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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Understanding Solar Photovoltaic System Performance: An Assessment of 75 Federal Photovoltaic Systems

This report presents a performance analysis of 75 photovoltaic systems based on PV system production data collected as part of a FEMP Federal PV Performance Assessment project combined with co-incident insolation, and ambient temperature to analyze how actual performance compares with a performance model. FEMP collaborated with 17 Federal agencies and sub-agencies to collect the information required to analyze the performance of each system. The systems represent a total capacity of 30,714 kW and range in size from 1 kW to 4,043 kW, with an average size of 410 kW, and were installed between 2011 and 2020. The data is analyzed for Key Performance Indicators, Availability, Performance Ratio and Energy Ratio by comparing the measured production data to model production data. The System Advisor Model (SAM) combines a description of the system (such as inverter capacity, de-rating for temperature, balance-of-system efficiency) with environmental parameters (coincident solar and temperature data) to calculate predicted performance. The performance metrics are calculated by lining up the measured production data with the model estimate on an hour-by-hour, day-by-day, or month-by-month basis (depending on the interval resolution of the production data). A report with system description, photo of the system, special assumptions made for the site, graph of measured production and model production, table of key performance indicators, and links to O&M resources that might improve performance was produced and delivered to site and agency staff with a short on-line briefing.

14 SOLAR ENERGY↗
DOE OSTI2024

Topological Interpretability for Deep Learning

With the growing adoption of AI-based systems across everyday life, the need to understand their decision-making mechanisms is correspondingly increasing. The level at which we can trust the statistical inferences made from AI-based decision systems is an increasing concern, especially in high-risk systems such as criminal justice or medical diagnosis, where incorrect inferences may have tragic consequences. Despite their successes in providing solutions to problems involving real-world data, deep learning (DL) models cannot quantify the certainty of their predictions. These models are frequently quite confident, even when their solutions are incorrect. This work presents a method to infer prominent features in two DL classification models trained on clinical and non-clinical text by employing techniques from topological and geometric data analysis. We create a graph of a model's feature space and cluster the inputs into the graph's vertices by the similarity of features and prediction statistics. We then extract subgraphs demonstrating high-predictive accuracy for a given label. These subgraphs contain a wealth of information about features that the DL model has recognized as relevant to its decisions. We infer these features for a given label using a distance metric between probability measures, and demonstrate the stability of our method compared to the LIME and SHAP interpretability methods. This work establishes that we may gain insights into the decision mechanism of a DL model. This method allows us to ascertain if the model is making its decisions based on information germane to the problem or identifies extraneous patterns within the data.

Spannaus, Adam↗
DOE OSTI2024

A Novel Framework to Quantify Power Grid Resilience

The quantification of an operating power grid’s resilience is highly significant today, given its criticality as an enabler of other infrastructures, complexity, and the threat it faces due to a wide range of detrimental events, from extreme climate to cyber attacks. Currently, there exist no standardized definitions and metrics for measuring the resilience of an operating grid. In this paper, we introduce a novel resilience quantification framework and demonstrate a method to measure the flexibility towards topological/structural changes due to potential failures in the power grid to assess operational resilience. We start with the state estimation data from a large utility and use the graph analysis methods and power flow simulation tools to compute the identified resilience parameters.

Yoginath, Srikanth↗
DOE OSTI2022

The Evolution of the Peridynamics Co-Authorship Network

We report peridynamics is a relatively new field in continuum mechanics that has developed over the past 20 years. This paper studies the evolution of collaborations in the field of peridynamics since its inception using social network analysis. For this purpose, we construct a network for each year from 2000 to 2019 describing co-authorship between scientists in peridynamics. In these networks, each node represents a scientist and each link connects two co-authoring scientists with a link weight representing the frequency and strength of their collaboration; each network as a whole can be thought of as a graph representation of the peridynamics community for the given year. By constructing a network for each year, we are able to analyze the evolution of the network in time and discuss the implications of this evolution for the peridynamics community. Our study demonstrates that the peridynamics community has been growing exponentially in size in recent years. Centrality metrics are also used to identify the most collaborative scientists in the community. Moreover, we compute link recommendations based on both elevating a scientist’s position in the network with respect to certain centrality metrics or closing structural holes in the network identified with persistent homology. We further extend the analysis to higher-order networks whose nodes represent groups of scientists in the community and whose links connect collaborating groups. In some sense, our work studies the past, present, and future of the peridynamics community.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Efficient Topology Design Algorithms for Power Grid Stability

The dynamic response of power grids to small disturbances influences their overall stability. This letter examines the effect of network topology on the linearized time-invariant dynamics of electric power systems. The proposed framework utilizes H 2 -norm based stability metrics to study the optimal placement of lines on existing networks as well as the topology design of new networks. The design task is first posed as an NP-hard mixed-integer nonlinear program (MINLP) that is exactly reformulated as a mixed-integer linear program (MILP) using McCormick linearization. To improve computation time, graph-theoretic properties are exploited to derive valid inequalities (cuts) and tighten bounds on the continuous optimization variables. Moreover, a cutting plane generation procedure is put forth that is able to interject the MILP solver and augment additional constraints to the problem on-the-fly. Finally, the efficacy of our approach in designing optimal grid topologies is demonstrated through numerical tests on the IEEE 39-bus network.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Database Performance Monitoring for DUNE

This report presents the research, design, and implementation of improved PostgreSQL monitoring for DUNE Rucio database services using Checkmk. The project began with a request to improve dashboard visibility for database performance metrics, including connection usage, configured connection limits, lock activity, wait behavior, storage trends, query performance, and saturation alerts. The initial implementation focused on the dune_rucio_prod database on the rucio_prod PostgreSQL instance because connection saturation and lock contention are direct reliability risks for database-backed services. Existing Checkmk PostgreSQL monitoring was investigated, and several gaps were identified. Built-in connection monitoring did not clearly separate active, idle, idle-in-transaction, total, and usage-percent metrics, while the built-in lock monitoring simplified PostgreSQL lock modes into shared and exclusive categories. To address these gaps, two DSG-specific Checkmk local checks were created: one for connection-state monitoring and one for lock-state monitoring. These checks supplement the built-in PostgreSQL checks and provide additional performance data for dashboard graphs, service states, and alerts.

Bowers, Elliot [Cabrillo Coll.]↗
DOE OSTI2023

Evaluation of global teleconnections in CMIP6 climate projections using complex networks

In climatological research, the evaluation of climate models is one of the central research subjects. As an expression of large-scale dynamical processes, global teleconnections play a major role in interannual to decadal climate variability. Their realistic representation is an indispensable requirement for the simulation of climate change, both natural and anthropogenic. Therefore, the evaluation of global teleconnections is of utmost importance when assessing the physical plausibility of climate projections. We present an application of the graph-theoretical analysis tool δ-MAPS, which constructs complex networks on the basis of spatio-temporal gridded data sets, here sea surface temperature and geopotential height at 500 hPa. Complex networks complement more traditional methods in the analysis of climate variability, like the classification of circulation regimes or empirical orthogonal functions, assuming a new non-linear perspective. While doing so, a number of technical tools and metrics, borrowed from different fields of data science, are implemented into the δ-MAPS framework in order to overcome specific challenges posed by our target problem. Those are trend empirical orthogonal functions (EOFs), distance correlation and distance multicorrelation, and the structural similarity index. δ-MAPS is a two-stage algorithm. In the first place, it assembles grid cells with highly coherent temporal evolution into so-called domains. In a second step, the teleconnections between the domains are inferred by means of the non-linear distance correlation. We construct 2 unipartite and 1 bipartite network for 22 historical CMIP6 climate projections and 2 century-long coupled reanalyses (CERA-20C and 20CRv3). Potential non-stationarity is taken into account by the use of moving time windows. The networks derived from projection data are compared to those from reanalyses. Our results indicate that no single climate projection outperforms all others in every aspect of the evaluation. But there are indeed models which tend to perform better/worse in many aspects. Differences in model performance are generally low within the geopotential height unipartite networks but higher in sea surface temperature and most pronounced in the bipartite network representing the interaction between ocean and atmosphere.

58 GEOSCIENCES↗
DOE OSTI2023

Atomic protein structure refinement using all-atom graph representations and SE(3)-equivariant graph transformer

Abstract Motivation The state-of-art protein structure prediction methods such as AlphaFold are being widely used to predict structures of uncharacterized proteins in biomedical research. There is a significant need to further improve the quality and nativeness of the predicted structures to enhance their usability. In this work, we develop ATOMRefine, a deep learning-based, end-to-end, all-atom protein structural model refinement method. It uses a SE(3)-equivariant graph transformer network to directly refine protein atomic coordinates in a predicted tertiary structure represented as a molecular graph. Results The method is first trained and tested on the structural models in AlphaFoldDB whose experimental structures are known, and then blindly tested on 69 CASP14 regular targets and 7 CASP14 refinement targets. ATOMRefine improves the quality of both backbone atoms and all-atom conformation of the initial structural models generated by AlphaFold. It also performs better than two state-of-the-art refinement methods in multiple evaluation metrics including an all-atom model quality score—the MolProbity score based on the analysis of all-atom contacts, bond length, atom clashes, torsion angles, and side-chain rotamers. As ATOMRefine can refine a protein structure quickly, it provides a viable, fast solution for improving protein geometry and fixing structural errors of predicted structures through direct coordinate refinement. Availability and implementation The source code of ATOMRefine is available in the GitHub repository (https://github.com/BioinfoMachineLearning/ATOMRefine). All the required data for training and testing are available at https://doi.org/10.5281/zenodo.6944368.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Genomic Metrics Applied to Rhizobiales ( Hyphomicrobiales ): Species Reclassification, Identification of Unauthentic Genomes and False Type Strains

Taxonomic decisions within the order Rhizobiales have relied heavily on the interpretations of highly conserved 16S rRNA sequences and DNA–DNA hybridizations (DDH). Currently, bacterial species are defined as including strains that present 95–96% of average nucleotide identity (ANI) and 70% of digital DDH (dDDH). Thus, ANI values from 520 genome sequences of type strains from species of Rhizobiales order were computed. From the resulting 270,400 comparisons, a ≥95% cut-off was used to extract high identity genome clusters through enumerating maximal cliques. Coupling this graph-based approach with dDDH from clusters of interest, it was found that: (i) there are synonymy between Aminobacter lissarensis and Aminobacter carboxidus, Aurantimonas manganoxydans and Aurantimonas coralicida, “Bartonella mastomydis,” and Bartonella elizabethae, Chelativorans oligotrophicus, and Chelativorans multitrophicus, Rhizobium azibense, and Rhizobium gallicum, Rhizobium fabae, and Rhizobium pisi, and Rhodoplanes piscinae and Rhodoplanes serenus; (ii) Chelatobacter heintzii is not a synonym of Aminobacter aminovorans; (iii) “Bartonella vinsonii” subsp. arupensis and “B. vinsonii” subsp. berkhoffii represent members of different species; (iv) the genome accessions GCF_003024615.1 (“Mesorhizobium loti LMG 6125T”), GCF_003024595.1 (“Mesorhizobium plurifarium LMG 11892T”), GCF_003096615.1 (“Methylobacterium organophilum DSM 760T”), and GCF_000373025.1 (“R. gallicum R-602 spT”) are not from the genuine type strains used for the respective species descriptions; and v) “Xanthobacter autotrophicus” Py2 and “Aminobacter aminovorans” KCTC 2477T represent cases of misuse of the term “type strain”. Aminobacter heintzii comb. nov. and the reclassification of Aminobacter ciceronei as A. heintzii is also proposed. To facilitate the downstream analysis of large ANI matrices, we introduce here ProKlust (“Prokaryotic Clusters”), an R package that uses a graph-based approach to obtain, filter, and visualize clusters on identity/similarity matrices, with settable cut-off points and the possibility of multiple matrices entries.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

LatticeAnalytics: Strut-Level Visualization and Inspection of Additively Manufactured Lattice Structures

Additive manufacturing (AM) is revolutionizing the production of custom components with complex internal geometries, essential for high-performance applications in diverse fields such as medicine and defense. These AM parts optimize strength while minimizing weight by utilizing internal lattice structures consisting of large quantities of small interconnected struts. However, the complexity of these structures, combined with the challenges of using X-ray Computed Tomography (XCT) data, makes validation of part reliability difficult. This ultimately inhibits the development of novel parts for our collaborating material scientists. Here, we introduce LatticeAnalytics, a novel framework specifically designed for visual inspection of defects in these lattice structures. Our framework offers an end-to-end solution that includes the data management of XCT scans, enables remote access for geographically dispersed teams through a web-based dashboard, and incorporates novel visualizations. Our analysis is facilitated by a coarse alignment between the lattice’s nominal model, a spatial graph, and the XCT data. We employ a simple VR-based approach for fast and rough alignment, followed by an offline registration and identification of the struts. With the nodes and struts aligned and identified in the volume, our framework allows querying of subvolumes containing a single strut at multiple resolutions. This avoids computation over the entire lattice and also allow for easy parallelization of down-stream computations, such as strut-specific metrics. To depict a fast overview of the strut quality, we introduce two innovative visual encodings, crucial for our collaborators’ research in creating novel AM parts: the Contour View and the Roughness Map, which depict critical geometrical and surface features of individual struts in standardized two 2D views. We evaluated the integrated system through expert interviews. The feedback confirms the framework’s practicality and its effectiveness in enhancing current inspection workflows. It solves major bottlenecks for our collaborators, ultimately helping them create novel parts with advanced properties.

Miao, Haichao [Lawrence Livermore National Laborat↗
DOE OSTI2024

Predicting Drug Effects from High-dimensional Asymmetric Drug Data Sets using Graph Neural Networks: A Comprehensive Analysis of Multi-target Drug Effect Prediction

Graph neural networks (GNNs) have emerged as one of the most effective Machine learning (ML) techniques for drug effect prediction from drug molecular graphs. Despite having immense potential, GNN models lack performance when using data sets that contain high dimensional asymmetrically co-occurrent drug effects as targets with complex correlations between them. Training individual learning models for each drug effect and incorporating every prediction result for a wide spectrum of drug effects is beyond practicality. Such an implication provides a testbed to address this challenge as multi-target prediction problems, aiming to predict all drug effects at a time. We develop standard and hybrid graph neural networks (GNNs)to perform two separate tasks that are multi-regression for continuous values and multi-label classification for categorical values contained in our data sets. Since this step makes the target data even more sparse and introduces asymmetric label co-occurrence, the learning of multi-label classification models becomes difficult and heavily impacts the GNN's performance. To address these challenges, we propose a new data oversampling technique to improve multi-label classification performances on all the given imbalanced molecular graph data sets. Using the technique, we improve the data imbalance ratio of the drug effects better than before while protecting the data set's integrity. Finally, we evaluate multi-label classification performance using the best-performant hybrid GNN model on all the oversampled data sets obtained from the proposed oversampling technique. These results outperform those of other ML models including GNN models when they are trained on the original data sets or oversampled data sets using MLSMOTE (a well-known oversampling technique) in all evaluation metrics precision, recall, and F1 score by a significant margin.

Bose, Avishek [ORNL]↗
DOE OSTI2023

Data efficiency and extrapolation trends in neural network interatomic potentials

Abstract Recently, key architectural advances have been proposed for neural network interatomic potentials (NNIPs), such as incorporating message-passing networks, equivariance, or many-body expansion terms. Although modern NNIP models exhibit small differences in test accuracy, this metric is still considered the main target when developing new NNIP architectures. In this work, we show how architectural and optimization choices influence the generalization of NNIPs, revealing trends in molecular dynamics (MD) stability, data efficiency, and loss landscapes. Using the 3BPA dataset, we uncover trends in NNIP errors and robustness to noise, showing these metrics are insufficient to predict MD stability in the high-accuracy regime. With a large-scale study on NequIP, MACE, and their optimizers, we show that our metric of loss entropy predicts out-of-distribution error and data efficiency despite being computed only on the training set. This work provides a deep learning justification for probing extrapolation and can inform the development of next-generation NNIPs.

36 MATERIALS SCIENCE↗
DOE OSTI2025

CuXASNet: Rapid and accurate prediction of copper L-edge x-ray absorption spectra using machine learning

In this work, we have developed CuXASNet, a dense neural network that predicts simulated Cu -edge x-ray absorption spectra (XAS) from atomic structures. Featurization of the Cu local environment is performed using a component of M3GNet, a graph neural network developed for predicting the potential energy surface. CuXASNet is trained on simulated spectra from FEFF9 at the multiple scattering level of theory, and can predict the and edges for Cu sites to quantitative accuracy. To validate our approach, we compare 14 experimental spectra extracted from the literature with the predictions of CuXASNet. The agreement of CuXASNet with experiments is shown by an average mean absolute error of 0.125 and an average Spearman's correlation coefficient of 0.891, which is comparable to FEFF9's values of 0.131 and 0.898 for the same metrics. As such, CuXASNet can rapidly predict a large number of -edge XAS spectra at the same accuracy as FEFF9 simulations. This can be used as a drop-in replacement for multiple scattering codes for fast screening of candidate atomic structure models of a measured system. This model establishes a general framework for Cu XAS prediction, and can be extended to more computationally expensive levels of theory and to other transition metal edges.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Decentralized Distributed Proximal Policy Optimization (DD-PPO) for High Performance Computing Scheduling on Multi-User Systems

Resource allocation in High Performance Computing (HPC) environments presents a complex and multifaceted challenge for job scheduling algorithms. Beyond the efficient allocation of system resources, schedulers must account for and optimize multiple performance metrics, including job wait time and system throughput. Traditional heuristic-based scheduling algorithms increasingly struggle and lack the efficiency needed to meet the demands and address the complexity and scale of modern HPC systems. Consequently, recent research efforts have focused on leveraging advancements in Artificial Intelligence (AI) and Deep Learning (DL), particularly Reinforcement Learning (RL), to develop more adaptable and intelligent scheduling strategies. Previous RL-based scheduling approaches have explored a range of algorithms, from Deep Q-Networks (DQN) to Proximal Policy Optimization (PPO), and more recently, hybrid methods that integrate Graph Neural Networks (GNNs) with RL techniques. However, a common limitation across these methods is their reliance on relatively small datasets, with few methods being evaluated using large-scale, multi-million-job trace datasets representative of real-world HPC workloads. Moreover, existing RL schedulers face scalability issues due to centralized policy updates, which hinder training efficiency and performance when applied to large datasets. This study introduces a novel RL-based scheduler utilizing Decentralized Distributed Proximal Policy Optimization (DD-PPO) algorithm, which supports large-scale distributed training across multiple workers without requiring parameter synchronization at every step. By eliminating reliance on centralized updates to a shared policy, the DD-PPO scheduler enhances scalability, training efficiency, and sample utilization. Experimental validation using a large real-world dataset containing over 11.5 million job traces collected from petascale HPC systems over six years assesses the influence of dataset scale on training effectiveness and compares DD-PPO performance to traditional and advanced scheduling approaches. The experimental results demonstrate improved scheduling performance in comparison to both heuristic-based schedulers and existing RL-based scheduling algorithms.

AI↗
DOE OSTI2025

Dataset for manuscript "Equipartition and the temperature of maximum density of TIP4P/2005 water"

We simulate TIP4P/2005 water in the temperature range of 257 K to 318 K with time-steps 0.25, 0.50, 1.00, 2.00, and 4.00 fs. The density-temperature behavior obtained using 0.25 or 0.50 fs are in excellent agreement with each other but differ from those obtained using time-steps that have been shown earlier to lead to a breakdown of equipartition. The temperature of maximum density (TMD) is 277.15 K with time-step 0.25 or 0.50 fs, but is shifted to progressively lower values for longer time-steps, a trend that holds for different thermostat/barostat combinations. Enhancing the water-water dispersion interaction, as has been recommended for simulating disordered proteins in TIP4P/2005, degrades the description of the liquid-vapor phase envelope. We present a simple physically transparent reasoning to highlight the separation of the time-scales between translational and rotational motion. We also develop a metric, Chi, that we term the equipartition anomaly, to detect equipartition violations in simulations that include molecules that are treated as rigid objects. Calculating Chi is shown to be straightforward and sensitive to equipartition violations. A key takeaway from this study is that using sufficiently short time-steps (less than or equal to 0.5 fs) to preserve equipartition is essential for obtaining meaningful liquid water properties and for producing reliable simulation data, as correct-ensemble sampling is fundamental to ensure reproducibility across codes and simulation alogrithms. The included dataset provides the raw data used in the preparation of the graphs noted in the manuscript.

36 MATERIALS SCIENCE↗
DOE OSTI2023

GAHLS: an optimized graph analytics based high level synthesis framework

The urgent need for low latency, high-compute and low power on-board intelligence in autonomous systems, cyber-physical systems, robotics, edge computing, evolvable computing, and complex data science calls for determining the optimal amount and type of specialized hardware together with reconfigurability capabilities. With these goals in mind, we propose a novel comprehensive graph analytics based high level synthesis (GAHLS) framework that efficiently analyzes complex high level programs through a combined compiler-based approach and graph theoretic optimization and synthesizes them into message passing domain-specific accelerators. This GAHLS framework first constructs a compiler-assisted dependency graph (CaDG) from low level virtual machine (LLVM) intermediate representation (IR) of high level programs and converts it into a hardware friendly description representation. Next, the GAHLS framework performs a memory design space exploration while account for the identified computational properties from the CaDG and optimizing the system performance for higher bandwidth. The GAHLS framework also performs a robust optimization to identify the CaDG subgraphs with similar computational structures and aggregate them into intelligent processing clusters in order to optimize the usage of underlying hardware resources. Finally, the GAHLS framework synthesizes this compressed specialized CaDG into processing elements while optimizing the system performance and area metrics. Evaluations of the GAHLS framework on several real-life applications (e.g., deep learning, brain machine interfaces) demonstrate that it provides 14.27× performance improvements compared to state-of-the-art approaches such as LegUp 6.2.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Interpretable design of Ir-free trimetallic electrocatalysts for ammonia oxidation with graph neural networks

The electrochemical ammonia oxidation to dinitrogen as a means for energy and environmental applications is a key technology toward the realization of a sustainable nitrogen cycle. The state-of-the-art metal catalysts including Pt and its bimetallics with Ir show promising activity, albeit suffering from high overpotentials for appreciable current densities and the soaring price of precious metals. Herein, the immense design space of ternary Pt alloy nanostructures is explored by graph neural networks trained on ab initio data for concurrently predicting site reactivity, surface stability, and catalyst synthesizability descriptors. Among a few Ir-free candidates that emerge from the active learning workflow, Pt 3 Ru-M (M: Fe, Co, or Ni) alloys were successfully synthesized and experimentally verified to be more active toward ammonia oxidation than Pt, Pt 3 Ir, and Pt 3 Ru. More importantly, feature attribution analyses using the machine-learned representation of site motifs provide fundamental insights into chemical bonding at metal surfaces and shed light on design strategies for high-performance catalytic systems beyond the d-band center metric of binding sites.

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

Comparing three generations of D-Wave quantum annealers for minor embedded combinatorial optimization problems

Abstract Quantum annealing (QA) is a novel type of analog computation that aims to use quantum mechanical fluctuations to search for optimal solutions of Ising problems. QA in the transverse Ising model, implemented on D-Wave quantum processing units, are available as cloud computing resources. In this study we report concise benchmarks across three generations of D-Wave quantum annealers, consisting of four different devices, for the NP-hard discrete combinatorial optimization problems unweighted maximum clique and unweighted maximum cut on random graphs. The Ising, or equivalently quadratic unconstrained binary optimization, formulation of these problems do not require auxiliary variables for order reduction, and their overall structure and weights are not highly variable, which makes these problems simple test cases to understand the sampling capability of current D-Wave quantum annealers. All-to-all minor embeddings of size 52, with relatively uniform chain lengths, are used for a direct comparison across the Chimera, Pegasus, and Zephyr device topologies. A grid-search over annealing times and the minor embedding chain strengths is performed in order to determine the level of reasonable performance for each device and problem type. Experiment metrics that are reported are approximation ratios for non-broken chain samples, chain break proportions, and time-to-solution for the maximum clique problem instances. How fairly the quantum annealers sample optimal maximum cliques, for instances which contain multiple maximum cliques, is quantified using entropy of the measured ground state distributions. The newest generation of quantum annealing hardware, which has a Zephyr hardware connectivity, performed the best overall with respect to approximation ratios and chain break frequencies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗