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All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Validation of statistical uncertainties in subcritical benchmark measurements: Part II – Measured data

Part I of this work presented an uncertainty approach which incorporates the singles and doubles counting rates determined by the Hage-Cifarelli formalism of the Feynman Variance-to-Mean method. This moments-based approach utilizes time correlations between prompt neutrons detections to assess the system multiplication. Additionally, it presented a validation which utilized simulated data generated using a 0-D point-kinetics Monte Carlo code. In Part II, this same method and validation approach is applied to measured data of a subcritical benchmark experiment. These measurements were performed with a 4.5 kg sphere of alpha-phase weapons grade plutonium reflected by copper and/or polyethylene. Finally, the results of 17 configurations are shown including detailed validation for four of the configurations.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Simulation based inference with domain adaptation for strong gravitational lensing

Simulation based inference leverages machine learning to carry out Bayesian inference in systems with intractable likelihoods. However, transitioning a network trained on simulated data to real data runs the risk of encountering domain shift, leading to performance losses. We attempt to implement domain adaptation into the sbi neural posterior estimation framework using the Maximum Mean Discrepancy as an additional network loss, using masked autoregressive fow (MAF) as our density estimator. We test the network on a set of 400,000 simulated strong gravitational lensing images generated using deeplenstronomy. The source domain is defined as low noise whereas the target domain has a noise profile sampled from experimentally derived DES survey conditions. We find that SBI appears robust against small changes in the data with similar performance on source and target. Moreover, while DA does lead to performance improvements, they are marginal at 6% less inference error.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

PLATO hare-and-hounds exercise: asteroseismic model fitting of main-sequence solar-like pulsators

ABSTRACT Asteroseismology is a powerful tool to infer fundamental stellar properties. The use of these asteroseismic-inferred properties in a growing number of astrophysical contexts makes it vital to understand their accuracy. Consequently, we performed a hare-and-hounds exercise where the hares simulated data for six artificial main-sequence stars and the hounds inferred their properties based on different inference procedures. To mimic a pipeline such as that planned for the PLATO mission, all hounds used the same model grid. Some stars were simulated using the physics adopted in the grid, others a different one. The maximum relative differences found (in absolute value) between the inferred and true values of the mass, radius, and age were 4.32, 1.33, and 11.25 per cent, respectively. The largest systematic differences in radius and age were found for a star simulated assuming gravitational settling, not accounted for in the model grid, with biases of −0.88 per cent (radius) and 8.66 per cent (age). For the mass, the most significant bias (−3.16 per cent) was found for a star with a helium enrichment ratio outside the grid range. Moreover, an ∼7 per cent dispersion in age was found when adopting different prescriptions for the surface corrections or shifting the classical observations by ±1σ. The choice of the relative weight given to the classical and seismic constraints also impacted significantly the accuracy and precision of the results. Interestingly, only a few frequencies were required to achieve accurate results on the mass and radius. For the age the same was true when at least one l = 2 mode was considered.

Cunha, M. S. (ORCID:0000000182377343)↗
DOE OSTI2015

Comparison between target margins derived from 4DCT scans and real-time tumor motion tracking: Insights from lung tumor patients treated with robotic radiosurgery

Purpose: A unique capability of the CyberKnife system is dynamic target tracking. However, not all patients are eligible for this approach. Rather, their tumors are tracked statically using the vertebral column for alignment. When using static tracking, the internal target volume (ITV) is delineated on the four-dimensional (4D) CT scan and an additional margin is added to account for setup uncertainty [planning target volume (PTV)]. Treatment margins are difficult to estimate due to unpredictable variations in tumor motion and respiratory pattern during the course of treatment. The inability to track the target and detect changes in respiratory characteristics might result in geographic misses and local tumor recurrences. The purpose of this study is to develop a method to evaluate the adequacy of ITV-to-PTV margins for patients treated in this manner. Methods: Data from 24 patients with lesions in the upper lobe (n = 12), middle lobe (n = 3), and lower lobe (n = 9) were included in this study. Each patient was treated with dynamic tracking and underwent 4DCT scanning at the time of simulation. Data including the 3D coordinates of the target over the course of treatment were extracted from the treatment log files and used to determine actual target motion in the superior–inferior (S–I), anterior–posterior (A–P), and left–right (L–R) directions. Different approaches were used to calculate anisotropic and isotropic margins, assuming that the tumor moves as a rigid body. Anisotropic margins were calculated by separating target motion in the three anatomical directions, and a uniform margin was calculated by shifting the gross tumor volume contours in the 3D space and by computing the percentage of overlap with the PTV. The analysis was validated by means of a theoretical formulation. Results: The three methods provided consistent results. A uniform margin of 4.5 mm around the ITV was necessary to assure 95% target coverage for 95% of the fractions included in the analysis. In the case of anisotropic margins, the expansion required in the S–I direction was larger (8.1 mm) than those in the L–R (4.9 mm) and A–P (4.5 mm) directions. This margin accounts for variations of target position within the same treatment fraction. Conclusions: The use of bony alignment for CyberKnife lung stereotactic body radiation therapy requires careful considerations, in terms of the potential for increased toxicity or local miss. Our method could be used by other centers to determine the adequacy of ITV-to-PTV margins for their patients.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

A method for volumetric imaging in radiotherapy using single x-ray projection

Purpose: It is an intriguing problem to generate an instantaneous volumetric image based on the corresponding x-ray projection. The purpose of this study is to develop a new method to achieve this goal via a sparse learning approach. Methods: To extract motion information hidden in projection images, the authors partitioned a projection image into small rectangular patches. The authors utilized a sparse learning method to automatically select patches that have a high correlation with principal component analysis (PCA) coefficients of a lung motion model. A model that maps the patch intensity to the PCA coefficients was built along with the patch selection process. Based on this model, a measured projection can be used to predict the PCA coefficients, which are then further used to generate a motion vector field and hence a volumetric image. The authors have also proposed an intensity baseline correction method based on the partitioned projection, in which the first and the second moments of pixel intensities at a patch in a simulated projection image are matched with those in a measured one via a linear transformation. The proposed method has been validated in both simulated data and real phantom data. Results: The algorithm is able to identify patches that contain relevant motion information such as the diaphragm region. It is found that an intensity baseline correction step is important to remove the systematic error in the motion prediction. For the simulation case, the sparse learning model reduced the prediction error for the first PCA coefficient to 5%, compared to the 10% error when sparse learning was not used, and the 95th percentile error for the predicted motion vector was reduced from 2.40 to 0.92 mm. In the phantom case with a regular tumor motion, the predicted tumor trajectory was successfully reconstructed with a 0.82 mm error for tumor center localization compared to a 1.66 mm error without using the sparse learning method. When the tumor motion was driven by a real patient breathing signal with irregular periods and amplitudes, the average tumor center error was 0.6 mm. The algorithm robustness with respect to sparsity level, patch size, and presence or absence of diaphragm, as well as computation time, has also been studied. Conclusions: The authors have developed a new method that automatically identifies motion information from an x-ray projection, based on which a volumetric image is generated.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

An Atomistic Carbide-Derived Carbon Model Generated Using ReaxFF-Based Quenched Molecular Dynamics

We report a novel atomistic model of carbide-derived carbons (CDCs), which are nanoporous carbons with high specific surface areas, synthesis-dependent degrees of graphitization, and well-ordered, tunable porosities. These properties make CDCs viable substrates in several energy-relevant applications, such as gas storage media, electrochemical capacitors, and catalytic supports. These materials are heterogenous, non-ideal structures and include several important parameters that govern their performance. Therefore, a realistic model of the CDC structure is needed in order to study these systems and their nanoscale and macroscale properties with molecular simulation. We report the use of the ReaxFF reactive force field in a quenched molecular dynamics routine to generate atomistic CDC models. The pair distribution function, pore size distribution, and adsorptive properties of this model are reported and corroborated with experimental data. Simulations demonstrate that compressing the system after quenching changes the pore size distribution to better match the experimental target. Ring size distributions of this model demonstrate the prevalence of non-hexagonal carbon rings in CDCs. Furthermore, these effects may contrast the properties of CDCs against those of activated carbons with similar pore size distributions and explain higher energy densities of CDC-based supercapacitors.

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

CLASS Survey Description: Coronal-line Needles in the SDSS Haystack

Coronal lines are a powerful, yet poorly understood, tool to identify and characterize active galactic nuclei. There have been few large-scale surveys of coronal lines in the general galaxy population in the literature so far. Using a novel preselection technique with a flux-to-rms ratio $\mathcal{F}$, followed by Markov Chain Monte Carlo fitting, we searched for the full suite of 20 coronal lines in the optical spectra of almost 1 million galaxies from the Sloan Digital Sky Survey Data Release 8. We present a catalog of the emission-line parameters for the resulting 258 galaxies with detections. The Coronal Line Activity Spectroscopic Survey includes line properties, host-galaxy properties, and selection criteria for all galaxies in which at least one line is detected. This comprehensive study reveals that a significant fraction of coronal-line activity is missed in past surveys based on a more limited set of coronal lines; ~60% of our sample do not display the more widely surveyed [Fe x] λ6374. In addition, we discover a strong correlation between coronal-line and Wide-field Infrared Survey Explorer W2 luminosities, suggesting that the mid-infrared flux can be used to predict coronal-line fluxes. For each line we also provide a confidence level that the line is present, generated by a novel neural network, trained on fully simulated data. We find that after training the network to detect individual lines using 100,000 simulated spectra, we achieve an overall true-positive rate of 75.49% and a false-positive rate of only 3.96%.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

The use of digital thread for reconstruction of local fiber orientation in a compression molded pin bracket via deep learning

A deep convolutional neural network (DCNN) was used for microstructure reconstruction using artificial intelligence (MR-AI) by predicting local average fiber orientation distributions (FOD) in a 3D prepreg platelet molded composite (PPMC) pin bracket. To train the MR-AI model, surface strain fields from residual stresses simulated in PPMC plates were used as the input to the DCNN. A training dataset included PPMC plates with various degrees of global fiber alignment, based on the information obtained from high-fidelity flow simulation of a pin bracket. Further, the MR-AI model was then deployed to analyze FOD in the 3D pin bracket by conducting thermo-elastic residual stress analysis. Initially, the MR-AI model was established entirely on the synthetic simulation data. Then, a μCT scan of a physically molded pin bracket was used to create a finite element model that provided data for additional validation of the DCNN model. For the μCT scan finite element pin bracket the MR-AI model predicted the distribution of fiber orientation tensor components with MAE of 0.10 indicating a global prediction error of 10%. For the flow simulated pin bracket, the MR-AI model predicted the distribution of fiber orientation tensor components with a global prediction error of 11%. The MR-AI model showed the ability to predict regions of varying alignment in the base and flange of the pin bracket. The proposed MR-AI methodology allows for rapid prediction of FOD in geometrically complex parts and offers a promising path to detecting unique fiber orientation states in molded components.

42 ENGINEERING↗
DOE OSTI2026

Photon temporal-mode readout for inference of neutron star merger remnant gravitational waves

Gravitational waves emitted after neutron star binary coalescences and the information they carry about dense matter are a high-priority target for next-generation detectors. Even though such detectors are expected to observe millions of signals, detectable postmerger emission will remain rare. Here, in this work, we explore postmerger detectability and inference through an alternative detector readout scheme for data dominated by quantum-noise, which is the case above 1 kHz; photon-counting. In such a readout, signals and noise become quantized into discrete distributions corresponding to the detection of single photons measured in a chosen basis of modes. Through simulated data, we demonstrate that photon counting can be efficient even for weak signals. We find ∼1 in 100 signals with a postmerger signal-to-noise ratio of 0.2 can result in a single photon and thus be detected. Furthermore, after 2 ×10 4 signals—equivalent to 10 −2 to 1.5 years of observation—photon counting results in a twofold improvement in the measurement of the radius of a 1.6⁢𝑀 ⊙ neutron star. Constraints can be further tightened if the detector classical noise is reduced. Photon counting offers a promising alternative to traditional homodyne readout techniques for extracting information from low signal-to-noise ratio postmerger signals.

gravitational wave detection↗
DOE OSTI2023

KamNet: An integrated spatiotemporal deep neural network for rare event searches in KamLAND-Zen

Rare event searches allow us to search for new physics at energy scales inaccessible with other means by leveraging specialized large-mass detectors. Machine learning provides a new tool to maximize the information provided by these detectors. The information is sparse, which forces these algorithms to start from the lowest level data and exploit all symmetries in the detector to produce results. In this work we present KamNet, which harnesses breakthroughs in geometric deep learning and spatiotemporal data analysis to maximize the physics reach of KamLAND-Zen, a kiloton scale spherical liquid scintillator detector searching for 0⁢νβ⁢β. Using a simplified background model for KamLAND, we show that KamNet outperforms a conventional convolutional neural network (CNN) on benchmarking Monte Carlo simulations with an increasing level of robustness. Using simulated data, we then demonstrate KamNet's ability to increase KamLAND-Zen's sensitivity to 0ν⁢ββ and 2⁢ν⁢β⁢β decay to excited states. A key component of this work is the addition of an attention mechanism to elucidate the underlying physics KamNet is using for the background rejection.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

An adaptive filtered back-projection for photoacoustic image reconstruction

Purpose: The purpose of this study is to develop an improved filtered-back-projection (FBP) algorithm for photoacoustic tomography (PAT), which allows image reconstruction with higher quality compared to images reconstructed through traditional algorithms. Methods: A rigorous expression of a weighting function has been derived directly from a photoacoustic wave equation and used as a ramp filter in Fourier domain. The authors’ new algorithm utilizes this weighting function to precisely calculate each photoacoustic signal’s contribution and then reconstructs the image based on the retarded potential generated from the photoacoustic sources. In addition, an adaptive criterion has been derived for selecting the cutoff frequency of a low pass filter. Two computational phantoms were created to test the algorithm. The first phantom contained five spheres with each sphere having different absorbances. The phantom was used to test the capability for correctly representing both the geometry and the relative absorbed energy in a planar measurement system. The authors also used another phantom containing absorbers of different sizes with overlapping geometry to evaluate the performance of the new method for complicated geometry. In addition, random noise background was added to the simulated data, which were obtained by using an arc-shaped array of 50 evenly distributed transducers that spanned 160° over a circle with a radius of 65 mm. A normalized factor between the neighbored transducers was applied for correcting measurement signals in PAT simulations. The authors assumed that the scanned object was mounted on a holder that rotated over the full 360° and the scans were set to a sampling rate of 20.48 MHz. Results: The authors have obtained reconstructed images of the computerized phantoms by utilizing the new FBP algorithm. From the reconstructed image of the first phantom, one can see that this new approach allows not only obtaining a sharp image but also showing the correct signal strength of the absorbers. The reconstructed image of the second phantom further demonstrates the capability to form clear images of the spheres with sharp borders in the overlapping geometry. The smallest sphere is clearly visible and distinguishable, even though it is surrounded by two big spheres. In addition, image reconstructions were conducted with randomized noise added to the observed signals to mimic realistic experimental conditions. Conclusions: The authors have developed a new FBP algorithm that is capable for reconstructing high quality images with correct relative intensities and sharp borders for PAT. The results demonstrate that the weighting function serves as a precise ramp filter for processing the observed signals in the Fourier domain. In addition, this algorithm allows an adaptive determination of the cutoff frequency for the applied low pass filter.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2016

POLARIMETRIC STUDIES OF MAGNETIC TURBULENCE WITH AN INTERFEROMETER

We study statistical properties of synchrotron polarization emitted from media with magnetohydrodynamic (MHD) turbulence. We use both synthetic and MHD turbulence simulation data for our studies. We obtain the spatial spectrum and its derivative with respect to the wavelength of synchrotron polarization arising from both synchrotron radiation and Faraday rotation fluctuations. In particular, we investigate how the spectrum changes with frequency. We find that our simulations agree with the theoretical predication in Lazarian and Pogosyan. We conclude that the spectrum of synchrotron polarization and its derivative can be very informative tools to obtain detailed information about the statistical properties of MHD turbulence from radio observations of diffuse synchrotron polarization. They are especially useful for recovering the statistics of a turbulent magnetic field as well as the turbulent density of electrons. We also simulate interferometric observations that incorporate the effects of noise and finite telescope beam size, and demonstrate how we recover statistics of underlying MHD turbulence.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

REFLECTION OF PROPAGATING SLOW MAGNETO-ACOUSTIC WAVES IN HOT CORONAL LOOPS: MULTI-INSTRUMENT OBSERVATIONS AND NUMERICAL MODELING

Slow MHD waves are important tools for understanding coronal structures and dynamics. In this paper, we report a number of observations from the X-Ray Telescope (XRT) on board HINODE and Solar Dynamic Observatory /Atmospheric Imaging Assembly (AIA) of reflecting longitudinal waves in hot coronal loops. To our knowledge, this is the first report of this kind as seen from the XRT and simultaneously with the AIA. The wave appears after a micro-flare occurs at one of the footpoints. We estimate the density and temperature of the loop plasma by performing differential emission measure (DEM) analysis on the AIA image sequence. The estimated speed of propagation is comparable to or lower than the local sound speed, suggesting it to be a propagating slow wave. The intensity perturbation amplitude, in every case, falls very rapidly as the perturbation moves along the loop and eventually vanishes after one or more reflections. To check the consistency of such reflection signatures with the obtained loop parameters, we perform a 2.5D MHD simulation, which uses the parameters obtained from our observation as inputs, and perform forward modeling to synthesize AIA 94 Å images. Analyzing the synthesized images, we obtain the same properties of the observables as for the real observation. From the analysis we conclude that a footpoint heating can generate a slow wave which then reflects back and forth in the coronal loop before fading. Our analysis of the simulated data shows that the main agent for this damping is anisotropic thermal conduction.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

How the Galaxy–Halo Connection Depends on Large-scale Environment

We investigate the connection between galaxies, dark matter halos, and their large-scale environments at z = 0 with Illustris TNG300 hydrodynamic simulation data. We predict stellar masses from subhalo properties to test two types of machine learning (ML) models: explainable boosting machines (EBMs) with simple galaxy environment features and E(3)-invariant graph neural networks (GNNs). The best-performing EBM models leverage spherically averaged overdensity features on 3 Mpc scales. Interpretations via SHapley Additive exPlanations also suggest that in the context of the TNG300 galaxy–halo connection, simple spherical overdensity on ∼3 Mpc scales is more important than cosmic web distance features measured using the DisPerSE algorithm. Meanwhile, a GNN with connectivity defined by a fixed linking length, L, outperforms the EBM models by a significant margin. As we increase the linking length scale, GNNs learn important environmental contributions up to the largest scales we probe (L = 10 Mpc). We conclude that 3 Mpc distance scales are most critical for describing the TNG galaxy–halo connection using the spherical overdensity parameterization, but that information on larger scales, which is not captured by simple environmental parameters or cosmic web features, can further augment these models. Our study highlights the benefits of using interpretable ML algorithms to explain models of astrophysical phenomena, and the power of using GNNs to flexibly learn complex relationships directly from data while imposing constraints from physical symmetries.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

A NEW METHOD FOR DERIVING THE STELLAR BIRTH FUNCTION OF RESOLVED STELLAR POPULATIONS

We present a new method for deriving the stellar birth function (SBF) of resolved stellar populations. The SBF (stars born per unit mass, time, and metallicity) is the combination of the initial mass function (IMF), the star formation history (SFH), and the metallicity distribution function (MDF). The framework of our analysis is that of Poisson Point Processes (PPPs), a class of statistical models suitable when dealing with points (stars) in a multidimensional space (the measurement space of multiple photometric bands). The theory of PPPs easily accommodates the modeling of measurement errors as well as that of incompleteness. Our method avoids binning stars in the color–magnitude diagram and uses the whole likelihood function for each data point; combining the individual likelihoods allows the computation of the posterior probability for the population's SBF. Within the proposed framework it is possible to include nuisance parameters, such as distance and extinction, by specifying their prior distributions and marginalizing over them. The aim of this paper is to assess the validity of this new approach under a range of assumptions, using only simulated data. Forthcoming work will show applications to real data. Although it has a broad scope of possible applications, we have developed this method to study multi-band Hubble Space Telescope observations of the Milky Way Bulge. Therefore we will focus on simulations with characteristics similar to those of the Galactic Bulge.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Characterizing in-stream turbulent flow for tidal energy converter siting in Cook Inlet, Alaska

Cook Inlet in Alaska is the most promising location for tidal energy development in the U.S. due to its significant tidal range of approximately 10 meters and high volume flux. The inlet's unique geometry and flow characteristics make it the most energetic tidal stream in the nation, with GW-scale potential energy capacity. With the growing interest in tidal energy converter (TEC) deployment in this area, we implemented a regional-scale, 3D hydrodynamic modeling framework to predict tidal current and turbulence characteristics that can assist TEC designers and project managers. We validated the model results extensively using various datasets collected with bottom-mounted acoustic Doppler current profilers and velocimeters. The comparison between the model outputs and observational data highlighted the effectiveness of the 3D FVCOM model and the Mellor-Yamada Level 2.5 Turbulence Model in accurately assessing macro-scale kinetic energy, turbulence intensity, and the production and dissipation rates at a prospective TEC site. Using two months of model simulation data, we examined the channel cross-section for TEC deployment, focusing on undisturbed power density and macro-scale turbulent properties. Further, our findings indicate that understanding the turbulence characteristics and flow properties can enhance Stage I/II resource characterization by identifying optimal locations for TECs and their layouts within the channel. Furthermore, we demonstrated that TEC designers can utilize macro-scale turbulence data from 3D coastal models as boundary conditions for other turbulence models, allowing for a more detailed resolution of the turbulence structure at TEC siting locations. Ultimately, this work emphasizes the importance of estimating flow and turbulence conditions in energetic systems to understand turbulent sites better and improve resource characterization.

16 TIDAL AND WAVE POWER↗
DOE OSTI2022

An algorithm for detecting and quantifying disturbance and recovery in high-frequency time series

Determining when a disturbance has occurred, its severity, and when the system recovered, is important to numerous questions in the aquatic sciences. This problem can be conceptualized as the timing and degree of perturbation from a typical state, and when the system returns to that typical state. We present an algorithm for detecting disturbance and recovery designed for high-frequency time series, e.g., data produced by automated sampling devices in instrumented buoys and flux towers. The algorithm quantifies differences in the empirical cumulative distribution functions of moving windows over reference and evaluation periods, and is sensitive to changes in the mean, variance, and higher statistical moments. Tests on simulated data show it accurately identifies disturbance and recovery. Three case studies illustrate the application of our algorithm in different empirical settings. A case study on dissolved oxygen in a Florida, USA estuary following a hurricane identified the disturbance and recovery 73 d later. A case study on air temperature and net ecosystem exchange in the Florida everglades identified cold snaps coinciding with periods of reduced carbon uptake. A case study on rotifer abundance following zebra mussel invasion in the Hudson River, NY showed rotifer collapse following invasion and recovery over a decade later. Methods such as ours can improve understanding response to disturbance and facilitate comparative and synthetic study of disturbance impacts across ecosystems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

A learned closure method applied to phase mixing in a turbulent gradient-driven gyrokinetic system in simple geometry

We present a new method for formulating closures that learn from kinetic simulation data. We apply this method to phase mixing in a simple gyrokinetic turbulent system – temperature-gradient-driven turbulence in an unsheared slab. The closure, called the learned multi-mode (LMM) closure, is constructed by, first, extracting an optimal basis from a nonlinear kinetic simulation using singular value decomposition. Subsequent nonlinear fluid simulations are projected onto this basis and the results are used to formulate the closure. We compare the closure with other closures schemes over a broad range of the relevant two-dimensional parameter space (collisionality and gradient drive). We find that the turbulent kinetic system produces phase-mixing rates much lower than the linear expectations, which the LMM closure is capable of capturing. We also compare radial heat fluxes. A Hammett–Perkins closure, generalized to include collisional effects, is quite successful throughout the parameter space, producing ${\sim }14\,\%$ root-mean-square (r.m.s.) error. The LMM closure is also very effective: when trained at three (two) points (in a 35 point parameter grid), the LMM closure produces $8\,\%$ ( $12\,\%$ ) r.m.s. errors. The LMM procedure can be readily generalized to other closure problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗