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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

PyJMAK: An Open-Source Python Toolkit for Modeling Solid-State Metallurgical Phase Transformations

Accurate prediction of metallurgical phase transformations is an essential basis for autonomous optimization and rapid part qualification. Several methods can be used to estimate the evolution of phase fractions such as JMAK kinetics-based models, phase-field models, thermodynamic models, and data-driven machine learning models. Thermodynamic and phase-field-based methodologies solve multiphysics equations requiring numerous calibration parameters and significant computational resources. As a result, the computation domain is limited to a point or on order of micron-meters. The data-driven models rely on large datasets from experiments and simulations. While the JMAK model only provides information about phase fraction evolution, it can predict this evolution in near real-time using thermal history and thermodynamic data without restriction on the domain. JMAK models have been popularly used by researchers to model phase transformations occuring during additive manufacturing or over arbitrary temperature profiles. Commercial proprietary software such as Abaqus and Ansys or closed-source in-house implementations offer the ability to model JMAK based kinetics to predict phase transformation. However, these software packages are not open-source or freely available for use and development in conjunction with manufacturing machines, sensors, and machine learning algorithms. In addition, the use of the model is restricted by a license token. In contrast, given temperature profiles at multiple points in the domain, this Python-based PyJMAK model can compute phase evolution in parallel due to its stand-alone modular, voxel-based structure, and it can be executed on high-performance computing resources without any license restrictions.

Prabhune, Bhagya [Oak Ridge National Laboratory (O↗
DOE OSTI2021

Measurements of the E-mode polarization and temperature-E-mode correlation of the CMB from SPT-3G 2018 data

We present measurements of the E -mode ( E E ) polarization power spectrum and temperature- E -mode ( T E ) cross-power spectrum of the cosmic microwave background using data collected by SPT-3G, the latest instrument installed on the South Pole Telescope. This analysis uses observations of a 1500 deg 2 region at 95, 150, and 220 GHz taken over a four-month period in 2018. We report binned values of the E E and T E power spectra over the angular multipole range 300 ≤ ℓ < 3000 , using the multifrequency data to construct six semi-independent estimates of each power spectrum and their minimum-variance combination. These measurements improve upon the previous results of SPTpol across the multipole ranges 300 ≤ ℓ ≤ 1400 for E E and 300 ≤ ℓ ≤ 1700 for T E , resulting in constraints on cosmological parameters comparable to those from other current leading ground-based experiments. We find that the SPT-3G data set is well fit by a Λ CDM cosmological model with parameter constraints consistent with those from Planck and SPTpol data. From SPT-3G data alone, we find H 0 = 68.8 ± 1.5 km s - 1 Mpc - 1 and σ 8 = 0.789 ± 0.016 , with a gravitational lensing amplitude consistent with the Λ CDM prediction ( A L = 0.98 ± 0.12 ). We combine the SPT-3G and the Planck data sets and obtain joint constraints on the Λ CDM model. The volume of the 68% confidence region in six-dimensional Λ CDM parameter space is reduced by a factor of 1.5 compared to Planck-only constraints, with no significant shifts in central values. We note that the results presented here are obtained from data collected during just half of a typical observing season with only part of the focal plane operable, and that the active detector count has since nearly doubled for observations made with SPT-3G after 2018.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Concordance and discordance in cosmology

The success of present and future cosmological studies is tied to the ability to detect discrepancies in complex data sets within the framework of a cosmological model. Tensions caused by the presence of unknown systematic effects need to be isolated and corrected to increase the overall accuracy of parameter constraints, while discrepancies due to new physical phenomena need to be promptly identified. We develop a full set of estimators of internal and mutual agreement and disagreement, whose strengths complement each other. These estimators take into account the effect of prior information and compute the statistical significance of both tensions and confirmatory biases. The estimators that we present optimally weight all parameter space directions that are either fully constrained by the data or the prior, allowing for complete and fair degree of freedom counting. We apply them to a wide range of state-of-the-art cosmological probes and show that these estimators can be easily used, regardless of model and data complexity. Here, we derive a series of results that show that discrepancies indeed arise within the standard ΛCDM model. Several of them exceed the probability threshold of 95% and deserve a dedicated effort to understand their origin.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Development of Thermal Scattering Law and Cross Sections of Hydrogen in Paraffin Wax

Paraffin wax is frequently used as a neutron moderator and shielding material. The main component of paraffin wax is straight-chain alkanes (n-alkanes). The deposition of paraffin wax is primarily attributed to the crystallization of n-alkanes. It is important to gain a deeper understanding of the mechanisms underlying the behavior of paraffin wax, which would impact the thermal scattering Law (TSL) and cross sections and affect the analysis of neutronic and critical systems. In this work, a classical molecular dynamics (CMD) simulation model was used in LAMMPS to create the TSL and cross sections at room temperature and pressure. To generate the required velocity autocorrelation functions (VACF), previously published data were used to validate the approach and models by comparing them with key model parameters. The phonon density of state (DOS) was calculated using Fourier transformation of the normalized VACF. This DOS was used as the primary input to estimate the TSL (S($a$, $β$)) and cross sections of hydrogen in paraffin wax. The TSL and cross sections of hydrogen were estimated using the Full Law Analysis Scattering System Hub (FLASSH) code. The cross section of hydrogen in paraffin wax is consistent with other hydrocarbon materials such as polyethylene with deviations due to structure in the lowest energy region.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Sorption testing and generalized composite surface complexation models for determining uranium sorption parameters at a proposed in-situ recovery site

Solid-phase iron concentrations and generalized composite surface complexation models were used to evaluate procedures in determining uranium sorption on oxidized aquifer material at a proposed U in situ recovery (ISR) site. At the proposed Dewey Burdock ISR site in South Dakota, USA, oxidized aquifer material occurs downgradient of the U ore zones. Solid-phase Fe concentrations did not explain our batch sorption test results,though total extracted Fe appeared to be positively correlated with overall measured U sorption. Batch sorption test results were used to develop generalized composite surface complexation models that incorporated the full genericsorption potential of each sample, without detailed mineralogiccharacterization. The resultant models provide U sorption parameters (site densities and equilibrium constants) for reactive transport modeling. The generalized composite surface complexation sorption models were calibrated to batch sorption data from three oxidized core samples using inverse modeling, and gave larger sorption parameters than just U sorption on the measured solidphase Fe. These larger sorption parameters can significantly influence reactive transport modeling, potentially increasing U attenuation. Because of the limited number of calibration points, inverse modeling required the reduction of estimated parameters by fixing two parameters. The best-fit models used fixed values for equilibrium constants, with the sorption site densities being estimated by the inversion process. While these inverse routines did provide best-fit sorption parameters, local minima and correlated parameters might require further evaluation. Despite our limited number of proxy samples, the procedures presented provide a valuable methodology to consider for sites where metal sorption parameters are required. Furthermore, these sorption parameters can be used in reactive transport modeling to assess downgradient metal attenuation, especially when no other calibration data are available, such as at proposed U ISR sites.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Inverse regression for ridge recovery: a data-driven approach for parameter reduction in computer experiments

Parameter reduction can enable otherwise infeasible design and uncertainty studies with modern computational science models that contain several input parameters. In statistical regression, techniques for sufficient dimension reduction (SDR) use data to reduce the predictor dimension of a regression problem. A computational scientist hoping to use SDR for parameter reduction encounters a problem: a computer prediction is best represented by a deterministic function of the inputs, so data comprised of computer simulation queries fail to satisfy the SDR assumptions. To address this problem, here we interpret SDR methods sliced inverse regression (SIR) and sliced average variance estimation (SAVE) as estimating the directions of a ridge function, which is a composition of a low-dimensional linear transformation with a nonlinear function. Within this interpretation, SIR and SAVE estimate matrices of integrals whose column spaces are contained in the ridge directions’ span; we analyze and numerically verify convergence of these column spaces as the number of computer model queries increases. Moreover, we show example functions that are not ridge functions but whose inverse conditional moment matrices are low-rank. Consequently, the computational scientist should beware when using SIR and SAVE for parameter reduction, since SIR and SAVE may mistakenly suggest that truly important directions are unimportant.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Improving Subsurface Stress Characterization for Carbon Dioxide Storage Projects by Incorporating Machine Learning Techniques

The overall objective of this project is to develop a framework for reliable characterization and prediction of the state of stress in the overburden and underburden (including the basement) in CO 2 storage reservoirs using machine learning and integrated geomechanics and geophysical methods. Specifically, we propose to develop workflow encompassing of technologies and/or methods to predict stress and pressure changes due to CO 2 injection in an active tertiary recovery site and their impacts on subtle fault activation, fractures and occurrence of microseismic events and compare responses to field observations. In this project, we anticipate using dataset from the Farnsworth field Unit (FWU) which is operated by Purdure Petroleum. A novel elastic-waveform VSP inversion technique will be used to estimate high-resolution spatial and temporal changes of elastic moduli in CO 2 storage reservoirs, which will be combined with velocity-stress relationship derived from laboratory tests to obtain subsurface pressure and stress. Clustered microseismic data will be jointly inverted for improved focal mechanisms. Least-squares reverse-time migration of microseismic waveform data will be performed to directly image fracture/fault zones. Additionally, a deep neural network machine learning technique with convolutional and recurrent layers will be used for learning the spectro-temporal structures in microseismic waveforms. The results of this geotechnical data analysis will be integrated to develop a high-resolution 3D mechanical earth model extending from the overburden sealing formations to the underburden including the basement. Mechanical properties will be derived through integration of mechanical logs, tests, available results from chemo-mechanical laboratory tests, and elastic inversion of seismic data using a combination of Bayesian and stochastic methods as well as machine learning technique. Failure features (faults/fractures) will be represented and/or modeled based on seismic and core data analysis. A transient hydrodynamic-geomechanical model will be developed through coupling with the calibrated FWU reservoir simulation model. The full physics coupled model will be used to train a reduced order proxy model using machine learning algorithm for estimating stress which will then be used with appropriate constitutive relationships and forward seismological models to simulate pressure changes and induced microseismicity. An advanced optimization framework will be developed to perform a history match to minimize error between field observations and simulated. The history matched proxy model will be verified against the full-physics equivalent. The field observations that will be used in the coupled model calibration process include pressure/stress inverted from VSP, moment magnitude from microseismic analysis, real time downhole pressure measurements, production and injection data. Parameter sensitivity and uncertainty analysis will be performed to characterize the impact of model parameter uncertainty on stress estimates. The proposed project will have significant impact on future field implementation of the proposed technology. Because the project field site is an ongoing CO 2 EOR development, the value of the new technology will be demonstrated in an operational context and evaluated as a viable risk mitigation strategy. Cost/benefit will be evaluated together with the various commercial incentives for CO 2 sequestration available to oil and gas operators. The extensive available dataset and ongoing data acquisition under the SWP Phase III work plan provides flexibility for investigation of multiple approaches and reduces technical risk.

58 GEOSCIENCES↗
DOE OSTI2017

astroABC : An Approximate Bayesian Computation Sequential Monte Carlo sampler for cosmological parameter estimation

Given the complexity of modern cosmological parameter inference where we arefaced with non-Gaussian data and noise, correlated systematics and multi-probecorrelated data sets, the Approximate Bayesian Computation (ABC) method is apromising alternative to traditional Markov Chain Monte Carlo approaches in thecase where the Likelihood is intractable or unknown. The ABC method is called"Likelihood free" as it avoids explicit evaluation of the Likelihood by using aforward model simulation of the data which can include systematics. Weintroduce astroABC, an open source ABC Sequential Monte Carlo (SMC) sampler forparameter estimation. A key challenge in astrophysics is the efficient use oflarge multi-probe datasets to constrain high dimensional, possibly correlatedparameter spaces. With this in mind astroABC allows for massive parallelizationusing MPI, a framework that handles spawning of jobs across multiple nodes. Akey new feature of astroABC is the ability to create MPI groups with differentcommunicators, one for the sampler and several others for the forward modelsimulation, which speeds up sampling time considerably. For smaller jobs thePython multiprocessing option is also available. Other key features include: aSequential Monte Carlo sampler, a method for iteratively adapting tolerancelevels, local covariance estimate using scikit-learn's KDTree, modules forspecifying optimal covariance matrix for a component-wise or multivariatenormal perturbation kernel, output and restart files are backed up everyiteration, user defined metric and simulation methods, a module for specifyingheterogeneous parameter priors including non-standard prior PDFs, a module forspecifying a constant, linear, log or exponential tolerance level,well-documented examples and sample scripts. This code is hosted online athttps://github.com/EliseJ/astroABC

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

An Experimental Study of Uncertainty Considerations Associated with Predicting Auto-ignition Timing using Livengood-Wu Integral Method

The application of the Livengood-Wu (LW) integral method as a tool to estimate knock onset in spark ignited (SI) engines and combustion phasing in advanced compression ignition (ACI) engines has been demonstrated through simulations several times. In this study, the effect of uncertainties associated with parameters required for the LW integral method, when used as a tool for model based control of ignition timing in an ACI engine, were experimentally studied using five full boiling range gasoline fuels. As a first step, the method was applied to experimental data from a rapid compression machine and it was found that the ability of the LW integral method to predict ignition timing was very sensitive to the performance of the chemical kinetic model of each fuel. The method was subsequently applied to experimental data from a single-cylinder gasoline engine with simple approximations for the LW integral input parameters, and it was found that the predicted time of ignition was significantly different from the actual start of combustion. Systematic evaluation of various parametric uncertainties conducted thereafter showed that the uncertainty in cylinder charge temperature has the greatest influence. Improved methods of estimating cylinder charge temperature are proposed to account for the previously determined corrections, to enable the use of the LW integral method for model based control of ignition timing.

Compression Ignition↗
DOE OSTI2014

Understanding boundary effects in quantum state tomography – One qubit case

For classical and quantum estimation with finite data sets, the estimation error can deviate significantly from its asymptotic (large data set) behavior. In quantum state tomography, a major reason for this is the existence of a boundary in the parameter space imposed by constraints, such as the positive semidefiniteness of density matrices. Intuitively, we should be able to reduce the estimation error by using our knowledge of these constraints. This intuition is correct for maximumlikelihood estimators, but the size of the reduction has not been evaluated quantitatively. In this proceeding, we evaluate the improvement in one qubit state tomography by using mathematical tools in classical statistical estimation theory. In particular, we show that the effect of the reduction decreases exponentially with respect to the number of data sets when the true state is mixed, and it remains at arbitrarily large data set when the true state is pure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Simulations of Brady's-Type Fault Undergoing CO2 Push-Pull: Pressure-Transient and Sensitivity Analysis

Input and output files used for fault characterization through numerical simulation using iTOUGH2. The synthetic data for the push period are generated by running a forward simulation (input parameters are provided in iTOUGH2 Brady GF6 Input Parameters.txt [InvExt6i.txt]). In general, the permeability of the fault gouge, damage zone, and matrix are assumed to be unknown. The input and output files are for the inversion scenario where only pressure transients are available at the monitoring well located 200 m above the injection well and only the fault gouge permeability is estimated. The input files are named InvExt6i, INPUT.tpl, FOFT.ins, CO2TAB, and the output files are InvExt6i.out, pest.fof, and pest.sav (names below are display names). The table graphic in the data files below summarizes the inversion results, and indicates the fault gouge permeability can be estimated even if imperfect guesses are used for matrix and damage zone permeabilities, and permeability anisotropy is not taken into account.

15 GEOTHERMAL ENERGY↗
DOE OSTI2018

Ecological analysis of associations between groundwater quality and hypertension and cardiovascular disease in rural Saskatchewan, Canada using Bayesian hierarchical models and administrative health data

Highlights: • Hardness and magnesium were associated with decreased risk of cardiovascular disease. • Arsenic concentrations were not associated with the risk of cardiovascular disease. • Summarized water health standards were not associated with cardiovascular disease. Associations between groundwater quality and the prevalence of hypertension and ischemic heart disease were investigated in rural areas of the Canadian province of Saskatchewan. The partially ecological study was analyzed using Bayesian hierarchical models to account for spatial variability in risk. Exposure measures and health outcomes were estimated based on previously collected water quality surveillance data from public water supplies and private wells and administrative health data. Water quality exposures for each study region were estimated by applying geostatistical techniques to arsenic concentrations and principal component (PC) scores. The PC scores summarized groups of parameters measuring either health standards or aesthetic objectives described by the province. Generalized linear mixed models with a log link assessed associations between water quality and observed count of health outcomes relative to the expected value. The Bayesian models contained uncorrelated and spatially correlated random effects for each geographic region. Effect estimates were controlled for sex and age by stratification of case and expected case counts, for smoking by inclusion of sex- and age-specific prevalence of chronic obstructive pulmonary disease as a surrogate covariate, and for education and income by use of census data. There was no evidence for associations between groundwater arsenic concentrations in public or private water supplies and increased risk of hypertension or cardiovascular disease. An increase in the second aesthetic objectives PC score from public supplies was associated with a protective effect against ischemic heart disease. This PC value summarized hardness and magnesium Similarly, an increase in the second aesthetic objectives PC in private supplies was associated with decreased prevalence of hypertension. The results of this study are consistent with others demonstrating a relationship between elevated hardness and magnesium concentrations in drinking water and reduced risk of hypertension and cardiovascular disease. Further investigation is warranted with individual exposure history, particularly with respect to the potential beneficial effect of hard water on the prevalence of hypertension and cardiovascular disease.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Localization of a radioactive source in an urban environment using Bayesian Metropolis methods [Bayesian Metropolis methods for source localization in an urban environment]

Here, we present a method for localizing an unknown source of radiation in an urban environment using a distributed detector network. This method employs statistical parameter estimation techniques, relying on an approximation for the response of a detector to the source based on a simplified model of the underlying transport phenomena, combined with a Metropolis-type sampler that is modified to propagate the effect of fixed epistemic uncertainties in the material macroscopic cross sections of objects in the scene. We apply this technique to data collected during a measurement campaign conducted in a realistic analog for an urban scene using a network of six mobile detectors. Our initial results are able to localize the source to within approximately 8 m over a scene of size 300 m 200 m in two independent trials with 30 min count times, including a characterization of the uncertainty associated with the poorly known macroscopic cross sections of objects in the scene. In these measurements, the nearest detectors were between 20 m to 30 m from the source, and recorded count rates between approximately 3 and 13 times background. A few detectors had line-of-sight to the source, while the majority were obscured by objects present in the scene. After extending our model to account for the orientation of the detectors and correcting for anomalies in the measurement data we were able to further improve the localization accuracy to approximately 2 m in both trials.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Extension of the flux fit method for estimating power deposition profiles

The flux fit method is used to self-consistently estimate the power deposition profile and heat transport profiles from temperature measurements originating from perturbative experiments with a modulated source. Furthermore, this letter improves on this method by addressing the limitations and assumptions. The most crucial improvement is the additional freedom in the source deposition profile. Allowing for a variable central deposition location and height and including a skewness parameter produces deposition profiles more consistent with the measurement data, but still wider than equilibrium ray tracing in two different DIII-D discharges. Moreover, we show that the quality of the estimated deposition profile is key to the accuracy of diffusivity and connectivity estimates, but inversely, the estimated transport parameters hardly affect the quality of the power deposition estimate. Using this method, we show that the power deposition profile estimate is broadened with respect to ray-tracing by about 1.7-1.8 times in two DIII-D discharges.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Estimating and Evaluating Roughness Length and Displacement Height in Heterogeneous Urban Environments

The roughness length (z 0 ) and displacement height (z d ) are essential surface-layer parameters in numerical models (e.g., weather, climate, wall-modeled LES, etc.). This work evaluates the consistency of z 0 and z d estimates from morphometric and anemometric methods using data from two eddy-covariance flux towers (AmeriFlux US-INg and US-INc) in Indianapolis, IN. Results show inconsistencies in estimated z 0 and z d values depending on the chosen method. The two evaluated anemometric methods estimate non-physical values of z d when compared to roughness elements surrounding both towers. Additionally, predictions of mean wind speed using surface-layer similarity theory with morphometric estimates exhibit a bias during near-neutral and stable conditions relative to observations. The overestimation of mean wind speed by surface layer similarity theory is consistent with previous observational and modeling studies in urban areas, suggesting that the application of similarity theories to urban environments may have limitations. Differentiation of vegetation from built structures appears to impact morphometric z 0 and z d estimates, particularly where vegetation is abundant; however, it has little impact on correcting biases in the similarity theory. Specifically, we find that existing similarity theories using morphometric estimates underestimate integral velocity and length scales, and the degree of underestimation depends on the stability conditions. Accounting for the degree of anisotropy in surface-layer turbulence helps reduce the biases between similarity theories and observations during unstable conditions, but not in near-neutral cases. Future work is needed to identify the cause of such biases for near-neutral conditions.

Aerodynamic roughness length↗
DOE OSTI2024

Validating automated resonance evaluation with synthetic data

The integrity and precision of nuclear data are crucial for a broad spectrum of applications, from national security and nuclear reactor design to medical diagnostics, where the associated uncertainties can significantly impact outcomes. A substantial portion of uncertainty in nuclear data originates from the subjective biases in the evaluation process, a crucial phase in the nuclear data production pipeline. Recent advancements indicate that automation of certain routines can mitigate these biases, thereby standardizing the evaluation process and enhancing reproducibility. This research aims to provide a methodology, framework, and metrics for the validation of automated nuclear data evaluation software leveraging high-quality synthetic data that closely mimic real experimental observables. An introduced error metric provides a scale and intuitive measure of the evaluation quality by quantifying the estimate’s accuracy and performance across the specified energy range. Synthetic data provides access to experimental observables and underlying resonance parameters, enabling comparison of different evaluations. The methodology is demonstrated using Ta-181 isotope data in the resolved resonance region. The Automated Resonance Identification Subroutine (ARIS), which operates without prior resonance information, was used to test and showcase the framework’s capabilities utilizing the proposed error metrics. The results demonstrate the effectiveness of the proposed approach and framework for optimizing software parameters and testing hypotheses through “what-if” controlled experiments, such as modifying assumptions about experimental conditions or average resonance parameters.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2017

A laboratory validation study of the time-lapse oscillatory pumping test for leakage detection in geological repositories

Geologic repositories are extensively used for disposing byproducts in mineral and energy industries. The safety and reliability of these repositories are a primary concern to environmental regulators and the public. Time-lapse oscillatory pumping test (OPT) has been introduced recently as a pressure-based technique for detecting potential leakage in geologic repositories. By routinely conducting OPT at a number of pulsing frequencies, an operator may identify the potential repository anomalies in the frequency domain, alleviating the ambiguity caused by reservoir noise and improving the signal-to-noise ratio. Building on previous theoretical and field studies, this work performed a series of laboratory experiments to validate the concept of time-lapse OPT using a custom made, stainless steel tank under relatively high pressures. The experimental configuration simulates a miniature geologic storage repository consisting of three layers (i.e., injection zone, caprock, and above-zone aquifer). Here results show that leakage in the injection zone led to deviations in the power spectrum of observed pressure data, and the amplitude of which also increases with decreasing pulsing frequencies. The experimental results are further analyzed by developing a 3D flow model, using which the model parameters are estimated through frequency domain inversion.

58 GEOSCIENCES↗
DOE OSTI2021

Matrix Completion for Improved Observability in Low-Voltage Distribution Grids

This paper considers the problem of recovering missing entries in a partially observed matrix from relatively few measurements (i.e., the so-called matrix completion problem) with the aim of increasing the presently limited observability of low-voltage distribution grids. To this end, the partially observed matrix is formed using scarce voltage magnitude measurements while accounting for their spatial information. Voltage readings are assumed to be collected from distribution utility sensors and/or geographically-distributed cable television network sensors located in immediate proximity to distribution grid nodes. A matrix completion approach built on the parameter-less singular value shrinkage technique is used to estimate voltage magnitudes at otherwise non-observable low-voltage nodes using a small number of single- or multiple-snapshot data. The effectiveness of the proposed approach is demonstrated using a U.S.-style distribution test system from the synthetic SMART- DS data set under very low- to moderate-observability conditions.

low-rank matrix completion↗