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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 613 records · Page 34
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

A Hybrid Biophysical‐Machine Learning Framework for Diurnal Surface Energy Flux Estimation Using Proximal Sensing

Thermal infrared-based remote sensing of surface energy fluxes has traditionally relied on high spatial resolution satellite data with revisit frequencies on the order of weeks. In this study, we evaluate a biophysics-based analytical surface energy balance model for predicting latent energy ( LE ) and sensible heat ( H ) fluxes using proximal sensing observations. The Surface Temperature Initiated Closure (STIC1.2) model has been extensively validated across a wide range of spatial and temporal scales using various satellite-derived thermal infrared data sets. Here we extend this validation by applying STIC at sub-hourly temporal resolution over multiple growing seasons for four distinct agricultural systems. We further develop and evaluate novel STIC variants that incorporate machine learning (ML) techniques to eliminate the need for surface energy balance observations, specifically net radiation and soil heat flux, thereby enhancing model applicability in data-sparse settings. The integration of a ML component to estimate surface available energy is shown to have strong predictive performance for both LE (R 2 = 0.81–0.94) and H (R 2 = 0.46–0.72) across all agricultural systems examined here, demonstrating the potential of hybrid biophysical-machine learning approaches for surface energy balance modeling with minimal data requirements. This study concludes with a novel application of explainable machine learning (exML) to diagnose sources of model error. This exML framework attributes residual prediction errors to both model input variables and environmental drivers not explicitly included in the simulation experiments. This approach provides a new pathway for improving model design and integrating previously overlooked yet influential variables into future model iterations.

evapotranspiration↗
DOE OSTI2025

Deep potential molecular dynamics simulations of ion-enhanced etching of silicon by atomic chlorine

The continued development of plasma-assisted processing techniques requires a fundamental understanding of plasma-surface interactions. Molecular dynamics (MD) simulations have been employed to complement experimental studies and better understand the properties of such systems. Recently, machine learning (ML) methods have enabled the development of ab initio-based interatomic potentials, which can be generalized to complex combinations of multiple atom types. In this work, we use ML potentials developed using the Deep Potential Molecular Dynamics (DeepMD) framework to provide a model of ion-enhanced etching of Si by Cl atoms. We demonstrate the importance of proper selection of the training data set to the accuracy of the DeepMD model and compare our results to MD results using empirical potentials, as well as to experimental measurements. Exposure of undoped Si at 300 K to thermal Cl atoms yields a steady-state Cl coverage of 1.25 monolayers, which is slightly lower than the value obtained in previous experimental studies. Predictions of Si etch yields by simultaneous Cl atom and Ar + ion impacts as a function of ion energy, neutral to ion flux ratio, and angle of incidence of the ions are in reasonably good agreement with classical MD results and experimental measurements. Finally, etch yields and SiCl x mixed layer thicknesses during simultaneous bombardment of the Si(100) surface by Cl atoms and Cl + ions are in good agreement with experimental data. In conclusion, the present work is a necessary condition for the extension of the DeepMD procedure to more complex systems of interest in plasma-surface interactions.

Artificial neural networks↗
DOE OSTI2024

Machine learning without a processor: Emergent learning in a nonlinear analog network

Standard deep learning algorithms require differentiating large nonlinear networks, a process that is slow and power-hungry. Electronic contrastive local learning networks (CLLNs) offer potentially fast, efficient, and fault-tolerant hardware for analog machine learning, but existing implementations are linear, severely limiting their capabilities. These systems differ significantly from artificial neural networks as well as the brain, so the feasibility and utility of incorporating nonlinear elements have not been explored. Here, we introduce a nonlinear CLLN—an analog electronic network made of self-adjusting nonlinear resistive elements based on transistors. We demonstrate that the system learns tasks unachievable in linear systems, including XOR (exclusive or) and nonlinear regression, without a computer. We find our decentralized system reduces modes of training error in order (mean, slope, curvature), similar to spectral bias in artificial neural networks. The circuitry is robust to damage, retrainable in seconds, and performs learned tasks in microseconds while dissipating only picojoules of energy across each transistor. This suggests enormous potential for fast, low-power computing in edge systems like sensors, robotic controllers, and medical devices, as well as manufacturability at scale for performing and studying emergent learning.

Science & Technology - Other Topics↗
DOE OSTI2021

ML Clustering to Identify Natural Gas Pipeline Infrastructure Vulnerabilities

The network of more than 2.5 million miles of natural gas pipelines the U.S. are exposed to a range of vulnerabilities, ranging from extreme weather, to human behavior, and increasingly, to cyber threats. Advanced, data-driven analytics, including the use of machine learning and artificial intelligence, afford an opportunity to identify potential vulnerabilities, better understand risks, and help mitigate vulnerabilities in the network. At NETL, machine learning is being used to explore pipeline vulnerabilities and identify significant clusters of failure events, including failures due to weather, human behavior, and materials. These findings are being used to support the development of new technologies, including sensors, but can also be used to evaluate and inform mitigation strategies to reduce risks and vulnerabilities throughout the network.

Bauer, Jennifer↗
DOE OSTI2020

ChIMES: A Machine-Learned Interatomic Model Targeting Improved Description of Condensed Phase Chemistry in Energetic Materials

In this report we detail completion of a Physics and Engineering Model Level Two Milestone targeting improved reactive interatomic potentials (IAPs) for energetic materials (EM) through machine learning. The specific goals of this milestone were to develop, validate, and document a new reactive molecular dynamics method for EM, based on machine learning by (1) generating databases of first-principles-derived forces, stresses, and energies for HN3 and 3,4-bis(3-nitrofurazan- 4-yl)furoxan (DNTF) (2) generate atomistic force fields from these databases via ML, and (3) benchmark model performance against first principles calculations. These goals were achieved by (1) further developing a machine learned reactive IAP and generation approach (i.e. the Chebyshev Interaction Model for Efficient Simulation or “ChIMES”), for which resulting IAPs can approach the predictive power of quantum-mechanical approaches at a fraction of the computational expense, and (2) applying the ChIMES framework to develop models for HN3 and DNTF. We find that for simple energetic materials like HN3, high accuracy ChIMES models can be obtained through application of a fitting approach that does not use active machine learning. We demonstrate the suitability of ChIMES models for simulations involving EM by using the HN3 model in multiscale shock technique simulations to predict the HN3 Chapman-Jouguet detonation state and investigate chemical evolution out to 1 ns following shock compression. This model is then used in larger direct shock (DS) simulations for a preliminary investigation of how bubbles (i.e. voids) influence material response under shock compression. We find that more complex EM (i.e. DNTF) necessitate a more sophisticated fitting approach, and develop a new active learning method and python tool to meet this challenge. We demonstrate that this fitting approach yields ChIMES models that out-perform commonly used standard reactive IAPs as well as semi-empirical quantum methods, and discuss the systematic improvability of these actively learned ChIMES models. We also describe challenges related to model development for EM such as DNTF, for which few experimental or previous simulation data are available (e.g. which could otherwise inform generation of training data). To overcome this issue, we establish a semi-empirical quantum ChIMES capability which can be used to efficiently map out relevant thermodynamic and configurational space, and generate ChIMES-IAP training data in a multiscale manner. We also show that these semi-empirical quantum ChIMES models can be used to generate predictions for the shock Hugoniot (the Hugoniot is the locus of thermodynamic states found in a shocked material) equation of state, investigate related thermochemistry, and explore carbon condensation following shock compression. This work represents a substantial advance in our atomistic modeling capability for EM that will provide much needed information on the chemistry of detonation for continued development of continuum models based on the Cheetah thermochemical code.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Indirect Tool Condition Monitoring Using Ensemble Machine Learning Techniques

Abstract Tool condition monitoring (TCM) has become a research area of interest due to its potential to significantly reduce manufacturing costs while increasing process visibility and efficiency. Machine learning (ML) is one analysis technique which has demonstrated advantages for TCM applications. However, the commonly studied individual ML models lack generalizability to new machining and environmental conditions, as well as robustness to the unbalanced datasets which are common in TCM. Ensemble ML models have demonstrated superior performance in other fields, but have only begun to be evaluated for TCM. As a result, it is not well understood how their TCM performance compares to that of individual models, or how homogeneous and heterogeneous ensemble models’ performances compare to one another. To fill in these research gaps, milling experiments were conducted using various cutting conditions, and the model groups were compared across several performance metrics. Statistical t-tests were also used to evaluate the significance of model performance differences. Through the analysis of four individual ML models and five ensemble models, all based on the processes’ sound, spindle power, and axial load signals, it was found that on average, the ensemble models performed better than the individual models, and that the homogeneous ensembles outperformed the heterogeneous ensembles.

Engineering↗
DOE OSTI2024

Machine learning the electric field response of condensed phase systems using perturbed neural network potentials

Abstract The interaction of condensed phase systems with external electric fields is of major importance in a myriad of processes in nature and technology, ranging from the field-directed motion of cells (galvanotaxis), to geochemistry and the formation of ice phases on planets, to field-directed chemical catalysis and energy storage and conversion systems including supercapacitors, batteries and solar cells. Molecular simulation in the presence of electric fields would give important atomistic insight into these processes but applications of the most accurate methods such as ab-initio molecular dynamics (AIMD) are limited in scope by their computational expense. Here we introduce Perturbed Neural Network Potential Molecular Dynamics (PNNP MD) to push back the accessible time and length scales of such simulations. We demonstrate that important dielectric properties of liquid water including the field-induced relaxation dynamics, the dielectric constant and the field-dependent IR spectrum can be machine learned up to surprisingly high field strengths of about 0.2 V Å −1 without loss in accuracy when compared to ab-initio molecular dynamics. This is remarkable because, in contrast to most previous approaches, the two neural networks on which PNNP MD is based are exclusively trained on molecular configurations sampled from zero-field MD simulations, demonstrating that the networks not only interpolate but also reliably extrapolate the field response. PNNP MD is based on rigorous theory yet it is simple, general, modular, and systematically improvable allowing us to obtain atomistic insight into the interaction of a wide range of condensed phase systems with external electric fields.

Science & Technology - Other Topics↗
DOE OSTI2025

Machine-Learned Force Field for Molecular Dynamics Simulations of Nonequilibrium Ammonia Synthesis on Iron Catalysts

Ammonia (NH 3 ) is one of the most important industrial chemicals. The conventional NH 3 synthesis method-the Haber–Bosch process-converts atmospheric nitrogen (N 2 ) into NH 3 using H 2 with an iron (Fe) catalyst. However, this process requires high pressures (100–200 atm) and temperatures (700–800 K) near thermal equilibrium. Recently, Fe-based nanocatalysts have been reported to produce promising NH 3 yields under atmospheric pressures and temperature-modulated nonequilibrium conditions. Understanding the mechanism of nonequilibrium catalysis with programmed temperature variation could help to optimize this fully electrified and less energy-intensive process. Although reactive molecular dynamics (RMD) simulations can be a useful tool to model nonequilibrium catalytic processes, they require the development of accurate force fields (i.e., interatomic potentials). Here, we present a machine-learned (ML) force field within the Deep Potential MD (DPMD) framework, trained using periodic density functional theory (DFT) calculations, to model NH 3 synthesis on Fe catalysts with various surface adsorbates such as *N, *H, *N 2 , *H 2 , *NH, *NH 2 , and *NH 3 . Here, we generated the DFT data from static models of elementary reactions on the most stable (110) surface of body-centered cubic Fe, which then were augmented by data from constant number of particles–volume–temperature (NVT) DFT-MD trajectories at various temperatures. Finally, we utilized the fully optimized ML force field to investigate reaction dynamics at an Fe(110) surface at linearly increasing temperatures using NVT-DPMD simulations. Our simulations indicate that pulsed temperature ramping could prove favorable for NH3 synthesis. For example, we conducted ramping under multiple sets of conditions: (i) from 900 to 1200 K over periods of 0.1–0.3 ns for Fe surfaces precovered with N or NH along with H; and (ii) from 300 to 600 K over 0.1–0.3 ns for Fe surfaces precovered with NH 3 . While our simulations so far are limited to short time scales (very rapid heating), these observations shed light on the mechanism of the high NH 3 synthesis rate achieved in a novel temperature-modulated nonequilibrium catalytic reactor using pulsed heating and cooling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Spatially-Explicit Prediction of Capacity Density Advances Geographic Characterization of Wind Power Technical Potential

Mounting interest in ambitious clean energy goals is exposing critical gaps in our understanding of onshore wind power potential. Conventional approaches to evaluating wind power technical potential at the national scale rely on coarse geographic representations of land area requirements for wind power. These methods overlook sizable spatial variation in real-world capacity densities (i.e., nameplate power capacity per unit area) and assume that potential installation densities are uniform across space. Here, we propose a data-driven approach to overcome persistent challenges in characterizing localized deployment potentials over broad extents. We use machine learning to develop predictive relationships between observed capacity densities and geospatial variables. The model is validated against a comprehensive data set of United States (U.S.) wind facilities and subjected to interrogation techniques to reveal that key explanatory features behind geographic variation of capacity density are related to wind resource as well as urban accessibility and forest cover. We demonstrate application of the model by producing a high-resolution (2 km × 2 km) national map of capacity density for use in technical potential assessments for the United States. Our findings illustrate that this methodology offers meaningful improvements in the characterization of spatial aspects of technical potential, which are increasingly critical to draw reliable and actionable planning and research insights from renewable energy scenarios.

17 WIND ENERGY↗
DOE OSTI2023

Use of machine learning to analyze chemistry card sort tasks

Education researchers are deeply interested in understanding the way students organize their knowledge. Card sort tasks, which require students to group concepts, are one mechanism to infer a student’s organizational strategy. However, the limited resolution of card sort tasks means they necessarily miss some of the nuance in a student’s strategy. Here in this work, we propose new machine learning strategies that leverage a potentially richer source of student thinking: free-form written language justifications associated with student sorts. Using data from a university chemistry card sort task, we use vectorized representations of language and unsupervised learning techniques to generate qualitatively interpretable clusters, which can provide unique insight in how students organize their knowledge. We compared these to machine learning analysis of the students’ sorts themselves. Machine learning-generated clusters revealed different organizational strategies than those built into the task; for example, sorts by difficulty or even discipline. There were also many more categories generated by machine learning for what we would identify as more novice-like sorts and justifications than originally built into the task, suggesting students’ organizational strategies converge when they become more expert-like. Finally, we learned that categories generated by machine learning for students’ justifications did not always match the categories for their sorts, and these cases highlight the need for future research on students’ organizational strategies, both manually and aided by machine learning. In sum, the use of machine learning to analyze results from a card sort task has helped us gain a more nuanced understanding of students’ expertise, and demonstrates a promising tool to add to existing analytic methods for card sorts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Effects of Substance Use and Antisocial Personality on Neuroimaging-Based Machine Learning Prediction of Schizophrenia

Abstract Background and hypothesis Neuroimaging-based machine learning (ML) algorithms have the potential to aid the clinical diagnosis of schizophrenia. However, literature on the effect of prevalent comorbidities such as substance use disorder (SUD) and antisocial personality (ASPD) on these models’ performance has remained unexplored. We investigated whether the presence of SUD or ASPD affects the performance of neuroimaging-based ML models trained to discern patients with schizophrenia (SCH) from controls. Study design We trained an ML model on structural MRI data from public datasets to distinguish between SCH and controls (SCH = 347, controls = 341). We then investigated the model’s performance in two independent samples of individuals undergoing forensic psychiatric examination: sample 1 was used for sensitivity analysis to discern ASPD (N = 52) from SCH (N = 66), and sample 2 was used for specificity analysis to discern ASPD (N = 26) from controls (N = 25). Both samples included individuals with SUD. Study results In sample 1, 94.4% of SCH with comorbid ASPD and SUD were classified as SCH, followed by patients with SCH + SUD (78.8% classified as SCH) and patients with SCH (60.0% classified as SCH). The model failed to discern SCH without comorbidities from ASPD + SUD (AUC = 0.562, 95%CI = 0.400–0.723). In sample 2, the model’s specificity to predict controls was 84.0%. In both samples, about half of the ASPD + SUD were misclassified as SCH. Data-driven functional characterization revealed associations between the classification as SCH and cognition-related brain regions. Conclusion Altogether, ASPD and SUD appear to have effects on ML prediction performance, which potentially results from converging cognition-related brain abnormalities between SCH, ASPD, and SUD.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2024

Smart CO2 Transport-Route Planning Tool

NETL has developed the Smart CO2 Transport-Route Planning Tool to help inform energy transport planning and development. The stand-alone, open-source tool applies data-driven, geospatial and machine-learning informed logic to identify potential routes or evaluate existing corridors based on current legislation, best construction practices, and more. Underpinning the interactive tool, is NETL’s CO2 Transport Planning Database (https://edx.netl.doe.gov/dataset/ccs-pipeline-route-planning-database-v1). This geospatial resource contains more than 70 gigabytes of data representing more than 60 critical factors for the spatial routing of CO2 transport, including land use requirements, existing infrastructure, high consequence areas, and natural hazards.

Bipartisan Infrastructure Law↗
DOE OSTI2024

Improving the Freight Productivity of a Heavy-Duty, Battery Electric Truck by Intelligent Energy Management

This project aimed to enhance the range and reduce the operating costs of battery electric Class 8 trucks traveling over 250 miles daily. This was achieved through the development and implementation of an intelligent-Energy Management System (i-EMS) that leverages vehicle and operations data, physics-aware machine learning algorithms, and vehicle-to-cloud (V2C) connectivity. The project hypothesized that advanced machine learning algorithms and real-time data analytics could significantly improve the energy efficiency and range of these trucks. Key objectives included developing a physics-aware machine learning algorithm, implementing an i-EMS with V2C connectivity and physics-aware spatial data analytics (PSDA), and validating the system’s effectiveness with fleet partners HEB Companies and Murphy Logistics. Extensive data collection from vehicle operations, including vehicle characteristics, road conditions, and payload, was conducted. A machine learning algorithm was developed to predict energy consumption and enable proactive decision-making. The i-EMS was implemented on two Volvo VNR BEVs, with operators receiving charging and routing recommendations. Charging stations were installed at depot locations in Texas and Minnesota, with an additional on-route charger in Minnesota. Significant findings included a 14% range improvement for Murphy Logistics on a highway-driving eco-route and a 22% range improvement for HEB Companies on a city-driving eco-route. The i-EMS utilized rule-based methods and physics-based algorithms to predict and reduce energy consumption, with real-time monitoring and analysis through V2C connectivity enabling proactive decision-making. The project demonstrated the feasibility and economic viability of battery electric Class 8 trucks for long-haul operations, showcasing the potential of physics-aware machine learning in optimizing energy management. The successful implementation of the i-EMS in real-world scenarios validates its practical application and effectiveness, paving the way for the widespread adoption of battery electric vehicles in the freight transportation industry.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Accelerated Sequence Design of Star Block Copolymers: An Unbiased Exploration Strategy via Fusion of Molecular Dynamics Simulations and Machine Learning

Star block copolymers (s-BCPs) have potential applications as novel surfactants or amphiphiles for emulsification, compatibilization, chemical transformations, and separations. s-BCPs have chain architectures where three or more linear diblock copolymer arms comprised of two chemically distinct linear polymers, e.g., solvophobic and solvophilic chains, are covalently joined at one point. The chemical composition of each of the subunit polymer chains comprising the arms, their molecular weights, and the number of arms can be varied to tailor the surface and interfacial activity of these architecturally unique molecules. Further, this makes identification of the optimal s-BCP design nontrivial as the total number of plausible s-BCP architectures is experimentally or computationally intractable. In this work, we use molecular dynamics (MD) simulations coupled with a reinforcement learning-based Monte Carlo tree search (MCTS) to identify s-BCP designs that minimize the interfacial tension between polar and nonpolar solvents. We first validate the MCTS approach for the design of small- and medium-sized s-BCPs and then use it to efficiently identify sequences of copolymer blocks for large-sized s-BCPs. The structural origins of interfacial tension in these systems are also identified by using the configurations obtained from MD simulations. Chemical insights into the arrangement of copolymer blocks that promote lower interfacial tension were mined using machine learning (ML) techniques. Overall, this work provides an efficient approach to solve design problems via fusion of simulations and ML and provides important groundwork for future experimental investigation of s-BCPs for various applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Machine Learning for Geothermal Resource Exploration in the Tularosa Basin, New Mexico

Geothermal energy is considered an essential renewable resource to generate flexible electricity. Geothermal resource assessments conducted by the U.S. Geological Survey showed that the southwestern basins in the U.S. have a significant geothermal potential for meeting domestic electricity demand. Within these southwestern basins, play fairway analysis (PFA), funded by the U.S. Department of Energy’s (DOE) Geothermal Technologies Office, identified that the Tularosa Basin in New Mexico has significant geothermal potential. This short communication paper presents a machine learning (ML) methodology for curating and analyzing the PFA data from the DOE’s geothermal data repository. The proposed approach to identify potential geothermal sites in the Tularosa Basin is based on an unsupervised ML method called non-negative matrix factorization with custom k-means clustering. This methodology is available in our open-source ML framework, GeoThermalCloud (GTC). Using this GTC framework, we discover prospective geothermal locations and find key parameters defining these prospects. Our ML analysis found that these prospects are consistent with the existing Tularosa Basin’s PFA studies. This instills confidence in our GTC framework to accelerate geothermal exploration and resource development, which is generally time-consuming.

15 GEOTHERMAL ENERGY↗
DOE OSTI2026

Deployment of Traditional and Hybrid Machine Learning for Critical Heat Flux Prediction in the CTF Thermal-Hydraulics Code

Critical heat flux (CHF) marks the transition from nucleate to film boiling, where heat transfer to the working fluid can rapidly deteriorate. Accurate CHF prediction is essential for efficiency, safety, and preventing equipment damage, particularly in nuclear reactors. Although widely used, empirical correlations frequently exhibit discrepancies when compared to experimental data, limiting their reliability in diverse operational conditions. Traditional machine learning (ML) approaches have demonstrated potential for CHF prediction but often suffer from limited interpretability, data scarcity, and insufficient knowledge of physical principles. Hybrid model approaches, which combine data-driven ML with base models, mitigate these concerns by incorporating prior knowledge of the domain. This study integrates an externally trained purely data-driven ML model and two hybrid models (using the Biasi and Bowring CHF correlations) within the CTF subchannel code via a custom Fortran framework. Performance was evaluated using two validation cases: a subset of the Nuclear Regulatory Commission (NRC) CHF database and the Bennett dryout experiments. In both cases, the hybrid models demonstrated significantly lower error metrics compared to conventional empirical correlations, with the best models often reducing relative error by about 5 percentage points. The pure ML model achieved comparable accuracy, outperforming the hybrid Biasi model in the NRC test case (3.3% versus 5.5% relative error) but exhibiting slightly higher error against the hybrid Bowring model in the Bennett test case (7.7% versus 6.1%). Trend analysis of error parity indicated that ML-based models reduced the tendency for CHF overprediction, improving overall accuracy. These results demonstrate that ML-based CHF models can be effectively integrated into subchannel codes and could potentially increase performance compared to conventional methods.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

A Review of Machine Learning Classification Using Quantum Annealing for Real-World Applications

Optimizing the training of a machine learning pipeline helps in reducing training costs and improving model performance. One such optimizing strategy is quantum annealing, which is an emerging computing paradigm that has shown potential in optimizing the training of a machine learning model. The implementation of a physical quantum annealer has been realized by D-wave systems and is available to the research community for experiments. Recent experimental results on a variety of machine learning applications using quantum annealing have shown interesting results where the performance of classical machine learning techniques is limited by limited training data and high dimensional features. This article explores the application of D-wave’s quantum annealer for optimizing machine learning pipelines for real-world classification problems. Finally, we review the application domains on which a physical quantum annealer has been used to train machine learning classifiers. We discuss and analyze the experiments performed on the D-Wave quantum annealer for applications such as image recognition, remote sensing imagery, computational biology, and particle physics. We discuss the possible advantages and the problems for which quantum annealing is likely to be advantageous over classical computation.

97 MATHEMATICS AND COMPUTING↗