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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Illuminating the pathways to carbon liberation: a systems approach to characterizing the consequential unknowns of carbon transformation and loss from thawing permafrost peatlands (Final Report)

The IsoGenie3 Project delivered new systems-level insights into carbon cycling in thawing permafrost landscapes, with an emphasis on methane and carbon dioxide emissions. From >200 samples from the site collected over a decade, co-analyzed for geochemistry and microbiology, the team recovered ~1,500 assembled microbial genomes and ~1,900 viral population genomes, revealing appreciable genetic novelty - from a new highly abundant bacterial phylum, to novel methane consumers and their activities, to rampant viral novelty. IsoGenie3 linked these organisms to carbon compound transformations (which define the cycling of organic matter in soils, and the loss of the greenhouse gases carbon dioxide and methane), and saw that the microbes at each stage of permafrost thaw had different genetic potential to degrade categories of compounds, expressed that genetic potential differently, and actually transformed carbon compounds into greenhouse gases in different ways. IsoGenie 3 identified that some of the thaw-stage differences were due to plant-microbiome relationships; the plant species across the thaw gradient contributed different carbon compounds into the soil, and hosted distinct microbiota (differing among parts of plants as well as species). Lastly, microbes in the saturated post-thaw conditions appeared likely to contribute to the mobilization and toxification of mercury released during thaw. In parallel with ongoing field sampling and analysis, hypotheses arising from field observations were tested via lab incubation experiments. When communities are taken out of their native habitats, they behave differently, and the team first rigorously quantified the magnitude of this effect on microbiome composition and functional capacity, organic matter composition, and gas production; overall the main system processes were maintained in the lab incubations under the conditions tested. Further, the microbial data could inform geochemical reaction network models of those processes. Then, the team ran experiments with additions of compounds, varying temperature, and “live” vs. “dead” peat (the latter having been gamma irradiated, with a few additional variants to control for methodological artifacts). From these, we (a) determined the importance of plant-derived soluble phenolic compounds in bogs’ extraordinary recalcitrance of organic matter, and carbon gas emissions skewed to carbon dioxide; (b) proposed an abiotic ‘tanning’ mechanism, which could contribute to Sphagnum’s inhibitory effect on anaerobic decomposition through alteration of N availability. IsoGenie3 illuminated longer-term and landscape-scale interactions of permafrost thaw and carbon cycling, advancing knowledge of the drivers of methane dynamics not only across in the permafrost-associated peatland (where hydrology and plant communities dictate microbiomes) but also their interconnected lakes (where sediment carbon quality and resident microbiota are determined by position within lake, and lake features). By leveraging observations of site methane dynamics extending well before this project, the team was able to construct a 44-year portrait of the interplay of permafrost thaw, hydrology, vegetation dynamics, and carbon gas emissions, and the doubling of the fully-thawed fens over this time. From the detailed study of this focal site, IsoGenie3 also aimed to improve model representation of these kinds of sites and processes. To improve predictions of methane transformations, we incorporated acetate and isotope dynamics into the ‘DNDC’ biogeochemistry model. In addition, recovered genomes were grouped into ‘functional groups’, i.e. the genomes that perform a specific function of interest, then used to parameterize maximum growth rate and optimum growth temperature (via signatures in their sequence composition) for the BioCrunch model. The BioCrunch model was then in turn used to test the impact of increasing functional resolution of the microbes, on the carbon gas emissions. Lastly for modeling, the ecosys model was parameterized from the microbial and other data, and used to evaluate drivers of e.g. change in methane emissions. Finally, this project also led to the development of a range of new methods and tools, a new metric of organic matter decomposability, as well as a graph-database solution to multidisciplinary data storage and querying. This project’s ongoing analyses at our focal site also contributed to broader advancements in understanding elements of genetic plasticity and methane metabolism, climate change microbiology and community assembly, global peatland geochemistry and Arctic lakes’ roles in climate feedbacks.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

NaroNet: Discovery of tumor microenvironment elements from highly multiplexed images

Understanding the spatial interactions between the elements of the tumor microenvironment -i.e. tumor cells. fibroblasts, immune cells- and how these interactions relate to the diagnosis or prognosis of a tumor is one of the goals of computational pathology. We present NaroNet, a deep learning framework that models the multi-scale tumor microenvironment from multiplex-stained cancer tissue images and provides patient-level interpretable predictions using a seamless end-to-end learning pipeline. Trained only with multiplex-stained tissue images and their corresponding patient-level clinical labels, NaroNet unsupervisedly learns which cell phenotypes, cell neighborhoods, and neighborhood interactions have the highest influence to predict the correct label. To this end, NaroNet incorporates several novel and state-of-the-art deep learning techniques, such as patch-level contrastive learning, multi-level graph embeddings, a novel max-sum pooling operation, or a metric that quantifies the relevance that each microenvironment element has in the individual predictions. We validate NaroNet using synthetic data simulating multiplex-immunostained images where a patient label is artificially associated to the -adjustable- probabilistic incidence of different microenvironment elements. We then apply our model to two sets of images of human cancer tissues: 336 seven-color multiplex-immunostained images from 12 high-grade endometrial cancer patients; and 382 35-plex mass cytometry images from 215 breast cancer patients. In both synthetic and real datasets, NaroNet provides outstanding predictions of relevant clinical information while associating those predictions to the presence of specific microenvironment elements.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Experimental Observations of the Topology of Convolutional Neural Network Activations

Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of parameters associated with a series of transformations defined by the model architecture resulting in high-dimensional, difficult to interpret internal representations of input data. As DNNs become more ubiquitous across multiple sectors of our society, there is increasing recognition that mathematical methods are needed to aid analysts, researchers, and practitioners in understanding and interpreting how these models' internal representations relate to the final classification. In this paper we apply cutting edge techniques from TDA with the goal of gaining insight towards interpretability of convolutional neural networks used for image classification. We use two common TDA approaches to explore several methods for modeling hidden layer activations as high-dimensional point clouds, and provide experimental evidence that these point clouds capture valuable structural information about the model's process. First, we demonstrate that a distance metric based on persistent homology can be used to quantify meaningful differences between layers and discuss these distances in the broader context of existing representational similarity metrics for neural network interpretability. Second, we show that a mapper graph can provide semantic insight as to how these models organize hierarchical class knowledge at each layer. These observations demonstrate that TDA is a useful tool to help deep learning practitioners unlock the hidden structures of their models.

topological data analysis, deep learning↗
DOE OSTI2024

Decode the Workload: Training Deep Learning Models for Efficient Compute Cluster Representation

Monitoring the status of a high throughput computing cluster running computationally intensive production jobs is a crucial yet challenging system administration task due to the complexity of such systems. To this end, we train autoencoders using the Linux kernel CPU metrics of the cluster. Additionally, we explore assisting these models with graph neural networks to share information across threads within a compute node. The models are compared in terms of their ability to: 1) Produce a compressed latent representation that captures the salient features of the input, 2) Detect anomalous activity, and 3) Make distinction between different kinds of jobs run at Jefferson Lab. The goal is to have a robust encoder whose compressed embeddings are used for several downstream tasks. We extend this study further by deploying these models in a human-in-the-loop production-based setting for the anomaly detection task and discuss the associated implementation aspects such as continual learning and the criterion to generate alarms. This study represents a first step in the endeavor towards building self-supervised large-scale foundation models for computing centers.

Mohammed, Ahmed↗
DOE OSTI2025

A framework to evaluate machine learning crystal stability predictions

The rapid adoption of machine learning in various scientific domains calls for the development of best practices and community agreed-upon benchmarking tasks and metrics. We present Matbench Discovery as an example evaluation framework for machine learning energy models, here applied as pre-filters to first-principles computed data in a high-throughput search for stable inorganic crystals. We address the disconnect between (1) thermodynamic stability and formation energy and (2) retrospective and prospective benchmarking for materials discovery. Alongside this paper, we publish a Python package to aid with future model submissions and a growing online leaderboard with adaptive user-defined weighting of various performance metrics allowing researchers to prioritize the metrics they value most. To answer the question of which machine learning methodology performs best at materials discovery, our initial release includes random forests, graph neural networks, one-shot predictors, iterative Bayesian optimizers and universal interatomic potentials. We highlight a misalignment between commonly used regression metrics and more task-relevant classification metrics for materials discovery. Accurate regressors are susceptible to unexpectedly high false-positive rates if those accurate predictions lie close to the decision boundary at 0 eV per atom above the convex hull. The benchmark results demonstrate that universal interatomic potentials have advanced sufficiently to effectively and cheaply pre-screen thermodynamic stable hypothetical materials in future expansions of high-throughput materials databases.

Riebesell, Janosh↗
DOE OSTI2025

AI-Assisted Conceptual Development of a Pre-Geometric Cosmological Model - An Exercise in AI-Assisted Conceptual Framework Generation, Paper II: Local Geometry and Metric Structure

This paper develops the geometric sector of the replication-driven cosmogenesis framework introduced in Paper I. Starting from a pre-geometric spectral substrate and a minimal set of replication axioms, we show how coherent self-replicating units generate a spatial adjacency graph whose continuum limit acquires an effective Riemannian structure. The replication dynamics determines a characteristic correlation length that seeds the local metric, while overlap relations among coherent units produce an isotropic neighborhood geometry with an emergent dimensionality $d_{\rm eff}\simeq 3$ across a broad range of replication factors. As replication slows and causal order stabilizes, a limiting signal speed $c_\ast$ appears, providing the basis for the Lorentzian structure of spacetime without assuming a pre-existing light cone. We derive conditions under which the adjacency graph converges to a smooth three-dimensional manifold, describe the transition from Euclidean to Lorentzian propagation, and identify geometric invariants controlled by the replication parameters. This work establishes the geometric and causal layer of the replication cosmogenesis program, bridging the spectral axioms of Paper I to the cosmological dynamics explored in Paper III.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

A Block-Based Triangle Counting Algorithm on Heterogeneous Environments

Triangle counting is a fundamental building block in graph algorithms. In this article, we propose a block-based triangle counting algorithm to reduce data movement during both sequential and parallel execution. Our block-based formulation makes the algorithm naturally suitable for heterogeneous architectures. The problem of partitioning the adjacency matrix of a graph is well-studied. Our task decomposition goes one step further: it partitions the set of triangles in the graph. By streaming these small tasks to compute resources, we can solve problems that do not fit on a device. We demonstrate the effectiveness of our approach by providing an implementation on a compute node with multiple sockets, cores and GPUs. The current state-of-the-art in triangle enumeration processes the Friendster graph in 2.1 seconds, not including data copy time between CPU and GPU. Using that metric, our approach is 20 percent faster. When copy times are included, our algorithm takes 3.2 seconds. This is 5.6 times faster than the fastest published CPU-only time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Improving Trustworthiness of Data-Driven Power Grid Contingency Analysis With Bayesian Residual Graph Neural Networks

The evolving energy landscape requires novel tools to efficiently perform contingency analysis and reliability assessment of power grids, potentially in real-time. The high computational cost of traditional power flow solvers limits their applicability in practice. Machine learning (ML) surrogates such as deep neural networks (NNs) accelerate power flow solvers computations, enabling high-order contingency analysis and real-time decision-making by learning highly nonlinear functions and integrating grid topology via graph architectures. However, (graph) NNs lack predictive power away from training data and do not provide predictive confidence estimates. Here, we present a Bayesian residual graph NN that integrates knowledge from low-fidelity data via residual training and embeds granular quantification of uncertainties, improving trustworthiness critical for high-consequence decision-making. Applying Bayesian concepts to NNs is challenging due to the high-dimensionality of both the parameter space, complicating derivation of a meaningful prior, and the output space in large grid systems, requiring enhanced techniques to assess the predicted high-dimensional uncertainties. Our contributions include: (1) Deriving a prior for fully connected and graph NNs that leverages low-fidelity data to guide mean predictions and appropriately control prior predictive uncertainty. (2) Integrating this prior within an ensembling with anchoring scheme for efficient approximate posterior inference. (3) Deriving enhanced metrics to assess accuracy of both the mean and uncertainty predictions in high dimensions, appropriately accounting for correlations propagated through graph layers. The resulting Bayesian residual graph NN is tested on a contingency analysis task for 14-bus and 118-bus grids.

24 - POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

MSASGCN : Multi-Head Self-Attention Spatiotemporal Graph Convolutional Network for Traffic Flow Forecasting

Traffic flow forecasting is an essential task of an intelligent transportation system (ITS), closely related to intelligent transportation management and resource scheduling. Dynamic spatial-temporal dependencies in traffic data make traffic flow forecasting to be a challenging task. Most existing research cannot model dynamic spatial and temporal correlations to achieve well-forecasting performance. The multi-head self-attention mechanism is a valuable method to capture dynamic spatial-temporal correlations, and combining it with graph convolutional networks is a promising solution. Therefore, we propose a multi-head self-attention spatiotemporal graph convolutional network (MSASGCN) model. It can effectively capture local correlations and potential global correlations of spatial structures, can handle dynamic evolution of the road network, and, in the time dimension, can effectively capture dynamic temporal correlations. Experiments on two real datasets verify the stability of our proposed model, obtaining a better prediction performance than the baseline algorithms. The correlation metrics get significantly reduced compared with traditional time series prediction methods and deep learning methods without using graph neural networks, according to MAE and RMSE results. Compared with advanced traffic flow forecasting methods, our model also has a performance improvement and a more stable prediction performance. We also discuss some problems and challenges in traffic forecasting.

Cao, Yang↗
DOE OSTI2023

Lorentz group equivariant autoencoders

Abstract There has been significant work recently in developing machine learning (ML) models in high energy physics (HEP) for tasks such as classification, simulation, and anomaly detection. Often these models are adapted from those designed for datasets in computer vision or natural language processing, which lack inductive biases suited to HEP data, such as equivariance to its inherent symmetries. Such biases have been shown to make models more performant and interpretable, and reduce the amount of training data needed. To that end, we develop the Lorentz group autoencoder (LGAE), an autoencoder model equivariant with respect to the proper, orthochronous Lorentz group $$\textrm{SO}^+(3,1)$$ SO + ( 3 , 1 ) , with a latent space living in the representations of the group. We present our architecture and several experimental results on jets at the LHC and find it outperforms graph and convolutional neural network baseline models on several compression, reconstruction, and anomaly detection metrics. We also demonstrate the advantage of such an equivariant model in analyzing the latent space of the autoencoder, which can improve the explainability of potential anomalies discovered by such ML models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Resilience Assessment Framework For Electric Distribution Systems Performance Under Extreme Conditions

The devastating impact of extreme weather-related events is increasingly evident on power grids, especially on distribution grids. The severity of their potential impact calls for 1) developing a suitable resilience assessment framework to capture the system performance and 2) assessing relevant mitigative strategies to lessen the impact of such events. This paper proposes a framework to identify grid vulnerabilities using the energy-at-risk concept to select, disconnect and isolate grid portions due to a resilience event. The proposed framework mainly consists of two steps; i) processing the utility's available infrastructure, i.e., a network model, possible switching combinations, and outage information for those combinations, as a graph-based database, and ii) implementing a novel optimal switching algorithm leveraging database and grid simulated metrics. These switching actions are generated to implement load curtailment in a rolling manner during anticipated grid scarcity conditions. In this study, a test case is created using two taxonomy feeders and is simulated against an extreme temperature event, e.g., a long, relatively cold, and prolonged freeze peak, thereby creating stress on the grid. It is demonstrated that the proposed framework allows utilities to predict the energy-at-risk during such resilience events and design suitable outage management strategies.

Poudel, Shiva↗
DOE OSTI2024

A Resilient Integrated Resource Planning Framework for Transmission Systems: Analysis and Optimization

This article presents a resilient Integrated Resource Planning (IRP) framework designed for transmission systems, with a specific focus on analyzing and optimizing responses to High-Impact Low-Probability (HILP) events. The framework aims to improve the resilience of transmission networks in the face of extreme events by prioritizing the assessment of events with significant consequences. Unlike traditional reliability-based planning methods that average the impact of various outage durations, this work adopts a metric based on the proximity of outage lines to generators to select HILP events. The system’s baseline resilience is evaluated by calculating load curtailment in different parts of the network resulting from HILP outage events. The transmission network is represented as an undirected graph. Graph-theoretic techniques are used to identify islands with or without generators, potentially forming segmented grids or microgrids. This article introduces Expected Load Curtailment (ELC) as a metric to quantify the system’s resilience. The framework allows for the re-evaluation of system resilience by integrating additional generating resources to achieve desired resilience levels. Optimization is performed in the re-evaluation stage to determine the optimal placement of distributed energy resources (DERs) for enhancing resilience, i.e., minimizing ELC. Case studies on the IEEE 24-bus system illustrate the effectiveness of the proposed framework. In the broader context, this resilient IRP framework aligns with energy sustainability goals by promoting robust and resilient transmission networks, as the optimal placement of DERs for resilience enhancement not only strengthens the system’s ability to withstand and recover from disruptions but also contributes to efficient resource utilization, advancing the overarching goal of energy sustainability.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Database Performance Monitoring for DUNE

This project improves Checkmk monitoring for DUNE Rucio PostgreSQL database services by adding clearer dashboard visibility for connection and lock behavior. The work began with a request to monitor database performance metrics such as connection usage, configured limits, lock activity, wait behavior, query performance, storage trends, and saturation alerts. Existing Checkmk PostgreSQL checks were reviewed, and gaps were identified in how connection states and lock modes were displayed. To address these gaps, two DSG-specific local checks were added for dune_rucio_prod: one for connection-state monitoring and one for lock-state monitoring. These checks report active, idle, idle-in-transaction, total, usage-percent, lock-mode, waiting-lock, and wait-age metrics. The added metrics supplement built-in Checkmk monitoring and provide DUNE application developers with clearer service states, history graphs, dashboard widgets, and alerts.

Bowers, Elliot [Cabrillo Coll.]↗
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 OSTI2025

Optimizing Traffic Signal Control to Enhance Transportation Efficiency and Maximize Pedestrian Benefits in the Road Network

Increasing urban mobility requirements demand efficient transportation system strategies for both vehicular and pedestrian movement. This study enhances the Decentralized Graph-based Multi-Agent Reinforcement Learning (DGMARL) approach, originally tailored for vehicular traffic signal timing, to incorporate pedestrian traffic dynamics. The improved algorithm considers crucial metrics such as Eco_PI, assesses vehicle fuel consumption by factoring in stops and delays, and addresses pedestrian waiting time, crucial for system efficiency while acknowledging driver waiting time impact. Utilizing Digital Twin simulation along the MLK Smart Corridor in Chattanooga, Tennessee, the algorithm's performance is compared for various pedestrian control scenarios. To evaluate the effectiveness of DGMARL, this study compared DGMARL-enabled signal management with automated pedestrian traffic detection and an actuated signal management system (real-word baseline) with pedestrian recall, which predetermingly enforces a pedestrian phase every cycle. Findings indicate substantial improvements with DGMARL, showing a 28.29% enhancement in vehicle Eco_PI, a 60.55 % reduction in pedestrian waiting time, and a 55.74% decrease in driver stop delay, on average, compared to the baseline actuated signal timing plan.

Kumarasamy, Vijayalakshmi K [The University of Ten↗
DOE OSTI2026

Intelligent Experiments through Real-Time AI: Fast Data Processing and Autonomous Detector Control for High-Energy Nuclear Experiments

The aim of this project is to develop software and hardware for fast real-time data processing and autonomous detector control and calibration for the sPHENIX and the future EIC experiments. Below summarizes Georgia Tech team efforts in the past year: 1. We developed a real-time clustering algorithm and FPGA-based pipeline architecture for processing fired pixel data from ALPIDE sensors in sPHENIX experiments. Our Columnar Clustering Co-Design introduces a hardware-aware, stream-friendly approach that segments pixel data by column pairs using a Column Pair Clustering (CPC) strategy, followed by Cluster Stitching to merge adjacent subclusters. Implemented in Vitis HLS, the pipeline comprises five stages—read-in, subclustering, stitching, analysis, and write-out—connected by tagged HLS streams with custom end-of-event signaling for robust synchronization. We designed a pipelined dataflow model optimized for throughput, low latency, and minimal buffering, enabling scalable clustering across events of arbitrary size. Our system maintains spatial precision via center-of-mass and shape key extraction and efficiently handles edge cases such as fragmented or nested clusters. Compared against DBSCAN in both software and hardware, our approach demonstrates competitive performance under FPGA constraints. 2. We also conducted a comprehensive algorithm-to-hardware co-design of connected component analysis tailored for sPHENIX experiments, focusing on real-time, low-latency processing using FPGAs and High-Level Synthesis (HLS). Starting from a Python-based particle tracking pipeline, the team translated the core logic—graph traversal via DFS and Union-Find—into an HLS-compatible C++ model, replacing dynamic memory and recursion with static arrays and pipelined control flow. The final design includes a fully streamed and dataflow-compatible Union-Find kernel optimized across five iterations, incorporating loop pipelining, array partitioning, AXI/FIFO interface tuning, and function flattening. Experimental results show up to 14.8× speedup over the CPU baseline, reducing per-graph latency to 1.58 μs and demonstrating strong resource efficiency with only ~7k LUTs and zero BRAM usage. The design maintains functional correctness against the Python reference using a Python-based C-simulation framework and Mean Squared Error metrics. This work validates the potential of HLS-driven FPGA designs for edge-level HEP data acquisition, laying a scalable foundation for future integration with real-time detector pipelines and multi-graph processing systems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Design and simulation of a SiPM-on-tile ZDC for the future EIC, and its performance with graph neural networks

We present a design for a high-granularity zero-degree calorimeter (ZDC) for the upcoming Electron-Ion Collider (EIC). The design uses SiPM-on-tile technology and features a novel staggered-layer arrangement that improves spatial resolution. To fully leverage the design’s high granularity and non-trivial geometry, we employ graph neural networks (GNNs) for energy and angle regression as well as signal classification. The GNN-boosted performance metrics meet, and in some cases, significantly surpass the requirements set in the report on science requirements and detector requirements for the EIC (Yellow Report), laying the groundwork for enhanced measurements that will facilitate a wide physics program. Our studies show that GNNs can significantly enhance the performance of high-granularity CALICE-style calorimeters by automating and optimizing the software compensation algorithms required for these systems. This improvement holds true even in the case of complicated geometries that pose challenges for image-based AI/ML methods.

Calorimeter↗
DOE OSTI2025

Power Flow Geometry and Approximation

Here, the power flow equations are important in numerous power systems problems of practical interest which consider alternating current power flow (ACPF) physics. Perhaps the most well studied being the alternating current optimal power flow problem (ACOPF), seeking to optimize the operation of an electric power system. Due to their non-linearity, problems which include the power flow equations are typically challenging, particularly in optimization. Interestingly, the set of solutions to the power flow equations forms a smooth manifold. As a result, differential geometry can be used to describe and analyze this set of equations. This approach has proven effective in several engineering applications (e.g., solving ACOPF and analyzing the solution space boundary). Central to the success of this approach is an understanding of the power flow manifold's geometry. In this work, we develop the geometric and topological properties of this manifold using concepts from differential geometry. After demonstrating the convenience of this manifold's representation as a function's graph, computational methods are emphasized: we develop retractions, error bounds for linear approximation, and formulas for evaluating the Riemannian metric (including associated objects such as geodesics and the curvature tensor). Scalar curvature and the second fundamental form play a new role in quantifying the quality of linear approximations, like the popular direct current approximation. All functions are implemented in Julia and available in an online repository. Proofs are included for completeness.

24 POWER TRANSMISSION AND DISTRIBUTION↗