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At least 1,531 records · Page 85

Accelerated Monte Carlo Fission Source Convergence with Fission Matrix and Kernel Density Estimators

Accurate solution of the k-eigenvalue form of the Boltzmann radiation transport equation is required in many application areas, including nuclear reactor analysis and criticality safety. Monte Carlo calculations are free of the discretization errors inherent to deterministic methods and therefore offer the most accurate solutions. However, converging the fission source can be difficult for many problems, resulting in either a substantial computational overhead or potential inaccuracies that negate many of the benefits of using Monte Carlo methods. Difficulty in converging the fission source occurs for two distinct reasons. The first is the existence of a high dominance ratio in the problem (i.e. the largest and second largest eigenvalues have approximately the same magnitude). The second difficulty arises due to undersampling of the fission source because an insufficient number of particle histories are simulated. The first difficulty is shared by deterministic solvers when using power iteration, while the second difficulty is unique to Monte Carlo solvers. In practice, both difficulties may be present in the same problem, compounding the difficulty in achieving a converged distribution. In this paper, we consider a new approach to accelerate the convergence of the fission source based on combining the use of fission matrix methods with kernel density estimators (KDEs). It has been observed that deterministic fission matrix methods show the potential to accelerate the convergence of the fission source in Monte Carlo criticality calculations but may introduce significant additional noise for difficult problems. In this paper, we have demonstrated the use of a KDE approach in combination with the fission matrix acceleration. Although the addition of the KDE initially slows the convergence of the fission matrix acceleration, it decreases the magnitude of the noise while still offering significantly improved convergence relative to analog Monte Carlo. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

TU-H-207A-08: Estimating Radiation Dose From Low-Dose Lung Cancer Screening CT Exams Using Tube Current Modulation

Purpose: The purpose of this work is to estimate effective and lung doses from a low-dose lung cancer screening CT protocol using Tube Current Modulation (TCM) across patient models of different sizes. Methods: Monte Carlo simulation methods were used to estimate effective and lung doses from a low-dose lung cancer screening protocol for a 64-slice CT (Sensation 64, Siemens Healthcare) that used TCM. Scanning parameters were from the AAPM protocols. Ten GSF voxelized patient models were used and had all radiosensitive organs identified to facilitate estimating both organ and effective doses. Predicted TCM schemes for each patient model were generated using a validated method wherein tissue attenuation characteristics and scanner limitations were used to determine the TCM output as a function of table position and source angle. The water equivalent diameter (WED) was determined by estimating the attenuation at the center of the scan volume for each patient model. Monte Carlo simulations were performed using the unique TCM scheme for each patient model. Lung doses were tallied and effective doses were estimated using ICRP 103 tissue weighting factors. Effective and lung dose values were normalized by scanspecific 32 cm CTDIvol values based upon the average tube current across the entire simulated scan. Absolute and normalized doses were reported as a function of WED for each patient. Results: For all ten patients modeled, the effective dose using TCM protocols was below 1.5 mSv. Smaller sized patient models experienced lower absolute doses compared to larger sized patients. Normalized effective and lung doses showed some dependence on patient size (R2 = 0.77 and 0.78, respectively). Conclusion: Effective doses for a low-dose lung screening protocol using TCM were below 1.5 mSv for all patient models used in this study. Institutional research agreement, Siemens Healthcare; Past recipient, research grant support, Siemens Healthcare; Consultant, Toshiba America Medical Systems; Consultant, Samsung Electronics.

60 APPLIED LIFE SCIENCES↗

E-Area LLWF Vadose Zone Model: Probabilistic Model for Estimating Subsided-Area Infiltration Rates

A probabilistic model employing a Monte Carlo sampling technique was developed in Python to generate statistical distributions of the upslope-intact-area to subsided-area ratio (Area UAi /Area SAi ) for closure cap subsidence scenarios that differ in assumed percent subsidence and the total number of intact plus subsided compartments. The plan is to use this model as a component in the probabilistic system model for the E-Area Performance Assessment (PA), contributing uncertainty in infiltration estimates.

97 MATHEMATICS AND COMPUTING↗

MO-FG-CAMPUS-IeP2-02: Effects of Metal On CT Size-Specific Dose Estimates

Purpose: To evaluate the accuracy of size-specific dose estimates (SSDE) in CT in the presence of simulated metal prostheses. Methods: Radiation dose in tissue (f-factor = 0.94) was measured at various chamber positions in a conventional nested CTDI phantom with nominal 0.5 inch metal rods inserted to simulate the presence of prosthetic implant(s). An average weighted tissue dose (AWTD) was calculated in a manner similar to CTDIw. Subsequent scans were performed with varying phantom diameter, number of metal rods and type of metal. The scan acquisition parameters were fixed for all such measurements (i.e. CTDIvol was constant). Axial CT images reconstructed both with and without a metal artifact reduction algorithm (SEMAR) were used to calculate the water-equivalent diameter (Dw) per AAPM TG Report 220. The Dw values were subsequently used to determine the SSDE from the known CTDIvol. In addition SSDE was also calculated from the effective diameter per AAPM TG Report 204. Accuracy of the calculated SSDE values were assessed by comparing to the AWTD measurements. Results: In the 32-cm diameter phantom the SSDE calculations from Dw (TG-220) were within ±1% of the AWTD measurements regardless of type of metal and number of metal rods while SSDE calculated from effective diameter (TG-204) overestimated the AWTD by 7–10%. In the 16-cm diameter phantom the SSDE calculations from Dw (TG-220) were within ±4% of the AWTD measurement. The Dw calculations used to determine SSDE varied by less than 0.2% between the images reconstructed with and without the metal artifact reduction algorithm. Conclusion: The TG-220 SSDE method can provide an accurate estimation of tissue dose in the presence of metal while TG-204 SSDE method overestimates the dose. The determination of Dw is independent of reconstruction algorithm.

60 APPLIED LIFE SCIENCES↗

Measurement of spleen fat on MRI-proton density fat fraction arises from reconstruction of noise

Purpose: This study compares splenic proton density fat fraction (PDFF) measured using confounder-corrected chemical shift-encoded (CSE)-MRI to magnetic resonance spectroscopy (MRS) in human patients at 3T. Methods: This was a prospectively designed ancillary study to various previously described single-center studies performed in adults and children with known or suspected nonalcoholic fatty liver disease. Patients underwent magnitude-based MRI (MRI-M), complex-based MRI (MRI-C), high signal-to-noise variants (Hi-SNR MRI-M and Hi-SNR MRI-C), and MRS at 3T for spleen PDFF estimation. PDFF from CSE-MRI methods were compared to MRS-PDFF using Wilcoxon signed-rank tests. Demographics were summarized descriptively. Spearman’s rank correlations were computed pairwise between CSE-MRI methods. Individual patient measurements were plotted for qualitative assessment. A significance level of 0.05 was used. Results: Forty-seven patients (20 female, 27 male) including 12 adults (median 55 years old) and 35 children (median 12 years old). Median PDFF estimated by MRS, MRI-M, Hi-SNR MRI-M, MRI-C, and Hi-SNR MRI-C was 1.0, 2.3, 1.9, 2.2, and 2.0%. The four CSE-MRI methods estimated statistically significant higher spleen PDFF values compared to MRS (p < 0.0001 for all). Pairwise associations in spleen PDFF values measured by different CSE-MRI methods were weak, with the highest Spearman’s rank correlations being 0.295 between MRI-M and Hi-SNR MRI-M; none were significant after correction for multiple comparisons. No qualitative relationship was observed between PDFF measurements among the various methods. Conclusion: Overestimation of PDFF by CSE-MRI compared to MRS and poor agreement between related CSE-MRI methods suggest that non-zero PDFF values in human spleen are artifactual.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

A Deep Neural Network for Simultaneous Estimation of b Jet Energy and Resolution

We describe a method to obtain point and dispersion estimates for the energies of jets arising from b quarks produced in proton–proton collisions at an energy of $\sqrt{s}=13\,\text {TeV} $ at the CERN LHC. The algorithm is trained on a large sample of simulated b jets and validated on data recorded by the CMS detector in 2017 corresponding to an integrated luminosity of 41 $\,\text {fb}^{-1}$. A multivariate regression algorithm based on a deep feed-forward neural network employs jet composition and shape information, and the properties of reconstructed secondary vertices associated with the jet. The results of the algorithm are used to improve the sensitivity of analyses that make use of b jets in the final state, such as the observation of Higgs boson decay to $\hbox {b}\bar{\hbox {b}}$.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Parallel multiple-chain DRAM MCMC for large-scale geosteering inversion and uncertainty quantification

Geosteering is the proactive control of a wellbore placement based on the downhole measurements, aiming at maximizing economic production from the well. We report the recent development of azimuthal resistivity logging-whiledrilling (LWD) tools have a much larger depth of detection, thus sets higher demands for geosteering inversion as more unknown parameters need to be taken into account in the earth model to be inverted. For complicated nonlinear problems, traditional deterministic inversion methods are more likely to be trapped near local optima. In general, Markov chain Monte Carlo (MCMC) inversion methods are more capable of finding the global optimal solution and providing additional uncertainty analyses by sampling from the target distribution. However, MCMC methods usually have the problem of slow convergence. Even though optimization methods like delayed rejection (DR) and adaptive Metropolis (AM) were proposed to speed up the convergence, using MCMC methods to solve geosteering inversion problems may still incur unacceptable time cost. To reduce the sampling cost of MCMC methods, we use parallel multiple-chain DRAM MCMC methods to solve geosteering inverse problems and estimate the corresponding uncertainty. A clustering method, density-based spatial clustering of applications with noise (DBSCAN), is applied to select the best solution among many results. Lastly, the simulation results show that running many relatively short MCMC chains for one problem can obtain a similar result as running a long single chain. Besides, avoiding communications between multiple Markov chains during the sampling process yields almost linear scalability.

97 MATHEMATICS AND COMPUTING↗

Extreme-Scale Bayesian Inference for Uncertainty Quantification of Complex Simulations

Uncertainty quantification (UQ)—that is, quantifying uncertainties in complex mathematical models and their large-scale computational implementations—is widely viewed as one of the outstanding challenges facing the field of CS&E over the coming decade. The EUREKA project set to address the most difficult class of UQ problems: those for which both the underlying PDE model as well as the uncertain parameters are of extreme scale. In the project we worked on these extreme-scale challenges in the following four areas: 1. Scalable parallel algorithms for sampling and characterizing the posterior distribution that exploit the structure of the underlying PDEs and parameter-to-observable map. These include structure-exploiting versions of the randomized maximum likelihood method, which aims to overcome the intractability of employing conventional MCMC methods for solving extreme-scale Bayesian inversion problems by appealing to and adapting ideas from large-scale PDE-constrained optimization, which have been very successful at exploring high-dimensional spaces. 2. Scalable parallel algorithms for construction of prior and likelihood functions based on learning methods and non-parametric density estimation. Constructing problem-specific priors remains a critical challenge in Bayesian inference, and more so in high dimensions. Another challenge is construction of likelihood functions that capture unmodeled couplings between observations and parameters. We will create parallel algorithms for non-parametric density estimation using high dimensional N-body methods and combine them with supervised learning techniques for the construction of priors and likelihood functions. 3. Bayesian inadequacy models, which augment physics models with stochastic models that represent their imperfections. The success of the Bayesian inference framework depends on the ability to represent the uncertainty due to imperfections of the mathematical model of the phenomena of interest. This is a central challenge in UQ, especially for large-scale models. We propose to develop the mathematical tools to address these challenges in the context of extreme-scale problems. 4. Parallel scalable algorithms for Bayesian optimal experimental design (OED). Bayesian inversion yields quantified uncertainties in the model parameters, which can be propagated forward through the model to yield uncertainty in outputs of interest. This opens the way for designing new experiments to reduce the uncertainties in the model parameters and model predictions. Such experimental design problems have been intractable for large-scale problems using conventional methods; we will create OED algorithms that exploit the structure of the PDE model and the parameter-to-output map to overcome these challenges. Parallel algorithms for these four problems were created, analyzed, prototyped, implemented, tuned, and scaled up for leading-edge supercomputers, including UT-Austin’s own 10 petaflops Stampede system, ANL’s Mira system, and ORNL’s Titan system. While our focus is on fundamental mathematical/computational methods and algorithms, we will assess our methods on model problems derived from several DOE mission applications, including multiscale mechanics and ice sheet dynamics.

97 MATHEMATICS AND COMPUTING↗

A Decade of Sporadic Meteoroid Mass Distribution Indices in the Southern Hemisphere Derived from SAAMER’s Meteor Observations

We present determinations of the meteoroid differential mass index, s, using over a decade of meteor observations from the Southern Argentina Agile MEteor Radar (SAAMER). For this, we employ an autonomous statistical technique to determine this parameter from the measured radar echo amplitudes. Unlike previous studies, we examine the role of the system noise in the determination of this parameter and found that if not taken into account appropriately, the results can yield significant over estimations of the mass index. In general we found that a value of s = 2.0 represents SAAMER’s results in general agreement with recent studies performed in the northern hemisphere. We explore both the index interannual and seasonal variability and, unlike previous studies, we found them to be constant, except during the presence of the Southern δ Aquariids meteor shower which is so strong that it dominates the meteor counts when present. Our study suggests that using the maximum echo amplitude for these studies is not ideal as it can be biased by many factors which make the inaccuracies larger than the precision estimated by the fitting routine. A method that results in a more direct estimate of the electron line density would be required which takes into account range, gain pattern, system noise, etc.

79 ASTRONOMY AND ASTROPHYSICS↗

Dynamic estimator for determining operating conditions in an internal combustion engine

Methods and systems are provided for estimating engine performance information for a combustion cycle of an internal combustion engine. Estimated performance information for a previous combustion cycle is retrieved from memory. The estimated performance information includes an estimated value of at least one engine performance variable. Actuator settings applied to engine actuators are also received. The performance information for the current combustion cycle is then estimated based, at least in part, on the estimated performance information for the previous combustion cycle and the actuator settings applied during the previous combustion cycle. The estimated performance information for the current combustion cycle is then stored to the memory to be used in estimating performance information for a subsequent combustion cycle.

42 ENGINEERING↗

A meshless stochastic method for Poisson–Nernst–Planck equations

A plethora of biological, physical, and chemical phenomena involve transport of charged particles (ions). Its continuum-scale description relies on the Poisson–Nernst–Planck (PNP) system, which encapsulates the conservation of mass and charge. The numerical solution of these coupled partial differential equations is challenging and suffers from both the curse of dimensionality and difficulty in efficiently parallelizing. We present a novel particle-based framework to solve the full PNP system by simulating a drift–diffusion process with time- and space-varying drift. We leverage Green’s functions, kernel-independent fast multipole methods, and kernel density estimation to solve the PNP system in a meshless manner, capable of handling discontinuous initial states. The method is embarrassingly parallel, and the computational cost scales linearly with the number of particles and dimension. We use a series of numerical experiments to demonstrate both the method’s convergence with respect to the number of particles and computational cost vis-à-vis a traditional partial differential equation solver.

Chemistry↗

GMLS-Nets: A Framework for Learning from Unstructured Data

Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gaining benefits from weight sharing and invariances. We generalize CNNs by introducing methods for data on unstructured point clouds based on Generalized Moving Least Squares (GMLS). GMLS is a non-parametric technique for estimating linear bounded functionals from scattered data, and has recently been used in the literature for solving partial differential equations. By parameterizing the GMLS estimator, we obtain learning methods for operators with unstructured stencils. In GMLS-Nets the necessary calculations are local, readily parallelizable, and the estimator is supported by a rigorous approximation theory. We show how the framework may be used for unstructured physical data sets to perform functional regression to identify associated differential operators and to regress quantities of interest. The results suggest the architectures to be an attractive foundation for data-driven model development in scientific machine learning applications

97 MATHEMATICS AND COMPUTING↗

A semiparametric latent factor model for large scale temporal data with heteroscedasticity

Large scale temporal data have flourished in a vast array of applications, and their sophisticated structures, especially the heteroscedasticity among subjects with inter- and intra-temporal dependence, have fueled a great demand for new statistical models. In this paper, with covariate information, we consider a flexible model for large scale temporal data with subject-specific heteroscedasticity. Formally, the model employs latent semiparametric factors to simultaneously account for the subject-specific heteroscedasticity and the contemporaneous and/or serial correlations. The subject-specific heteroscedasticity is modeled as the product of the unobserved factor process and subject’s covariate effect, which is further characterized via additive models. For estimation, we propose a two-step procedure. First, the latent factor process and nonparametric loading are recovered through projection-based methods, and following, we estimate the regression components by approaches motivated from the generalized least squares. By scrupulously examining the non-asymptotic rates for recovering the factor process and its loading, we show the consistency and efficiency of estimated regression coefficients in the absence of prior knowledge of latent factor process and subject’s covariate effect. Here, the statistical guarantees remain valid even for finite time points that makes our method particularly appealing when the subjects significantly outnumber the observation time points. Using comprehensive simulations, we demonstrate the finite sample performance of our method, which corroborates the theoretical findings. Finally, we apply our method to a data set of air quality and energy consumption collected at 129 monitoring sites in the United States in 2015.

97 MATHEMATICS AND COMPUTING↗

Estimators and Fusers for Fiber Delay Estimation Using Environmental Measurements

The properties of deployed network fiber are affected by environmental factors due to their exposure to the elements. Particularly for quantum networks, the resultant delay variations may have significant impacts due to the extreme sensitivity of synchronization, coincidence counting, and other critical operations. In this paper, the delays of 15 km aerial-inground fiber connections are measured, and effects due to temperature, humidity and wind speed are analyzed over multiple periods spanning four seasons of a year. Machine learning methods are first utilized to reveal surprisingly pronounced effects of humidity on the delay, in addition to the expected temperature and its seasonal variations. Estimator and fusion methods are developed to estimate the delay using temperature, humidity and wind speed measurements, by utilizing smooth Gaussian Process Regression (GPR) and nonsmooth Ensemble of Trees (EOT) methods. Measurements from winter and summer periods are temporally fused using twelve different methods, and eight methods provide estimates for the delay throughout the year with median test errors under 1.28%. The results reveal distinct temperature-humidity trends across the seasons, and the ability of estimator and temporal fusion methods to exploit them for estimating the delay. These results constitute a case study of machine learning analytical results, wherein generalization equations explain the performance of various estimator and fuser methods.

Rao, Nageswara [ORNL] (ORCID:0000000234085941)↗

A genetic meta-algorithm-assisted inversion approach: hydrogeological study for the determination of volumetric rock properties and matrix and fluid parameters in unsaturated formations

An evolutionary inversion approach is suggested for the interpretation of nuclear and resistivity logs measured by direct-push tools in shallow unsaturated sediments. The efficiency of formation evaluation is improved by estimating simultaneously (1) the petrophysical properties that vary rapidly along a drill hole with depth and (2) the zone parameters that can be treated as constant, in one inversion procedure. In the workflow, the fractional volumes of water, air, matrix and clay are estimated in adjacent depths by linearized inversion, whereas the clay and matrix properties are updated using a float-encoded genetic meta-algorithm. The proposed inversion method provides an objective estimate of the zone parameters that appear in the tool response equations applied to solve the forward problem, which can significantly increase the reliability of the petrophysical model as opposed to setting these parameters arbitrarily. The global optimization meta-algorithm not only assures the best fit between the measured and calculated data but also gives a reliable solution, practically independent of the initial model, as laboratory data are unnecessary in the inversion procedure. The feasibility test uses engineering geophysical sounding logs observed in an unsaturated loessy-sandy formation in Hungary. The multi-borehole extension of the inversion technique is developed to determine the petrophysical properties and their estimation errors along a profile of drill holes. The genetic meta-algorithmic inversion method is recommended for hydrogeophysical logging applications of various kinds to automatically extract the volumetric ratios of rock and fluid constituents as well as the most important zone parameters in a reliable inversion procedure.

58 GEOSCIENCES↗

Dark Energy Survey Year 3 results: calibration of lens sample redshift distributions using clustering redshifts with BOSS/eBOSS

ABSTRACT We present clustering redshift measurements for Dark Energy Survey (DES) lens sample galaxies used in weak gravitational lensing and galaxy clustering studies. To perform these measurements, we cross-correlate with spectroscopic galaxies from the Baryon Acoustic Oscillation Survey (BOSS) and its extension, eBOSS. We validate our methodology in simulations, including a new technique to calibrate systematic errors that result from the galaxy clustering bias, and we find that our method is generally unbiased in calibrating the mean redshift. We apply our method to the data, and estimate the redshift distribution for 11 different photometrically selected bins. We find general agreement between clustering redshift and photometric redshift estimates, with differences on the inferred mean redshift found to be below |Δz| = 0.01 in most of the bins. We also test a method to calibrate a width parameter for redshift distributions, which we found necessary to use for some of our samples. Our typical uncertainties on the mean redshift ranged from 0.003 to 0.008, while our uncertainties on the width ranged from 4 to 9 per cent. We discuss how these results calibrate the photometric redshift distributions used in companion papers for DES Year 3 results.

79 ASTRONOMY AND ASTROPHYSICS↗

Lifetime Extension Report: Progress on the SAVY-4000 Lifetime Extension Program

The 3-year accelerated aging study of the SAVY-4000 O-ring shows very little evidence of significant degradation to samples subjected to aggressive elevated temperature and radiation conditions. Whole container thermal aging studies followed by helium leakage testing and compression set measurements were used to establish an estimate for a failure criterion for O-ring compression set of ≥65 %. The whole container aging studies further show that the air flow and efficiency functions of the filter do not degrade significantly after thermal aging. However, the degradation of the water-resistant function leads to water penetration failure after four months at 210°C, but does not cause failure after 10 months at 120°C (130°C is the maximum operating temperature for the PTFE membrane). The thermal aging data for O-ring compression set do not meet the assumptions of standard time-temperature superposition analysis for accelerated aging studies. Instead, the data suggest that multiple degradation mechanisms are operative, with a reversible mechanism operative at low aging temperatures and an irreversible mechanism dominating at high aging temperatures. To distinguish between these mechanisms, we have measured compression set after allowing the sample to physically relax, thereby minimizing the effect of the reversible mechanism. The resulting data were analyzed using two distinct mathematical methods to obtain a lifetime estimate based on chemical degradation alone. Both methods support a lifetime estimate of greater than 150 years at 80°C. Although the role of the reversible mechanism is not fully understood, it is clear that the contribution to the total compression set is small in comparison to that due to the chemical degradation mechanism. To better understand the chemical degradation mechanism, thermally aged O-ring samples have been characterized by Fourier Transform Infrared (FTIR), Electron Paramagnetic Resonance (EPR), Gel Permeation Chromatography (GPC), and Differential Scanning Calorimetry (DSC). These experiments detect no significant O-ring degradation below 80°C. Furthermore, durometer measurements indicate that there is no significant change in O-ring hardness at all aging conditions examined. Therefore, our current conservative lifetime estimate for the O-ring and the filter is 10 years at 80°C. In FY17, we will continue to probe the chemical degradation mechanism using oxygen consumption measurements under accelerated aging conditions to reveal temperatures at which oxidation occurs, along with any differences in oxidation rate at the low vs. high aging temperatures. We will also refine the failure criteria and finalize the radiation/thermal synergistic studies to determine a final design lifetime.

42 ENGINEERING↗

ASTEROSEISMIC-BASED ESTIMATION OF THE SURFACE GRAVITY FOR THE LAMOST GIANT STARS

Asteroseismology is one of the most accurate approaches to estimate the surface gravity of a star. However, most of the data from the current spectroscopic surveys do not have asteroseismic measurements, which is very expensive and time consuming. In order to improve the spectroscopic surface gravity estimates for a large amount of survey data with the help of the small subset of the data with seismic measurements, we set up a support vector regression (SVR) model for the estimation of the surface gravity supervised by 1374 Large Sky Area Multi-object Fiber Spectroscopic Telescope (LAMOST) giant stars with Kepler seismic surface gravity. The new approach can reduce the uncertainty of the estimates down to about 0.1 dex, which is better than the LAMOST pipeline by at least a factor of 2, for the spectra with signal-to-noise ratio higher than 20. Compared with the log g estimated from the LAMOST pipeline, the revised log g values provide a significantly improved match to the expected distribution of red clump and red giant branch stars from stellar isochrones. Moreover, even the red bump stars, which extend to only about 0.1 dex in log g, can be discriminated from the new estimated surface gravity. The method is then applied to about 350,000 LAMOST metal-rich giant stars to provide improved surface gravity estimates. In general, the uncertainty of the distance estimate based on the SVR surface gravity can be reduced to about 12% for the LAMOST data.

79 ASTRONOMY AND ASTROPHYSICS↗