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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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Real-Time, Adaptive Radiological Anomaly Detection and Isotope Identification Using Non-Negative Matrix Factorization

Spectroscopic anomaly detection and isotope identification algorithms are integral components in nuclear nonproliferation applications such as search operations. The task is especially challenging in the case of mobile detector systems because the observed gamma-ray background changes more than for a static detector system, and a pretrained background model can easily find itself out of domain. The result is that algorithms may exceed their intended false alarm rate or sacrifice detection sensitivity to maintain the desired false alarm rate. Non-negative matrix factorization (NMF) is a powerful tool for spectral anomaly detection and identification, but, like many similar algorithms that rely on data-driven background models, in its conventional implementation, it is unable to update in real time to account for environmental changes that affect the background spectroscopic signature. Here, we have developed a novel NMF-based algorithm that periodically updates its background model to accommodate changing environmental conditions. The adaptive NMF algorithm involves fewer assumptions about its environment, making it more generalizable than existing NMF-based methods while maintaining or exceeding detection performance on simulated and real-world datasets.

Anomaly detection↗
DOE OSTI2024

Pairing a Global Optimization Algorithm with EXAFS to Characterize Lanthanide Structure in Solution

Ensemble-average sampling of structures from ab initio molecular dynamics (AIMD) simulations can be used to predict theoretical extended X-ray absorption fine structure (EXAFS) signals that closely match experimental spectra. However, AIMD simulations are time-consuming and resource-intensive, particularly for solvated lanthanide ions, which often form multiple nonrigid geometries with high coordination numbers. Here, to accelerate the characterization of lanthanide structures in solution, we employed the Northwest Potential Energy Surface Search Engine (NWPEsSe), an adaptive-learning global optimization algorithm, to efficiently screen first-shell structures. As case studies, we examine two systems: Eu(NO 3 ) 3 dissolved in acetonitrile with a terpyridine ligand (terpyNO 2 ), and Nd(NO 3 ) 3 dissolved in acetonitrile. The theoretical spectra for structures identified by NWPEsSe were compared to both experimental and AIMD-derived EXAFS spectra. The NWPEsSe algorithm successfully identified the proper solvation structure for both Eu(NO 3 ) 3 (terpyNO 2 ) and Nd(NO 3 )(acetonitrile) 3 , with the calculated EXAFS signals closely matching the experimental spectra for the Eu-ligand complex and showing good similarity for the Nd salt; the better agreement with the ligand-containing structure is attributed to a less dynamic coordination environment due to the rigid ligand. The key advantage of the global optimization algorithm lies in its ability to sample the coordination environment across the potential energy surface and reduce the time required to identify structures from generally a month to within a week. Additionally, this approach is versatile and can be adapted to characterize main-group metal complexes.

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

Peer-to-Peer Communication Trade-Offs for Smart Grid Applications: Preprint

Peer-to-peer energy management systems for smart grids require developers to consider the trade-offs between the amount of communication traffic generated and the quality and speed of convergence of the control algorithms that are deployed. Employing a fully connected communication causes messages to scale exponentially with the number of nodes, while using a sparse connectivity causes less information dissemination leading to degradation of the algorithm performance. The best communication topology for a particular application lies somewhere in between and often requires empirical evaluation by application designers. Existing methods do not put focus on the needs for smart grid applications, which is information dissemination throughout the network and they do not provide a flexible solution for application developers to prototype and deploy different topologies without modifying the application code. This paper introduces a configurable virtual communication topology framework TopLinkMgr, allowing users to specify any chosen communication topology and deploy peer-to-peer applications using it. It also introduces a self-adaptive, fault-tolerant topology management algorithm, Bounded Path Dissemination that can ensure the dissemination of information to all peers within a specified threshold for a sparsely connected topology. Experiments show that the algorithm improves on convergence speed and accuracy over state-of-the-art methods and is also robust against node failures. The results indicate the possibility of achieving a close-to optimal convergence without overloading the network allowing the realization of peer-to-peer control platforms covering larger and more complex power systems.

Bounded Path Dissemination↗
DOE OSTI2023

Accelerating Markov Chain Monte Carlo sampling with diffusion models

Global fits of physics models require efficient methods for exploring high-dimensional and/or multimodal posterior functions. We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a Metropolis-Hastings algorithm with a diffusion model that can draw global samples with the aim of approximating the posterior. We briefly review diffusion models in the context of image synthesis before providing a streamlined diffusion model tailored towards low-dimensional data arrays. We then present our adapted Metropolis-Hastings algorithm which combines local proposals with global proposals taken from a diffusion model that is regularly trained on the samples produced during the MCMC run. Our approach leads to a significant reduction in the number of likelihood evaluations required to obtain an accurate representation of the Bayesian posterior across several analytic functions, as well as for a physical example based on a global fit of parton distribution functions. Our method is extensible to other MCMC techniques, and we briefly compare our method to similar approaches based on normalising flows. A code implementation can be found at https://github.com/NickHunt-Smith/MCMC-diffusion.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Rapid retrieval of first-order spatiotemporal distortions for ultrashort laser pulses

High-intensity, ultrashort laser sources are a foundational pillar for High-Energy-Density (HED) physics, and as the repetition-rates of these systems increase, diagnostics must be developed to match their data collection speed. Characterization of any spatiotemporal distortions in the laser pulse is necessary in order to standardize results across facilities. Here, we have previously developed a laser diagnostic called Spatially and Temporally Resolved Intensity and Phase Evaluation Device: Full Information from a Single Hologram, or STRIPED FISH, to measure the full spatiotemporal laser electric field on a single shot. In order to provide rapid feedback, we here adapt the STRIPED FISH retrieval algorithm, which typically has computation times of up to 30 minutes due to the high spatial resolution of the device and its retrieval of the complete four-dimensional pulse field, to distill the key electric field quantities into a handful of scalars for rapid assessment of the pulse's first order distortions. Here, our new, rapid non-iterative retrieval algorithm is validated with simulated and experimental data, and it provides, within seconds, the same first-order information as given by the full analysis. This algorithm is suitable for on-shot assessment of spatiotemporal distortions and can be adapted to assess high repetition-rate laser quality in HED experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Grid-tied Multilevel Inverter with Phase-locked Loop Algorithm

A multilevel inverter is an electronic device capable of changing direct current energy to alternant current energy with a voltage and frequency established by the user. They are ideal for connecting renewable energy sources to the AC grid, energy plants, and smart grids. The voltage must be balanced and synchronized with the electrical network for adequate performance. This paper shows the voltage synchronization between an inverter output voltage and the AC grid using a phase-locked loop based on an adaptive observer. The proposed algorithm can perform under grid uncertainties such as noise and generates a reference signal for the modulation used in the inverter. The algorithm is robust and computationally efficient and can be implemented through basic elements such as operational amplifiers, resistors, and capacitors, reducing its difficulty in executing it in a system.

42 ENGINEERING↗
DOE OSTI2020

Energy Impact of Connected and Automated Vehicle Technologies. Final report

The overarching goal of this project is to understand the potential impact of connected and automated vehicles. The goal was achieved through data collection, model development, algorithm designs, simulations, and limited field tests. The main outcomes from this project include: (1) we collected energy consumption and GPS data from 500 vehicles over one year, with a total mileage of 8 million miles; (2) Based on the collected data and other datasets collected at the University of Michigan, we developed a calibrated Ann Arbor model in Polaris (model developed by ANL), and the fuel economy accuracy was found to be around 3.9% by comparison with field collected data; (3) An open-source SUMO model of Ann Arbor was developed; (4) Eco-Routing algorithms in Ann Arbor using the SUMO model shows 6% fuel saving potential; (5) Experiments conducted at the Mcity test facility shows that human drivers roughly follow the Eco-driving suggestions roughly 70% of the time; (6) Based in the Ann Arbor travel patterns, we found that each shared automated vehicle can replace around 4 individually owned vehicles; and (7) Adaptive Traffic Signal Control Algorithm developed through this project has been validated both in simulations and preliminary test results. For connected and automated vehicles, on average the performance is 13% delay reduction, and 10% fuel reduction. While connected and automated vehicles are in their early stage of deployment, the results from this project confirm that there is significant potential for energy saving if the technologies are developed and used properly. The three main technologies studied in this project include eco-routing, shared autonomous rides, and adaptive traffic signal controls. The data collected and model developed through the project can be used to study many other connected and automated vehicle technologies.

02 PETROLEUM↗
DOE OSTI2026

Asymptotic-preserving semi-implicit finite volume scheme for extended magnetohydrodynamics

A Finite Volume (FV) scheme is developed for solving the extended magnetohydrodynamic (XMHD) equations, yielding accurate results in the ideal, resistive, and Hall MHD limits. This is accomplished by first re-writing the XMHD equations such that it allows the algorithm to retain the use of ideal MHD Riemann solvers and the constrained transport method to preserve divergence-free magnetic fields. Incorporation of electron inertia and displacement current introduces additional numerical stiffness which motivates a semi-implicit FV scheme that re-formulates the XMHD model as a relaxation system. The equations are then advanced in time using an explicit 2nd-order Runge–Kutta scheme with operator splitting applied to the implicit source term updates at each sub-stage. For additional numerical stability, a density-dependent slope limiter is implemented to increase flux diffusivity at low density regions where non-ideal effects become significant. The algorithm is subsequently implemented in a scalable adaptive mesh refinement (AMR) framework. As the new algorithm retains many aspects of the ideal MHD formulations, it asymptotes naturally to the ideal MHD limit. Moreover, it shows promising results at the resistive and Hall MHD limits. This is verified against reference test problems for ideal, resistive and Hall MHD.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Evaluating the potential of short-term instrument deployment to improve distributed wind resource assessment

Distributed wind projects, which are connected at the distribution level of an electricity system or in off-grid applications to serve specific or local energy needs, often rely solely on wind resource models to establish wind speed and energy generation expectations. Historically, anemometer loan programs have provided an affordable avenue for more accurate onsite wind resource assessment, and the lowering cost of lidar systems has shown similar advantages for more recent assessments. While a full 12 months of onsite wind measurement is the standard for correcting model-based long-term wind speed estimates for utility-scale wind farms, the time and capital investment involved in gathering onsite measurements must be reconciled with the energy needs and funding opportunities that drive expedient deployment of distributed wind projects. Much literature exists to quantify the performance of correcting long-term wind speed estimates with 1 or more years of observational data, but few studies explore the impacts of correcting with months-long observational periods. This study aims to answer the question of how short you can go in terms of the observational time period needed to make impactful improvements to model-based long-term wind speed estimates. Three algorithms, multivariable linear regression, adaptive regression splines, and regression trees, are evaluated for their skill at correcting long-term wind resource estimates from the European Centre for Medium-Range Weather Forecasts Reanalysis version 5 (ERA5) using months-long periods of observational data from 66 locations across the US. On average, correction with even 1 month of observations provides significant improvement over the baseline ERA5 wind speed estimates and produces median bias magnitudes and relative errors within 0.22 m s −1 and 4 percentage points of the median bias magnitudes and relative errors achieved using the standard 12 months of data for correction. However, in cases when the shortest observational periods (1 to 2 months) used for correction are not well correlated with the overlapping ERA5 reference, the resultant long-term wind speed errors are worse than those produced using ERA5 without correction. Summer months, which are characterized by weaker relative wind speeds and standard deviations for most of the evaluation sites, tend to produce the worst results for long-term correction using months-long observations. The three tested algorithms perform similarly for long-term wind speed bias; however, regression trees perform notably worse than multivariable linear regression and adaptive regression splines in terms of correlation when using 6 months or less of observational data for correction. Translating the analysis to wind energy, median relative errors in the capacity factor are on average within 10 % using 1 month of training. If the observation period used for correction is not well correlated with the reference data, however, misrepresentation of the observed capacity factor can be substantial. The risk associated with poor correlation between the observed and reference datasets decreases with increasing training period length. In the worst-correlation scenarios, the median capacity factor relative errors from using 1, 3, and 6 months are within 47 %, 26 %, and 16 %, respectively.

17 WIND ENERGY↗
DOE OSTI2023

Projection pursuit adaptation on polynomial chaos expansions

Here, the present work addresses the issue of accurate stochastic approximations in high-dimensional parametric space using tools from uncertainty quantification (UQ). The basis adaptation method and its accelerated algorithm in polynomial chaos expansions (PCE) were recently proposed to construct low-dimensional approximations adapted to specific quantities of interest (QoI). The present paper addresses one difficulty with these adaptations, namely their reliance on quadrature point sampling, which limits the reusability of potentially expensive samples. Projection pursuit (PP) is a statistical tool to find the “interesting” projections in high-dimensional data and thus bypass the curse-of-dimensionality. In the present work, we combine the fundamental ideas of basis adaptation and projection pursuit regression (PPR) to propose a novel method to simultaneously learn the optimal low-dimensional spaces and PCE representation from given data. While this projection pursuit adaptation (PPA) can be entirely data-driven, the constructed approximation exhibits mean-square convergence to the solution of an underlying governing equation and thus captures the supports and probability distributions associated with the physics constraints. The proposed approach is demonstrated on a borehole problem and a structural dynamics problem, demonstrating the versatility of the method and its ability to discover low-dimensional manifolds with high accuracy with limited data. In addition, the method can learn surrogate models for different quantities of interest while reusing the same data set.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

DeepAstroUDA: semi-supervised universal domain adaptation for cross-survey galaxy morphology classification and anomaly detection

Abstract Artificial intelligence methods show great promise in increasing the quality and speed of work with large astronomical datasets, but the high complexity of these methods leads to the extraction of dataset-specific, non-robust features. Therefore, such methods do not generalize well across multiple datasets. We present a universal domain adaptation method, DeepAstroUDA , as an approach to overcome this challenge. This algorithm performs semi-supervised domain adaptation (DA) and can be applied to datasets with different data distributions and class overlaps. Non-overlapping classes can be present in any of the two datasets (the labeled source domain, or the unlabeled target domain), and the method can even be used in the presence of unknown classes. We apply our method to three examples of galaxy morphology classification tasks of different complexities (three-class and ten-class problems), with anomaly detection: (1) datasets created after different numbers of observing years from a single survey (Legacy Survey of Space and Time mock data of one and ten years of observations); (2) data from different surveys (Sloan Digital Sky Survey (SDSS) and DECaLS); and (3) data from observing fields with different depths within one survey (wide field and Stripe 82 deep field of SDSS). For the first time, we demonstrate the successful use of DA between very discrepant observational datasets. DeepAstroUDA is capable of bridging the gap between two astronomical surveys, increasing classification accuracy in both domains (up to 40 % on the unlabeled data), and making model performance consistent across datasets. Furthermore, our method also performs well as an anomaly detection algorithm and successfully clusters unknown class samples even in the unlabeled target dataset.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Human Factors and Technologies Design to Improve User Acceptance of Pooled Rideshare for Increasing Transportation System Energy Efficiency

This multi-year project delivered a comprehensive, human-factors-driven framework to understand, model, and improve pooled rideshare (PR) adoption in the United States. Through three large-scale national survey studies involving more than 16,000 participants across multiple cities and demographic groups, the research established one of the most extensive datasets to date on user perceptions, behavioral barriers, and service expectations related to pooled rideshare. These data revealed key human factors barriers of user acceptance of PR and suggested potential actionable experience optimizations that could lead to increased PR usage. This foundational knowledge guided the development of novel human-factors models and behavioral choice models that quantify how psychological, demographic, and trip-level factors influence willingness to pool. Building on these empirical insights, the project developed advanced behavioral modeling tools, including mixed logit and integrated choice and latent variable models, to capture both observable and latent influences on PR adoption. These models significantly improved the ability to predict riders’ acceptance of pooled trips, explaining choice heterogeneity through latent constructs such as safety, service experience, privacy concerns, time sensitivity, and environmental attitudes. Together, these models provide a robust analytical foundation for designing PR systems that more effectively meet user needs. The project translated human-factors insights and behavioral models into actionable technology innovations by extending POLARIS—an agent-based, activity-based travel simulation platform—into a fully functional pooled rideshare simulation environment. New PR modules, acceptance models, and regional scenarios were implemented for Greenville, SC and Austin, TX, enabling high-fidelity validation of algorithmic strategies under realistic demand and traffic conditions. The simulation platform supported the development and evaluation of adaptive discount-based assignment algorithms, enhanced willingness-to-pay formulations, demographic-aware incentive mechanisms, and a proactive joint assignment and repositioning strategy. Simulation results demonstrated substantial gains in pooling uptake, average vehicle occupancy, energy efficiency, and fleet profitability. In Greenville, pooling adoption more than doubled, while reductions in vehicle-miles traveled and energy consumption were significant. In Austin, pooling improvements were achieved with minimal service-quality trade-offs, and profitability increased across all fleet sizes. Through this research, we developed a comprehensive understanding of the human factors barriers that limit user acceptance of pooled rideshare services. These insights enabled the design of human-factors-aware pooled rideshare technologies that more effectively address user concerns and improve adoption rates. By integrating these models into an advanced agent-based simulation framework, we demonstrated that higher adoption of pooled rideshare can lead to measurable improvements in energy efficiency and system performance. Together, these contributions establish a validated pathway from human-centered analysis to technology development and energy-saving outcomes, supporting national goals for more sustainable and efficient mobility systems.

Jia, Yunyi↗
DOE OSTI2024

Low Precision for Lower Energy Consumption: Preprint

Low-precision numeric types offer significant efficiency and energy benefits for computing applications. Mixed-precision algorithms, combining low and high precision types, maintain accuracy while improving performance. Despite advantages, there exist challenges on adapting existing mixed-precision algorithms to new technologies, such as new hardware architectures and new low-precision data types. This paper presents current challenges and opportunities to advance science in this domain targetting more energy efficient solutions.

energy efficiency↗
DOE OSTI2022

$χ$-$MeRA$: Computationally efficient adaptive mesh refinement of Monte Carlo mesh based tallies

Here, the reactor physics community is always focused on reducing the computational time and memory required for simulations. $χ$-$MeRA$, which stands for flux-based-($χ$)-Mesh tally Refinement Adaptively, was built to reduce the computational time and memory required to solve the neutronics side of a multiphysics problem when compared to traditional methods for mesh based tallies in Monte Carlo (MC) simulations. $χ$-$MeRA$ couples a MC code with an adaptive mesh refinement (AMR) algorithm to take advantage of the accuracy of a MC code and the efficiency of an AMR algorithm. Also developed within $χ$-$MeRA$ was a set of metrics to assess the effects of the refinement on various parameters in the simulation space. For a plutonium sphere, $χ$-$MeRA$ shows a reduction in memory usage and computation time when compared to a fully refined mesh by a factor of 14.7 and 6.7, respectively. When compared to an unstructured mesh, improvement of 1.3 and 4.8 was achieved for memory usage and computation time. The development of $χ$-$MeRA$ helps solve the neutronics side of a multiphysics problem in a faster, more computationally efficient manner than traditional methods, and the final mesh created contains accurate results that can be passed onto the next physics code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Multi-objective surrogate-assisted calibration of CPFEM models using macroscopic response and in situ EBSD measurements of grain reorientation trajectories

Crystal plasticity finite element method (CPFEM) models are widely used to simulate the deformation behaviour of polycrystalline materials, but their calibration is often limited by their high computational cost and the non-convexity of the optimisation landscape. Here, this study develops a multi-objective surrogate-assisted calibration workflow that couples a multi-objective genetic algorithm (MOGA) with an adaptively trained deep neural network (DNN) surrogate model to efficiently identify CPFEM parameters from experimental data. The workflow is demonstrated on three crystal plasticity (CP) formulations of increasing complexity — Voce hardening (VH), two-coefficient latent hardening (LH2), and six-coefficient latent hardening (LH6) — using in situ electron backscatter diffraction (EBSD) measurements of Alloy 617 under uniaxial tensile loading. The CPFEM models are calibrated against the experimentally observed stress–strain response and reorientation trajectories of eight grains, then validated against eight additional trajectories and overall texture evolution. Across the CP formulations, the macroscopic response was reproduced reliably, while differences emerged in the robustness and accuracy of the grain-scale predictions. Including grain reorientation trajectories in the multi-objective calibration improved texture evolution predictions and filtered out physically inconsistent parameter sets that can arise from calibrating against only the stress–strain data. The workflow also demonstrates good transferability of calibrated parameters from a low- to a high-fidelity microstructural model. These results provide practical guidance for integrating in situ microstructural data into CPFEM through efficient, repeatable, and physically meaningful multi-objective calibration.

Crystal plasticity finite element method↗
DOE OSTI2020

Evaluation of smart charging for electric vehicle-to-building integration: A case study

Higher electric vehicle (EV) adoption will stress the importance of demand flexibility to achieve more economic, efficient, and reliable grid operation. Charging technologies will be paramount in shifting temporally to better fit the variable generation of wind and solar. As such, analysis is warranted on the benefits of EV charge scheduling with respect to installation cost, operation cost, difficulty of implementation, and grid flexibility. We tackle this by analyzing the cost savings of implementing an EV charge scheduling infrastructure to reduce demand charges and installation costs. In this paper, we analyze a case study for operation of 16 level 2 chargers and 1 fast charger for two different building types. We then evaluate various test phases for controlling building and charging loads using an adaptive charging network (ACN) algorithm to characterize the ACN’s potential to reduce overall project cost.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2026

Protonation Dynamics of Confined Ethanol–Water Mixtures in H-ZSM-5 from Machine Learning-Driven Metadynamics

Zeolites are indispensable heterogeneous catalysts in industrial chemical processes, valued for their strong Brønsted acidity, well-defined microporous frameworks, and tunable pore structures. Their catalytic activity arises primarily from Brønsted acid sites (BAS), typically present as bridging hydroxyl groups (Si–OH–Al). Under aqueous reaction conditions, these protons interact dynamically with water and alcohol molecules, leading to complex solvation and protonation behavior within confined pores. In this study, we investigate the protonation equilibrium occurring between ethanol and water at the BAS of acidic zeolites under varying hydration levels, i.e., C2H5OH–(H2O)n, n=1–4. Local structure was analyzed through an adaptive-learning global optimization algorithm, while enhanced sampling molecular dynamics simulations with Well-Tempered Metadynamics (WMetaD) and machine learning interatomic potentials (MLPs) provide free-energy surfaces (FES) at variable hydration levels. The results reveal a strong dependence of proton localization on the degree of hydration. At low hydration (1 water molecule), the proton resides predominantly on ethanol; with 2 water molecules, it shifts toward water, and at higher hydration (3 or more water molecules), it becomes extensively delocalized over the water cluster. These findings underscore the critical role of solvation in modulating acid site behavior and suggest that a minimum of three water molecules is necessary to fully stabilize the proton on water within the zeolite framework. This solvation threshold has significant implications for catalytic processes, particularly in biomass conversion reactions where alcohol protonation is a key step in dehydration mechanisms.

machine learning↗
DOE OSTI2021

Deep Learning Segmentation of Complex Features in Atomic-Resolution Phase-Contrast Transmission Electron Microscopy Images

Phase-contrast transmission electron microscopy (TEM) is a powerful tool for imaging the local atomic structure of materials. TEM has been used heavily in studies of defect structures of two-dimensional materials such as monolayer graphene due to its high dose efficiency. However, phase-contrast imaging can produce complex nonlinear contrast, even for weakly scattering samples. It is, therefore, difficult to develop fully automated analysis routines for phase-contrast TEM studies using conventional image processing tools. For automated analysis of large sample regions of graphene, one of the key problems is segmentation between the structure of interest and unwanted structures such as surface contaminant layers. In this study, we compare the performance of a conventional Bragg filtering method with a deep learning routine based on the U-Net architecture. We show that the deep learning method is more general, simpler to apply in practice, and produces more accurate and robust results than the conventional algorithm. We provide easily adaptable source code for all results in this paper and discuss potential applications for deep learning in fully automated TEM image analysis.

47 OTHER INSTRUMENTATION↗