flex technology is being targeted for the construction of the SpaceCube Mini, which will make the extremely compact and low-weight design feasible. The SpaceCube Mini is designed to fit in the compact CubeSat form factor, thus allowing deployment in a new class of missions that the previous SpaceCube versions were not suited for. At the time of this reporting, engineering units should be available in the summer 2012.

Michael Lin↗
DOE OSTI2021

On Distributed Model-Free Reinforcement Learning Control with Stability Guarantee

Distributed learning can enable scalable and effective decision making in numerous complex cyber-physical systems such as smart transportation, robotics swarm, power systems, etc. However, the stability of the system is usually not guaranteed in most existing learning paradigms; and this limitation can hinder the wide deployment of machine learning in decision making of safety-critical systems. This paper presents a stability guaranteed distributed reinforcement learning (SGDRL) framework for interconnected linear subsystems, without knowing the subsystem models. While the learning process requires data from a peer-to-peer (p2p) communication architecture, the control implementation of each subsystem is only based on its local state. The stability of the interconnected subsystems will be ensured by a diagonally dominant eigenvalue condition, which will then be used in a model-free RL algorithm to learn the feedback control gains. The RL algorithm structure follows an off-policy iterative framework, with interleaved policy evaluation and policy update steps. We numerically validate our theoretical results by performing simulations on four interconnected sub-systems.

Mukherjee, Sayak↗
DOE OSTI2021

Distributional Deep Reinforcement Learning-Based Emergency Frequency Control

Emergency frequency control is one of the most critical approaches to maintain power system stability after major disturbances. With the increasing number of grid-connected renewable energy sources, existing model-based methods of frequency control are facing up with challenges of computational speed and scalability for large-scale systems. In this paper, the emergency frequency control problem is formulated as a Markov Decision Process (MDP) and solved through a novel Distributional Deep Reinforcement Learning (DDRL) method, namely the distributional soft actor critic (DSAC) method. Compared with other RL methods that only estimate the mean value, the proposed DSAC model estimates the distribution of value function over returns. This advancement can lead to more insights and knowledge for the agent, with the benefit of a much faster and more stable learning process, and the improved frequency control performance. Here, the simulation results on IEEE 39-bus and IEEE 118-bus systems demonstrate the effectiveness and robustness of proposed models, as well as the advantage compared to other state-of-the-art DRL algorithms.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

FAIR Data and Interpretable AI Framework for Architectured Metamaterials (Final Report)

This research program established a transformative framework for the discovery and design of mechanical metamaterials, which are architected structures engineered to control physical phenomena like sound and vibration in ways natural materials cannot. To overcome the traditional reliance on trial-and-error, the project developed an interpretable Artificial Intelligence (AI) framework that moves beyond "black box" models to reveal the specific geometric patterns—such as "unit-cell templates"—that govern a material’s performance. A major breakthrough was the development of a hierarchical design method, which allows a single material to block vibrations across multiple frequency ranges simultaneously by layering patterns at different scales without them interfering with one another. This was further expanded to include irregular, graph-based designs that use spanning tree algorithms to ensure structural connectivity while allowing for customized, direction-dependent properties like stiffness and acoustic impedance. Beyond design, the project addressed the practicalities of real-world production by developing uncertainty quantification techniques that account for manufacturing defects and material variability, reducing the need for expensive physical testing by orders of magnitude. To speed up the discovery process, the team implemented Gaussian Process Regression and other surrogate models that provide accurate performance predictions at a fraction of the traditional computational cost. The AI-generated designs were successfully validated through fabrication of physical samples and wave propagation experiments, confirming their ability to accurately guide or reflect waves as predicted. By contributing these tools and high-quality FAIR benchmark datasets to the wider scientific community, this work provides a scalable foundation for advancing technologies in aerospace vibration control, medical imaging, and noise reduction.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Application of Banking Scoring and Rating for Coherent Risk Measures in Electricity Systems ABSCORES

This project developed a framework for asset and system risk management that can be incorporated into current electricity system operations to improve economic efficiency and establish an Electric Assets Risk Bureau. We leveraged scoring and ratings from banking and financial institutions alongside current optimization methods in dispatching power systems to help system operators and electricity markets schedule resources. This approach is based on the observation that there are major discrepancies between the power scheduled by a system operator and the actual power generated/consumed. These discrepancies—exacerbated by unplanned contingencies (e.g., natural disasters)—are caused by multiple factors, including the different financial, environmental and risk preferences of power producers, consumers, and aggregators. We developed a framework that counteracts two failures in electricity system operations: imperfect information and missing markets for products. The technical approach included five tasks. Tasks 1 and 2 supported the development of risk scores at the asset level with historical data collected for this project. Tasks 3, 4, and 5 incorporated scoring into decision-making at the system level. The proposed effort achieved PERFORM's Program Objectives because the proposed outputs and algorithms do not exist in the electricity industry and are an innovative approach to managing risk. Since the acknowledged need to better assess and act upon risk profiles for grid assets has not been met by the industry, this project will also impact ARPA-E's Mission Areas, including improving energy efficiency and giving the U.S. a technological lead in advanced energy technologies.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2020

Library for Evolutionary Algorithms in Python (LEAP)

There are generally three types of scientific software users: users that solve problems using existing science software tools, researchers that explore new approaches by extending existing code, and educators that teach students scientific concepts. Python is a general-purpose programming language that is accessible to beginners, such as students, but also as a language that has a rich scientific programming ecosystem that facilitates writing research software. Additionally, as high-performance computing (HPC) resources become more readily available, software support for parallel processing becomes more relevant to scientific software.There currently are no Python-based evolutionary computation frameworks that support all three types of scientific software users. Moreover, some support synchronous concurrent fitness evaluation that do not efficiently use HPC resources. We pose here a new Python-based EC framework that uses an established generalized unified approach to EA concepts to provide an easy to use toolkit for users wishing to use an EA to solve a problem, for researchers to implement novel approaches, and for providing a low-bar to entry to EA concepts for students. Additionally, this toolkit provides a scalable asynchronous fitness evaluation implementation friendly to HPC that has been vetted on hardware ranging from laptops to the world’s fastest supercomputer, Summit.

Coletti, Mark↗
DOE OSTI2024

Advanced Shuttle Strategies for Parallel QCCD Architectures

Trapped ions (TIs) are at the forefront of quantum computing implementation, offering unparalleled coherence, fidelity, and connectivity. However, the scalability of TI systems is hampered by the limited capacity of individual ion traps, necessitating intricate ion shuttling for advanced computational tasks. The quantum charge-coupled device (QCCD) framework has emerged as a promising solution, facilitating ion mobility for universal quantum computation. Current QCCD architectures predominantly feature a linear topology, which is increasingly recognized as inefficient for complex quantum operations. Anticipating the shift toward more efficacious designs, this article introduces an innovative quantum scheduling strategy optimized for parallel QCCD topologies. Our strategy proposes a probabilistic formula for ion movement, alongside ingenious methods for local layer generation and layer compression, yielding a significant reduction in ion shuttle times. Through simulations, we demonstrate that our strategy not only substantially outstrips the linear model but also exhibits better performance over other parallel strategies that employ greedy algorithms. This is achieved through our nuanced resolution of complexities, such as traffic blocks and trap capacity limitations. The consequent reduction in shuttle operations leads to lower energy consumption and an enhancement in the quantum computer's fidelity, ultimately accelerating program execution times.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Multi-modal Energy-optimal Trip Scheduling in Real-time (METS-R) for Transportation Hubs (Final Report)

This report summarizes the work performed under the award number EE0008524. The project develops the Multi-modal Energy-optimal Trip Scheduling in Real-time (METS-R) platform as the next-generation transportation solution based on autonomous electric vehicles (AEV) serving passenger trips from and to urban transportation hubs, to substantially reduce transportation energy consumption. Extensive data collection and analyses were first conducted to understand the demand patterns and energy consumption of hub-based on-road trips. Then, a data-driven framework that consists of an analytical module and a simulation module was proposed. For the analytical module, five planning + operation tools were developed to support the planning and energy-efficient operations of urban AEV services: the charging station planning that robotically allocates charging supplies based on the stationary charging demand distribution; the transit planning and demand adaptive scheduling model that efficiently generates\ candidate transit routes from hubs to other places and dynamically adjusts the transit time table to fit the current demand; the online energy-efficient routing that learns the energy-optimal paths from observations of link-level energy consumption in real-time; the hub-based ridesharing that matches trip requests together with account for the uncertainty of future trip demand and vehicle supply; and finally, the integrated demand prediction and anomaly detection pipeline that leverages the flight/train time table and support other planning/operation tools. To demonstrate the performance of these tools, a scalable high-performance agent-based simulator was built. We divided the urban space into multiple service zones where each zone was considered as an agent for passenger generation and vehicle charging. Two types of AEV agents were coded to model two types of mobility services: AEV taxi and AEV transit. For the AEV taxi, the team implemented the functions of pickup/drop-off passengers, energy-efficient routing, ridesharing, fleet rebalancing, and recharging. For the AEV bus, the team implemented the functions of demand-adaptive route scheduling, passenger boarding, and recharging. A high-performance computing framework was introduced to receive various profiling information (such as link energy updates, vehicle speed) from the simulator instances and communicate the operational commands back to the instances. The numerical experiments show that each of the proposed operational algorithms can reduce energy consumption and improve system efficiency. Furthermore, there exists the need to collectively consider multiple planning + operational strategies as multiple strategies can influence each other in terms of performance impacts. Recommendations for future work related to AEV planning and simulation are discussed.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2025

Basic Research Needs for Inverse Methods for Complex Systems under Uncertainty

Inverse problems, which aim to infer unknown properties of a system using experimental and observational data, are central to addressing many of the U.S. Department of Energy’s (DOE) most critical scientific and engineering challenges. Accurate, computationally efficient, and data-efficient solutions to inverse problems are essential for advancing DOE mission-critical science drivers, including analyzing data from large-scale experimental facilities, optimizing fusion reactor performance, accelerating materials discovery, enhancing geophysical imaging, improving wildfire predictions, and enabling autonomous systems and digital twins. However, these problems are becoming increasingly complex, often involving nonlinear, highdimensional, and interconnected systems and models that span multiple physics and scales, while relying on data with varying quantity, quality, and information content. Compounding these challenges is the uncertainty inherent in DOE-relevant systems, where errors in inputs, noise in data, incompleteness of data, and discrepancies between models and reality constrain the accuracy and precision of solutions. At the same time, the convergence of recent scientific computing trends—scientific machine learning, artificial intelligence, and computing advances such as exascale computing—is creating unprecedented opportunities for tackling these challenges. The cross-cutting nature of inverse problems, combined with their growing complexity and rapidly evolving data and algorithmic demands, strongly motivates the formulation of a prioritized research agenda to maximize their capabilities and impact. In response to this need, DOE’s Advanced Scientific Computing Research (ASCR) program in the Office of Science convened the Workshop on Basic Research Needs for Inverse Problems for Complex Systems Under Uncertainty in June 2025. This workshop brought together experts across disciplines to identify grand challenges and major opportunities in the field. Through collaborative discussions, the workshop defined transformative research directions aimed at addressing the mathematical, statistical, and computational challenges posed by inverse problems under uncertainty. As a result of these efforts, four priority research directions (PRDs) were identified to guide future research and development in this area. These PRDs, summarized below, represent a roadmap for advancing the foundational science and mathematics of inverse problems, enabling robust, scalable, and uncertainty-aware solutions that are critical for DOE applications.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2000

Parallel Conjugate Gradient: Effects of Ordering Strategies, Programming Paradigms, and Architectural Platforms

The Conjugate Gradient (CG) algorithm is perhaps the best-known iterative technique to solve sparse linear systems that are symmetric and positive definite. A sparse matrix-vector multiply (SPMV) usually accounts for most of the floating-point operations within a CG iteration. In this paper, we investigate the effects of various ordering and partitioning strategies on the performance of parallel CG and SPMV using different programming paradigms and architectures. Results show that for this class of applications, ordering significantly improves overall performance, that cache reuse may be more important than reducing communication, and that it is possible to achieve message passing performance using shared memory constructs through careful data ordering and distribution. However, a multi-threaded implementation of CG on the Tera MTA does not require special ordering or partitioning to obtain high efficiency and scalability.

Oliker, Leonid↗
NASA NTRSDate not supplied

Sheaf Theoretic Models for Routing in Delay Tolerant Networks

One key to communications scalability is routing; as such the goal of this paper is to build upon successful efforts towards general routing for space-based networks. With the ever-increasing accessibility of space, the number of assets is increasing, which becomes a critical communications burden in terms of scheduling, spectrum allocation, and resource allocation. In order to mitigate these concerns, a true networking approach is necessary; a standard approach for space systems is Delay Tolerant Networking (DTN). For DTN to be a meaningful answer to the Solar System Internet (SSI) question, DTN must offer meaningful routing solutions that span the heterogeneous collection of links and nodes. This, in turn, depends on the general structure of these disconnected networks -- a structure that remains largely unknown. In ground communications networks, routing decisions are made based on several pathfinding algorithms working in tandem. In previous work, we modeled Dijkstra's pathfinding algorithm using sheaves and provided a more general framework for determining paths using sheaves over graphs. Continuing our sheaf-theoretic approach, we introduce here an expansion of our pathfinding sheaf to handle more general information, and we expand on additional pathfinding algorithms that can be represented using sheaves. Moreover, we demonstrate means of combining multiple algorithms into a single sheaf structure so that changes of scale can be presented in the language of sheaves. In addition, space communications networks rely upon radio transmitter antennas which can establish broadcast and multicast communications options, rather than the primarily unicast options available to wired networks. Last year, we also introduced a multicast routing sheaf for presenting broadcast, unicast, and multicast communications over a graph. Extending that work, we also introduce queuing sheaves so that we can blend these communications options together to simulate a variety of routing options across space networks. In addition, we include examples to illustrate the applicability of this abstract theory to routing in disconnected networks.

Robert Short↗