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Calibration sources for the LEGEND-200 experiment

In the search for a monochromatic peak as the signature of neutrinoless double beta decay an excellent energy resolution and an ultra-low background around the Q-value of the decay are essential. The LEGEND-200 experiment performs such a search with high-purity germanium detectors enriched in 76 Ge immersed in liquid argon. To determine and monitor the stability of the energy scale and resolution of the germanium diodes, custom-made, low-neutron emission 228 Th sources are regularly deployed in the vicinity of the crystals. Here we describe the production process of the 17 sources available for installation in the experiment, the measurements of their alpha- and gamma- activities, as well as the determination of the neutron emission rates with a low-background LiI(Eu) detector operated deep underground. With a flux of ( 4.27 ± 0.60 stat ± 0.92 syst ) × 10 -4 n / (kBq·s), approximately one order of magnitude below that of commercial sources, the neutron-induced background rate, mainly from the activation of 76 Ge, is negligible compared to other background sources in LEGEND-200.

47 OTHER INSTRUMENTATION↗

Fabrication, Modeling, and Testing of a Prototype Thermal Energy Storage Containment

Increasing penetration of variable renewable energy resources requires the deployment of energy storage at a range of durations. Long-duration energy storage (LDES) technologies will fulfill the need to firm variable renewable energy resource output year round; lithium-ion batteries are uneconomical at these durations. Thermal energy storage (TES) is one promising technology for LDES applications because of its siting flexibility and ease of scaling. Particle-based TES systems use low-cost solid particles that have higher temperature limits than the molten salts used in traditional concentrated solar power systems. A key component in particle-based TES systems is the containment silo for the high-temperature (>1100 degrees C) particles. This study combined experimental testing and computational modeling methods to design and characterize the performance of a particle containment silo for LDES applications. A laboratory-scale silo prototype was built and validated the congruent transient finite element analysis (FEA) model. The performance of a commercial-scale silo was then characterized using the validated model. The commercial-scale model predicted a storage efficiency above 95% after 5 days of storage with a design storage temperature of 1200 degrees C. Insulation material and concrete temperature limits were considered as well. The validation of the methodology means the FEA model can simulate a range of scenarios for future applications. This work supports the development of a promising LDES technology with implications for grid-scale electrical energy storage, but also for thermal energy storage for industrial process heating applications.

clean energy↗

Fabrication, Modeling, and Testing of a Prototype for Particle Thermal Energy Storage Containment

Increasing penetration of variable renewable energy resources requires the deployment of energy storage at a range of durations. Long-duration energy storage (LDES) technologies will fulfill the need to firm variable renewable energy resource output throughout the year. Conventional electrochemical batteries (e.g., lithium-ion) are uneconomical in this role due to high energy capacity costs. Thermal energy storage (TES) is one promising technology for LDES applications because of its siting flexibility and ease of scaling. Particle-based TES systems use low-cost solid particles that have higher temperature limits than the molten salts used in traditional concentrated solar power systems. A key component in particle-based TES systems is the containment silo for the high-temperature (> 1100 degrees C) particles. This study combined experimental testing and computational modeling methods to design and characterize the performance of a particle containment silo for LDES applications. A containment silo prototype was built at a laboratory scale and used to validate a congruent transient finite element analysis (FEA) model. The validation compared the actual and predicted temperature profile through the prototype over six days as the particles cooled from their initial temperature. The performance of a commercial scale (> 5 GWhth) was then characterized using the validated model. The transient FEA model was subject to several charge-discharge cycles to mimic a possible operating schedule. The commercial-scale model predicted a storage efficiency in excess of 95% after five days of storage with a design storage temperature of 1200 degrees C. Insulation material and concrete temperature limits were considered as well. The validation of the methodology means the FEA model can simulate a range of scenarios for future applications. This work supports the development of a promising LDES technology with implications for grid-scale electrical energy storage, but also for thermal energy storage for industrial process heating applications.

ENERGY STORAGE↗

Investigation of Coincidence Counting for Improving Minimal Detectable Activity of 110m Ag in Single Particle Gamma Analysis

Post-irradiation examination (PIE) of fuel particles from the fourth Advanced Gas Reactor Fuel Development and Qualification (AGR) Program irradiation (AGR-5/6/7) is being performed at Oak Ridge National Laboratory (ORNL). Tristructural isotropic (TRISO)-coated particles and associated compacts for the AGR-5/6/7 experiment fabricated by BWX Technologies Nuclear Operations Group were formed into a graphite matrix compact and irradiated at the Advanced Test Reactor at Idaho National Laboratory. At ORNL, particles are deconsolidated from the graphite matrix compact and individually scanned for emitted gamma rays with the Irradiated Microsphere Gamma Analyzer (IMGA). The IMGA system comprises a single high purity germanium (HPGe) detector, an automated particle handling vacuum system, and an ORTEC DSPEC-50 digital spectrometer for gamma ray analysis. IMGA quantifies gamma ray-emitting fission product inventories of individual TRISO particles, and these inventories can be compared with the measured average inventories per particle and radionuclide inventories predicted by AGR-5/6/7 physics calculations to determine if a particle experienced radionuclide release. Details on IMGA data collection methods can be found in the literature. The TRISO particle’s SiC layer provides structural support, as well as a barrier for fission product release during irradiation or subsequent safety testing. A weakened or compromised SiC layer can be identified by the release of radionuclides, such as 137 Cs, which is detected by IMGA. However, select radionuclides, such as 90 Sr, 110 mAg, and 154 Eu have been shown to migrate through an intact SiC layer. Measurement of the radionuclide 110 mAg is significant as its release has been shown to be particularly sensitive to in-reactor conditions (e.g., temperature) with broad variable particle to-particle release behaviors observed within a single compact. As such, 110 mAg activity is often used for particle selection for comprehensive PIE as bounding 110 mAg retention particles are hypothesized to represent limits in particle behaviors within a compact. As TRISO particle fuel PIE activities continue over time, IMGA measurements of the 110 mAg inventory are eventually hindered because of its relatively short half-life (~250 days). As the fuel ages from its end of irradiation (EOI) date, the measurement uncertainty and minimum detectable activity (MDA) of 110m Ag increase because the detector background continuum begins to dominate. For particles from the second AGR irradiation experiment (AGR-2), the 110m Ag MDA was above 20% of the calculated average particle inventory after approximately five half-lives, and 110m Ag activity was no longer measurable with IMGA after approximately seven half-lives. Therefore, coincidence counting approaches have been explored to determine feasibility of leveraging new approaches to overcome limitations associated with increasing MDA over time.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Leveraging unlabeled SEM datasets with self-supervised learning for enhanced particle segmentation

Scanning Electron Microscopes (SEMs) are widely used in experimental science laboratories, often requiring cumbersome and repetitive user analysis. Automating SEM image analysis processes is highly desirable to address this challenge. In particle sample analysis, Machine Learning (ML) has emerged as the most effective approach for particle segmentation. However, the time-intensive process of manually annotating thousands of SEM images limits the applicability of supervised learning approaches. Self-Supervised Learning (SSL) offers a promising alternative by enabling knowledge extraction from raw, unlabeled data. This study presents a framework for evaluating SSL techniques in SEM image analysis, focusing on novel methods leveraging the ConvNeXtV2 architecture for particle detection. A dataset comprising 25,000 SEM images is curated to benchmark these proposed SSL methods. The results demonstrate that ConvNeXtV2 models, with varying parameter counts, consistently outperform other techniques in particle detection across different length scales, achieving up to a 34% reduction in relative error compared to established SSL methods. Furthermore, an ablation study explores the relationship between dataset size and SSL performance, providing actionable insights for practitioners regarding model selection and resource efficiency. This research advances the integration of SSL into autonomous analysis pipelines and supports its application in accelerating materials science discovery.

Rettenberger, Luca↗

Kinetic simulations of collision-less plasmas in open magnetic geometries

Laboratory plasmas in open magnetic geometries can be found in many different applications such as (a) scrape-of-layer (SOL) and divertor regions in toroidal confinement fusion devices, (b) linear divertor simulators, (c) plasma-based thrusters and (d) magnetic mirrors etc. A common feature of these plasma systems is the need to resolve, in addition to velocity space, at least one physical dimension (e.g. along flux lines) to capture the relevant physics. In general, this requires a kinetic treatment. Fully kinetic particle-in-cell (PIC) simulations can be applied but at the expense of large computational effort. A common way to resolve this is to use a hybrid approach: kinetic ions and fluid electrons. In the present work, the development of a hybrid PIC computational tool suitable for open magnetic geometries is described which includes (a) the effect of non-uniform magnetic fields, (b) finite fully-absorbing boundaries for the particles and (c) volumetric particle sources. Analytical expressions for the momentum transport in the paraxial limit are presented with their underlying assumptions and are used to validate the results from the PIC simulations. A general method is described to construct discrete particle distribution functions in a state of mirror-equilibrium. This method is used to obtain the initial state for the PIC simulation. Collisionless simulations in a mirror geometry are performed. The results show that the effect of magnetic compression is correctly described and momentum is conserved. The self-consistent electric field is calculated and is shown to modify the ion velocity distribution function in a manner consistent with analytic theory. Based on this analysis, the ion distribution function is understood in terms of a loss-cone distribution and an isotropic Maxwell-Boltzmann distribution driven by a volumetric plasma source. Finally, the inclusion of a Monte Carlo based Fokker-Planck collision operator is discussed in the context of future work.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A Novel Approach to Fast Calculation of High-Order Q-Cumulants

The method of Q-cumulants has been shown as a powerful tool to study the fine details of the azimuthal anisotropies in high-energy nucleus-nucleus collisions. A new method for the fast calculation of arbitrary order Q-cumulant $v_{n}\{2k\}$ values, based on the partition of a non-negative integer l $\le$ m for calculation of the 2m-particle azimuthal correlations is presented in this paper. Unlike the standard Q-cumulants method in which the calculation of high-order multi-particle calculations is impractical, the newly proposed method enables easy calculation. The validity of the method is proven via a toy model that uses the elliptic power distribution to simulate anisotropic emission of particles. The method enables the study of fine details of the $v_{2}$ distribution, such as higher-order central moments of the $v_{2}$ distribution, as well as the hydrodynamic behavior of the Quark-Gluon Plasma.

FOS: Physical sciences↗

VOPO 4 cathode for sodium ion batteries

An electrode comprising a space group Pna2 1 VOPO 4 lattice, capable of electrochemical insertion and release of alkali metal ions, e.g., sodium ions. The VOPO 4 lattice may be formed by solid phase synthesis of KVOPO 4 , milled with carbon particles to increase conductivity. A method of forming an electrode is provided, comprising milling a mixture of ammonium metavanadate, ammonium phosphate monobasic, and potassium carbonate; heating the milled mixture to a reaction temperature, and holding the reaction temperature until a solid phase synthesis of KVOPO 4 occurs; milling the KVOPO 4 together with conductive particles to form a conductive mixture of fine particles; and adding binder material to form a conductive cathode. A sodium ion battery is provided having a conductive NaVOPO 4 cathode derived by replacement of potassium in KVOPO 4 , a sodium ion donor anode, and a sodium ion transport electrolyte. The VOPO 4 , preferably has a volume greater than 90 Å 3 per VOPO 4 .

Whittingham, M. Stanley↗

Comparison of integral equations used to study ${T}_{cc}^{+}$ for a stable D *

We perform a detailed comparison between three formalisms used in recent studies of DD* scattering at heavier-than-physical pion masses, which aim to understand the properties of the doubly-charmed tetraquark, ${T}_{cc}^{+}$ (3875). These methods are the three-particle relativistic field theory (RFT) formalism, the two-body Lippmann-Schwinger (LS) equation with chiral effective field theory potentials, and the two-particle relativistic framework proposed by Baião Raposo and Hansen (BRH approach). In a simplified single-channel setting, we derive the conditions under which the infinite-volume integral equations from the RFT and BRH approaches reduce to the LS form. We present numerical examples showing that differences between these methods can be largely removed by adjusting short-range couplings. We also address a number of technical issues in the RFT approach.

Hadronic Spectroscopy↗

Toward closure between predicted and observed particle viscosity over a wide range of temperatures and relative humidity

Abstract. Atmospheric aerosols can exist in amorphous semi-solid or glassy phase states whose viscosity varies with atmospheric temperature and relative humidity. The temperature and humidity dependence of viscosity has been hypothesized to be predictable from the combination of a water–organic binary mixing rule of the glass transition temperature, a glass-transition-temperature-scaled viscosity fragility parameterization, and a water uptake parameterization. This work presents a closure study between predicted and observed viscosity for sucrose and citric acid. Viscosity and glass transition temperature as a function of water content are compiled from literature data and used to constrain the fragility parameterization. New measurements characterizing viscosity of sub-100 nm particles using the dimer relaxation method are presented. These measurements extend the available data of temperature- and humidity-dependent viscosity to −28 ∘C. Predicted relationships agree well with observations at room temperature and with measured isopleths of constant viscosity at ∼107 Pa s at temperatures warmer than −28 ∘C. Discrepancies at colder temperatures are observed for sucrose particles. Simulations with the kinetic multi-layer model of gas–particle interactions suggest that the observed deviations at colder temperature for sucrose can be attributed to kinetic limitations associated with water uptake at the timescales of the dimer relaxation experiments. Using the available information, updated equilibrium phase-state diagrams (-80∘C

54 ENVIRONMENTAL SCIENCES↗

CCN data from TAMU TRACER campaign in the Houston TX region from July to September 2022

During TRACER, the Texas A&M Rapid Onsite Atmospheric Measurements Van (ROAM-V) was deployed to capture airmasses behind (maritime) and ahead (continental) of the passage of the sea-breeze front through Houston. On select sampling days, ROAM-V sampled in the morning/mid-day on the coast and then transited to a second inland site for the afternoon/evening. The suite of instruments deployed on ROAM-V included a Condensation Particle Counter (CPC; GRIMM Model 5.403 CPC), Scanning Mobility Particle Sizer (SMPS; TSI 3750 detector, TSI 3082 classifier, TSI 3088 neutralizer, TSI 3081A Differential Mobility Analyzer), Cloud Condensation Nuclei counter (Droplet Measurement Technologies CCN Counter), micro pulse lidar (Droplet Measurement Technologies Micro Pulse LiDAR (miniMPL)), and a Davis Rotating Uniform size-cut Monitor (DRUM; DRUMAir 4-DRUM). Before sampling at each location, the latitude and longitude were recorded using the GPS on the phone application “My Altitude”. Onboard the ROAM-V, aerosol samples are drawn through a shared isokinetic inlet at a flow rate ranging from 3.5 to 7.0 LPM. A portion of this flow is directed through a cyclone impactor (Brechtel, Inc. Model SCC 0.732) and 0.5 LPM is directed to the CCN. To calculate particle losses, we used a two-step method. First, the measured SMPS size distributions were used to calculate particle loss through the inlet during sampling. Second, the corrected SMPS data was used to calculate the average of the total losses per scan down the CCN line. Then, the correction was applied to the CCN data. This calculation was done separately for each deployment location due to changes in the measured size distributions between locations. Particle loss from diffusion (based on Kesten, 1991 and Gormley, 1949), inertial impaction in 90-degree bends (based on Aerosol Measurement, 2011 and Crane, 1977), and cyclone impactor efficiency (based on Dirgo, 1985) were included in the loss calculation. When the SMPS was not sampling at a location (in the case of an instrument malfunction or operator error), the reported CPC data was corrected with an average of the total losses for the entire campaign at the specified deployment location (e.g., if we needed to correct Galveston data, then the average of all calculated losses at Galveston was taken). These flatline corrections were used for all data on 22/07/13, 22/07/20, 22/07/22, and the data from Galveston on 22/08/09. The supersaturation uncertainty is estimated conservatively at +/- 0.03%, where variation in the inlet temperature, pressure, and calibration technique prevents a more accurate measurement. Confidence in the reported supersaturation measurements is based on a pre-campaign calibration (following the methods from our previous work and Deng, 2014 based on Rose, 2008) in addition to inter-comparisons with the DOE for two days (22/08/18 and 22/09/01) where TAMU was co-located with AMF1. The inter-comparisons show good agreement between our instrument and the DOEs instrument on both days at all supersaturations. After the last inter-comparison on 22/09/01, there was no indication of a malfunction by our instrument through the rest of the campaign. Unfortunately, the instrument was dropped during demobilization. A post-campaign calibration was conducted, which showed a substantial departure from the pre-campaign calibration. The drop may have damaged the instrument’s ability to produce the desired supersaturations. Therefore, we do consider the data after 22/09/01 to be correct, but it should be used with caution. The CCN counter sampled for 3 minutes at each supersaturation setpoint (0.2, 0.4, 0.6, 0.8, 1.0, and 1.2%). At the end of a cycle, the instrument was set to 0.01% supersaturation for 5 minutes. The data is comprised of the last 60 seconds of each supersaturation set point (0.2, 0.4, 0.6, 0.8, 1.0, and 1.2%) to ensure the instrument stabilized and was able to reach thermal equilibrium. We removed the data during the periods where there were operational difficulties, setup, or maintenance. This data was collected for ARM Field Campaign AFC07055 and supported by DOE ASR grant DE-SC0021047. For any further questions, please feel free to contact the instrument PI, Sarah D. Brooks, sbrooks@tamu.edu. Rose et. al. Calibration and Measurement Uncertainties of a Continuous-Flow Cloud Condensation Nuclei Counter (DMT-CCNC): CCN Activation of Ammonium Sulfate and Sodium Chloride Aerosol Particles in Theory and Experiment. Atmos. Chem. Phys., 8, 1153-1179, 2008. Deng et. al. Using Raman Microspectroscopy to Determine Chemical Composition and Mixing State of Airborne Marine Aerosols over the Pacific Ocean. Aerosol Science and Technology, Vol 48, Issue 2, 2014. Kesten et. al. Calibration of a TSI Model 3025 Ultrafine Condensation Particle Counter. Aerosol Science and Technology, 15:2, 107-111, 1991. Gormley et. al. Diffusion from a Stream Flowing through a Cylindrical Tube. Proceedings of the Royal Irish Academy, Vol 52, 163-169, 1948. Aerosol Measurement: Principles, Techniques, and Applications, Third Edition. John Wiley & Sons, Inc, 2011. Crane et. al. Inertial Deposition of Particles in a Bent Pipe. Journal of Aerosol Science, Vol 8, 161-170, 1977. Dirgo et. al. Cyclone Collection Efficiency: Comparison of Experimental Results with Theoretical Predictions. Aerosol Science and Technology, 4:4, 401-415, 1985.

54 ENVIRONMENTAL SCIENCES↗

Exploiting a Shortcoming of Coupled-Cluster Theory: The Extent of Non-Hermiticity as a Diagnostic Indicator of Computational Accuracy

The fundamental non-Hermitian nature of the forms of the coupled-cluster (CC) theory widely used in quantum chemistry has usually been viewed as a negative, but the present paper shows how this can be used to an advantage. Specifically, the non-symmetric nature of the reduced one-particle density matrix (in the molecular orbital basis) is advocated as a diagnostic indicator of computational quality. In the limit of the full coupled-cluster theory [which is equivalent to full configuration interaction (FCI)], the electronic wave function and correlation energy are exact within a given one-particle basis set, and the symmetric character of the exact density matrix is recovered. The extent of the density matrix asymmetry is shown to provide a measure of “how difficult the problem is” (like the well-known T 1 diagnostic), but its variation with the level of theory also gives information about “how well this particular method works”, irrespective of the difficulty of the problem at hand. The proposed diagnostic is described and applied to a select group of small molecules, and an example of its overall utility for the practicing quantum chemist is illustrated through its application to the beryllium dimer (Be 2 ). Future application of this idea to excited states, open-shell systems, and symmetry-breaking problems and an extension of the method to the two-particle density are then proposed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Revisiting the empirical particle-fluid coupling model used in DEM-CFD by high-resolution DEM-LBM-IMB simulations: A 2D perspective

The work investigates the applicability of the unresolved Computational Fluid Dynamics and Discrete Element Method (CFDDEM) technique based on empirical equations for fluid-particle coupling. We first carry out a series of representative volume element simulations using the high-resolution particle-resolved Lattice Boltzmann method and Discrete Element Method (LBMDEM) coupled by an Immersed Moving Boundary (IMB) scheme. Then, we compare the results obtained by both LBMDEM and empirical equations used in unresolved CFDDEM with analytical solutions. It is found that the existing empirical equations used in solving fluid-particle interactions in 2D CFDDEM fail to accurately calculate the hydrodynamic force applied to solid particles. The underlying reason is that the existing empirical models are obtained based on 3D experimental results and thus are not applicable to 2D problems. Based on the simulation results, a new drag coefficient model is then proposed. The estimated drag forces using the new model are compared favourably with the simulated ones, indicating the good performance of the proposed model.

42 ENGINEERING↗

Attribute-Aware RBFs: Interactive Visualization of Time Series Particle Volumes Using RT Core Range Queries

Smoothed-particle hydrodynamics (SPH) is a mesh-free method used to simulate volumetric media in fluids, astrophysics, and solid mechanics. Visualizing these simulations is problematic because these datasets often contain millions, if not billions of particles carrying physical attributes and moving over time. Radial basis functions (RBFs) are used to model particles, and overlapping particles are interpolated to reconstruct a high-quality volumetric field; however, this interpolation process is expensive and makes interactive visualization difficult. Existing RBF interpolation schemes do not account for color-mapped attributes and are instead constrained to visualizing just the density field. To address these challenges, we exploit ray tracing cores in modern GPU architectures to accelerate scalar field reconstruction. We use a novel RBF interpolation scheme to integrate per-particle colors and densities, and leverage GPU-parallel tree construction and refitting to quickly update the tree as the simulation animates over time or when the user manipulates particle radii. We also propose a Hilbert reordering scheme to cluster particles together at the leaves of the tree to reduce tree memory consumption. Finally, we reduce the noise of volumetric shadows by adopting a spatially temporal blue noise sampling scheme. Our method can provide a more detailed and interactive view of these large, volumetric, time-series particle datasets than traditional methods, leading to new insights into these physics simulations.

Particle Volumes↗

A comprehensive review on regeneration strategies for direct air capture

Direct air capture (DAC), which removes CO 2 directly from ambient air, is a critical negative emission technology for mitigating global climate change. Efficiency and the source of energy are crucial considerations for DAC to enable negative emissions. Substantial technological progress has been made in DAC technologies, and promising opportunities exist for commercial-scale deployments. However, DAC technologies require high regeneration energy to release CO 2 from sorbents. Various approaches have been tested and optimized for different DAC systems. This review demonstrates that the work equivalent regeneration energy demand (supported by either the electric grid or fossil fuel combustion) ranges from 0.5–18.75 GJ/t-CO 2 for solid sorbent DAC systems and 0.62–17.28 GJ/t-CO 2 for liquid solvent DAC systems. The regeneration process is the energy-demanding process in DAC that is a key step for efficient operation. Potential methods to lower the regeneration energy demand include microwave, ultrasound, magnetic particle heating, and electric swing. Although the potential methods to date are still at the lab scale, significant work is being done to optimize DAC system processes.

54 ENVIRONMENTAL SCIENCES↗

Collective mode Brownian dynamics: A method for fast relaxation of statistical ensembles

Sampling equilibrium configurations of correlated systems of particles with long relaxation times (e.g., polymeric solutions) using conventional molecular dynamics and Monte Carlo methods can be challenging. This is especially true for systems with complicated, extended bond network topologies and other interactions that make the use and design of specialized relaxation protocols infeasible. We introduce a method based on Brownian dynamics simulations that can reduce the computational time it takes to reach equilibrium and draw decorrelated samples. Importantly, the method is completely agnostic to the particle configuration and the specifics of interparticle forces. In particular, we develop a mobility matrix that excites non-local, collective motion of N particles and can be computed efficiently in $\mathcal{O}(N)$ time. Particle motion in this scheme is computed by integrating the overdamped Langevin equation with an Euler–Maruyama scheme, in which Brownian displacements are drawn efficiently using a low-rank representation of the mobility matrix in position and wave space. We demonstrate the efficacy of the method with various examples from the realm of soft condensed matter and release a massively parallel implementation of the code as a plugin for the open-source package HOOMD-blue [J. A. Anderson et al., J. Comput. Phys. 227, 5342 (2008) and J. Glaser et al., Comput. Phys. Commun. 192, 97 (2015)] which runs on graphics processing units

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

End-to-end orientation estimation from 2D cryo-EM1images

Cryo-electron microscopy (cryo-EM) is a Nobel Prize-winning technique for deter-mining high-resolution 3D structures of biological macromolecules. A 3D structure is reconstructed from hundreds of thousands of noisy 2D projection images. However, existing 3D reconstruction methods are still time-consuming, and one of the major computational bottlenecks is to recover the unknown orientation of the particle in16each 2D image. The dominant methods typically exploit expensive global search on each image to estimate the missing orientations. Here, a novel end-to-end supervised learning method is introduced to directly recover the missing orientations from 2D cryo-EM images. A neural network is used to approximate the mapping from images to orientations. Furthermore, a robust loss function is proposed for optimizing the parameters of the network, which can handle both asymmetric and symmetric 3D structures. Experiments on synthetic datasets with various symmetry types confirm that the neural network is capable of recovering orientations from 2D cryo-EM images, and the results on one real cryo-EM dataset further demonstrate its potential in more challenging imaging conditions.

3D reconstruction↗