Search NASA⌕ Search

SEARCH · Search NASA

Results for “Scaling and squaring method”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Interferometric detection of freeze-thaw displacements of Alaskan permafrost using ERS-1 data

The possibility of making large scale (50 km) measurements of motions of the earth's surface with high resolution (10 m) and very high accuracy (1 cm) from multipass SAR interferometry was established in 1989. Other experiments have confirmed the viability and usefulness of the method. Work is underway in various groups to measure displacements from volcanic activity, seismic events, glacier motion, and in the present study, freeze-thaw cycles in Alaskan permafrost. The ground is known to move significantly in these cycles, and provided that freezing does not cause image decorrelation, it should be possible to measure both ground swelling and subsidence. The authors have obtained data from multiple passes of ERS-1 over the Toolik Lake region of northern Alaska of suitable quality for interferometry. The data are processed into images, and single interferograms are formed in the usual manner. Phase unwrapping is performed, and the multipass baselines are estimated from the images using both orbit ephemerides and scene tie points. The phases are scaled by the baseline ratio, and a double-difference interferogram (DDI) is formed. It is found that there is a residual 'saddle-shape' phase error across the image, which is postulated to be caused by a small divergence (10(exp -2) deg.) in the orbits. A simulation of a DDI from divergent orbits confirms the shape and magnitude of the error. A two-dimensional least squares fit to the error is performed, which is used to correct the DDI. The final, corrected DDI shows significant phase (altitude) changes over the period of the observation.

Werner, Charles L.↗
NASA NTRS2021

Mapping Global Forest Age from Forest Inventories, Biomass and Climate Data

Forest age can determine the capacity of a forest to uptake carbon from the atmosphere. However, a lack of global diagnostics that reflect the forest stage and associated disturbance regimes hampers the quantification of age-related differences in forest carbon dynamics. This study provides a new global distribution of forest age circa 2010, estimated using a machine learning approach trained with more than 40 000 plots using forest inventory, biomass and climate data. First, an evaluation against the plot-level measurements of forest age reveals that the data-driven method has a relatively good predictive capacity of classifying old-growth vs. non-old-growth (precision = 0.81 and 0.99 for old-growth and non-old-growth, respectively) forests and estimating corresponding forest age estimates (NSE = 0.6 – Nash–Sutcliffe efficiency – and RMSE = 50 years – root-mean-square error). However, there are systematic biases of overestimation in young- and underestimation in old-forest stands, respectively. Globally, we find a large variability in forest age with the old-growth forests in the tropical regions of Amazon and Congo, young forests in China, and intermediate stands in Europe. Furthermore, we find that the regions with high rates of deforestation or forest degradation (e.g. the arc of deforestation in the Amazon) are composed mainly of younger stands. Assessment of forest age in the climate space shows that the old forests are either in cold and dry regions or warm and wet regions, while young–intermediate forests span a large climatic gradient. Finally, comparing the presented forest age estimates with a series of regional products reveals differences rooted in different approaches and different in situ observations and global-scale products. Despite showing robustness in cross-validation results, additional methodological insights on further developments should as much as possible harmonize data across the different approaches. The forest age dataset presented here provides additional insights into the global distribution of forest age to better understand the global dynamics in the forest water and carbon cycles. The forest age datasets are openly available at https://doi.org/10.17871/ForestAgeBGI.2021 (Besnard et al., 2021).

Simon Besnard↗
NASA NTRS1994

Analysis of small-scale microwave background radiation anisotropy in the presence of foreground contamination

Many of the current round of experiments searching for anisotropies in the microwave background radiation (MBR) are confronting the problem of how to disentangle the cosmic signal from contamination due to Galactic and intergalactic foreground sources. Here we show how commonly used likelihood function techniques can be generalized to account for foreground. Specifically we set some restrictions on the spectrum of foreground contamination but allow the amplitude to vary arbitrarily. The likelihood function thus generalized gives reasonable limits on the MBR anisotropy which, in some cases, are not much less restrictive than what one would get from more detailed modeling of the foreground. Furthermore, the likelihood function is exactly the same as one would obtain by simply projecting out foreground contamination and looking at the reduced data set. We apply this generalized analysis to the recent medium-angle data sets of ACME-HEMT (Gaier et al. 1992; Schuster et al. 1993) and MAX (Meinhold et al. 1993; Gunderson et al. 1993). The resulting analysis constrains the one free parameter in the standard cold dark matter theory to be Q(sub rms-ps) = 18(sub -5 sup +8) microKelvin. This best fit value, although in striking agreement with the normalization from Cosmic Background Explorer (COBE), is not a very good fit, with an overall chi-squared/degrees of freedom = 208/168. We also argue against three commonly used methods of dealing with foreground: (1) ignoring it completely; (2) subtracting off a best-fit foreground and treating the residuals as if uncontaminated; and (3) culling data which appears to be contaminated by foreground.

Dodelson, Scott↗
NASA NTRS2012

Earth Radiation Imbalance from a Constellation of 66 Iridium Satellites: Climate Science Aspects

The "global warming hiatus" since the 1998 El Nino, highlighted by Meehl et al., and the resulting "missing energy" problem highlighted by Trenberth et al., has opened the door to a more fundamental view of climate change than mere surface air temperature. That new view is based on two variables which are strongly correlated: the rate of change of ocean heat content d(OHC)/dt; and Earth Radiation Imbalance (ERI) at the top of the atmosphere, whose guesstimated range is 0.4 to 0.9 Watts per square meters (this imbalance being mainly due to increasing CO2). The Argo float array is making better and better measurements of OHC. But existing satellite systems cannot measure ERI to even one significant digit. So, climate model predictions of ERI are used in place of real measurements of it, and the satellite data are tuned to the climate model predictions. Some oceanographers say "just depend on Argo for understanding the global warming hiatus and the missing energy", but we don't think this is a good idea because d(OHC)/dt and ERI have different time scales and are never perfectly correlated. We think the ERB community needs to step up to measuring ERI correctly, just as oceanographers have deployed Argo to measure OHC correctly. This talk will overview a proposed constellation of 66 Earth radiation budget instruments, hosted on Iridium satellites, that will actually be able to measure ERI to at least one significant digit, thus enabling a crucial test of climate models. This constellation will also be able to provide ERI at two-hourly time scales and 500-km spatial scales without extrapolations from uncalibrated narrowband geostationary instruments, using the highly successful methods of GRACE to obtain spatial resolution. This high time resolution would make ERI a synoptic variable like temperature, and allow studies of ERI's response to fast-evolving phenomena like dust storms and hurricanes and even brief excursions of Total Solar Irradiance. Time permitting, we will also discuss the emerging view of clear vs. cloudy and its implications for the traditional ERB approach.

Wiscombe, W.↗
NASA NTRS2016

Validation of High-Resolution CFD Method for Slosh Damping Extraction of Baffled Tanks

Determination of slosh damping is a very challenging task as there is no analytical solution. The damping physics involve the vorticity dissipation which requires the full solution of the nonlinear Navier-Stokes equations. As a result, previous investigations and knowledge were mainly carried out by extensive experimental studies. A Volume-Of-Fluid (VOF) based CFD program developed at NASA MSFC was applied to extract slosh damping in a baffled tank from the first principle. First, experimental data using water with subscale smooth wall tank were used as the baseline validation. CFD simulation was demonstrated to be capable of accurately predicting natural frequency and very low damping value from the smooth wall tank at different fill levels. The damping due to a ring baffle at different liquid fill levels from barrel section and into the upper dome was then investigated to understand the slosh damping physics due to the presence of a ring baffle. Based on this study, the Root-Mean-Square error of our CFD simulation in estimating slosh damping was less than 4.8%, and the maximum error was less than 8.5%. Scalability of subscale baffled tank test using water was investigated using the validated CFD tool, and it was found that unlike the smooth wall case, slosh damping with baffle is almost independent of the working fluid and it is reasonable to apply water test data to the full scale LOX tank when the damping from baffle is dominant. On the other hand, for the smooth wall, the damping value must be scaled according to the Reynolds number. Comparison of experimental data, CFD, with the classical and modified Miles equations for upper dome was made, and the limitations of these semi-empirical equations were identified.

Yang, H. Q.↗
NASA NTRS1999

Lidar Altimeter Measurements of Canopy Structure: Methods and Validation for Closed Canopy, Broadleaf Forests

Lidar altimeter observations of vegetated landscapes provide a time-resolved measure of laser pulse backscatter energy from canopy surfaces and the underlying ground. Airborne lidar altimeter data was acquired using the Scanning Lidar Imager of Canopies by Echo Recovery (SLICER) for a successional sequence of four, closed-canopy, deciduous forest stands in eastern Maryland. The four stands were selected so as to include a range of canopy structures of importance to forest ecosystem function, including variation in the height and roughness of the outer-most canopy surface and the vertical organization of canopy stories and gaps. The character of the SLICER backscatter signal is described and a method is developed that accounts for occlusion of the laser energy by canopy surfaces, transforming the backscatter signal to a canopy height profile (CHP) that quantitatively represents the relative vertical distribution of canopy surface area. The transformation applies an increased weighting to the backscatter amplitude as a function of closure through the canopy and assumes a horizontally random distribution of the canopy components. SLICER CHPs, averaged over areas of overlap where lidar ground tracks intersect, are shown to be highly reproducible. CHP transects across the four stands reveal spatial variations in vegetation, at the scale of the individual 10 m diameter laser footprints, within and between stands. Averaged SLICER CHPs are compared to analogous height profile results derived from ground-based sightings to plant intercepts measured on plots within the four stands. Tbe plots were located on the segments of the lidar ground tracks from which averaged SLICER CHPs were derived, and the ground observations were acquired within two weeks of the SLICER data acquisition to minimize temporal change. The differences in canopy structure between the four stands is similarly described by the SLICER and ground-based CHP results, however a Chi-square test of similarity documents differences that are statistically significant. The differences are discussed in terms of measurement properties that define the smoothness of the resulting CHPs and Lidar Altimeter Measurements of Canopy Structure - Harding et al. canopy properties that may vertically bias the CHP representations of canopy structure. The statistical differences are most likely due to the more noisy character of the ground-based CHPs, especially high in the canopy where ground-based sightings are rare resulting in an underestimate of canopy surface area and height, and to departures from the assumption of horizontal randomness which bias the CHPs toward the observer (upward for SLICER and downward for ground-based CHPs). The results demonstrate that the SLICER observations reliably provide a measure of canopy structure that reveals ecologically interesting structural variations such as those characterizing a successional sequence of closed-canopy, broadleaf forest stands.

Harding, D. J.↗
NASA NTRSDate not supplied

Validation Experiments for Turbulent Separation over an Axisymmetric Body of Revolution

Historically, the flow physics involved with most turbulent separated flows have presented fundamental challenges to validating numerical approaches. As recognized by the CFD Vision 2030 study commissioned by NASA, validation of Reynolds-averaged Navier-Stokes (RANS) models and other scale-resolving methods for turbulent separated flow requires data from advanced, high-fidelity experiments designed specifically for CFD implementation. In accordance with this effort, a new test platform, referred to as the NASA Axisymmetric Afterbody, was designed to obtain detailed measurements of the flow field undergoing a smooth, adverse pressure gradient induced separation for a fixed Reynolds number, Re = 180,000. The parametric body offers a range of flow states progressing from fully attached, to incipient separation, and finally to small-scale separated flow based on variable afterbody geometries. In an initial effort to evaluate RANS turbulence model capabilities, the present configurations of the axisymmetric model host a mild adverse pressure gradient over the contoured boattail section, inducing incipient turbulent separation, as well as a slightly larger adverse pressure gradient, inducing a small-scale region of turbulent separation. Experiments include steady pressure measurements and 2-D PIV to provide the preliminary dataset for simulation studies, which examine the effect of variable grid domains and RANS turbulence models. This is done in an effort to understand and evaluate the critical variability between solutions for the present model configurations. Results indicate potential discrepancies may be due to the effect of the square tunnel test section walls, relatively large blockage ratio, and slight variability in reference parameters. Ongoing work will focus on higher fidelity experimental campaigns to obtain surface flow visualizations and Stereo-Particle Image Velocimetry (SPIV) to deliver higher spatial resolution of the three-dimensional flow field to aid turbulence modelers.

Validation↗
DOE OSTI2021

Influence of geometry on columnar to equiaxed transition during electron beam powder bed fusion of IN718

Correlation between spot-melt scan parameters (linear spot-density aka areal energy density), build geometry, and solidification microstructure evolution (columnar vs equiaxed) in a powder bed fusion technology is investigated. It is shown that to maintain the equiaxed solidification microstructure evolution in electron beam powder bed additive manufacturing (AM), the areal energy density per layer needs to be scaled with respect to the 2D cross-sectional area of the layer being melted. Samples with two different cross-sectional areas (40 × 40 mm and 20 × 20 mm) have been fabricated with varying areal energy densities. For a given square cross-section (20 × 20 mm), increasing the areal energy density (4.8 MJ/sq.m to 14.7 MJ/sq.m) transitioned the solidification microstructure from columnar to equiaxed. The observed microstructure data (Electron Back Scattered Diffraction - EBSD) is quantified by calculating the principal component (PC) score using a spatial statistics methodology. The sample with equiaxed grains is found to have a low PC score while the sample with columnar grain had a high PC score. A semi-analytical model is used to simulate the heat transfer and the local solidification conditions as a function of processing parameters (linear spot-density). The result from the heat transfer model is correlated with previously quantified microstructure data. Space-Time analysis of the melt pattern is done and correlated with the observed microstructure. In addition, from the findings, appropriate parameters have been used to additively manufacture a turbine blade with site-specific or hybrid solidification microstructure (traditional fabrication possible via a patented method of localized cold working and heat treatment).

36 MATERIALS SCIENCE↗
DOE OSTI2022

Analytics-at-scale of Sensor Data for Digital Monitoring in Nuclear Plants (3 rd Annual Report)

Nuclear power plants collect and store large volumes of heterogeneous data from various components and systems. With recent advances in machine learning (ML) techniques, these data can be leveraged to develop diagnostic and short-term forecasting models to better predict future equipment condition. Maintenance operations can then be planned in advance whenever degraded performance is predicted, thus resulting in fewer unplanned outages and the optimization of maintenance activities. This enables lower maintenance costs and improves the overall economics of nuclear power. This report primarily focuses on developing a short-term forecasting process that leverages a feature selection process to distill large volumes of heterogeneous data and predict specific equipment parameters. A variety of feature selection methods, including Shapley Additive Explanations (SHAP) and variance inflation factor (VIF), were used to select the optimal features as inputs for three ML methods: long short-term memory (LSTM) networks, support vector regression (SVR), and random forest (RF). Each combination of model and input features was used to predict a pump bearing temperature both 1 and 24 hours in advance, based on actual plant system data. The optimal inputs for the LSTM and SVR were selected using the SHAP values, while the optimal input for the RF consisted solely of the response variable itself. Each model produced similar 1-hour-ahead predictions, with root mean square errors (RMSEs) of roughly 0.006. For the 24-hour-ahead predictions, differences could be seen between LSTM, SVR, and RF, as reflected by model performances of 0.036 ± 0.014, 0.0026 ± 0, and 0.063 ± 0.004 RMSE, respectively. As big data and continuous online monitoring become more widely available, the proposed feature selection process can be used for many applications beyond the prediction of process parameters within nuclear infrastructure. This report summarizes the Fiscal Year 2021 research progress encompassing the (1) data cleaning and feature selection necessary for ML applications; (2) development of short-term forecasting models to predict future plant process parameters for both single and multiple time steps ahead; and (3) validation of the feature selection methods and short-term forecasting models given new data from different systems.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

DESI 2024 III: baryon acoustic oscillations from galaxies and quasars

We present the DESI 2024 galaxy and quasar baryon acoustic oscillations (BAO) measurements using over 5.7 million unique galaxy and quasar redshifts in the range 0.1 < z < 2.1. Divided by tracer type, we utilize 300,017 galaxies from the magnitude-limited Bright Galaxy Survey with 0.1 < z < 0.4, 2,138,600 Luminous Red Galaxies with 0.4 < z < 1.1, 2,432,022 Emission Line Galaxies with 0.8 < z < 1.6, and 856,652 quasars with 0.8 < z < 2.1, over a ∼ 7,500 square degree footprint. The analysis was blinded at the catalog-level to avoid confirmation bias. All fiducial choices of the BAO fitting and reconstruction methodology, as well as the size of the systematic errors, were determined on the basis of the tests with mock catalogs and the blinded data catalogs. We present several improvements to the BAO analysis pipeline, including enhancing the BAO fitting and reconstruction methods in a more physically-motivated direction, and also present results using combinations of tracers. We employ a unified BAO analysis method across all tracers. We present a re-analysis of SDSS BOSS and eBOSS results applying the improved DESI methodology and find scatter consistent with the level of the quoted SDSS theoretical systematic uncertainties. With the total effective survey volume of ∼ 18 Gpc3, the combined precision of the BAO measurements across the six different redshift bins is ∼0.52%, marking a 1.2-fold improvement over the previous state-of-the-art results using only first-year data. We detect the BAO in all of these six redshift bins. The highest significance of BAO detection is 9.1σ at the effective redshift of 0.93, with a constraint of 0.86% placed on the BAO scale. We find that our observed BAO scales are systematically larger than the prediction of the Planck 2018-ΛCDM at z < 0.8. We translate the results into transverse comoving distance and radial Hubble distance measurements, which are used to constrain cosmological models in our companion paper.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2016

Derivation and Validation of Supraglacial Lake Volumes on the Greenland Ice Sheet from High-Resolution Satellite Imagery

Supraglacial meltwater lakes on the western Greenland Ice Sheet (GrIS) are critical components of its surface hydrology and surface mass balance, and they also affect its ice dynamics. Estimates of lake volume, however, are limited by the availability of in situ measurements of water depth,which in turn also limits the assessment of remotely sensed lake depths. Given the logistical difficulty of collecting physical bathymetric measurements, methods relying upon in situ data are generally restricted to small areas and thus their application to largescale studies is difficult to validate. Here, we produce and validate spaceborne estimates of supraglacial lake volumes across a relatively large area (1250 km(exp 2) of west Greenland's ablation region using data acquired by the WorldView-2 (WV-2) sensor, making use of both its stereo-imaging capability and its meter-scale resolution. We employ spectrally-derived depth retrieval models, which are either based on absolute reflectance (single-channel model) or a ratio of spectral reflectances in two bands (dual-channel model). These models are calibrated by usingWV-2multispectral imagery acquired early in the melt season and depth measurements from a high resolutionWV-2 DEM over the same lake basins when devoid of water. The calibrated models are then validated with different lakes in the area, for which we determined depths. Lake depth estimates based on measurements recorded in WV-2's blue (450-510 nm), green (510-580 nm), and red (630-690 nm) bands and dual-channel modes (blue/green, blue/red, and green/red band combinations) had near-zero bias, an average root-mean-squared deviation of 0.4 m (relative to post-drainage DEMs), and an average volumetric error of b1%. The approach outlined in this study - image-based calibration of depth-retrieval models - significantly improves spaceborne supraglacial bathymetry retrievals, which are completely independent from in situ measurements.

Spectrally-based depth-retrieval models↗
DOE OSTI2022

Machine Learning Assisted HPC Workload Trace Generation for Leadership Scale Storage Systems

Monitoring and analyzing a wide range of I/O activities in an HPC cluster is important in maintaining mission-critical performance in a large-scale, multi-user, parallel storage system. Center-wide I/O traces can provide high-level information and fine-grained activities per application or per user running in the system. Studying such large-scale traces can provide helpful insights into the system. It can be used to develop predictive methods for making predictive decisions, adjusting scheduling policies, or providing decisions for the design of next-generation systems. However, sharing real-world I/O traces to expedite such research efforts leaves a few concerns; i) the cost of sharing the large traces is expensive due to this large size, and ii) privacy concern is an issue.We address such issues by building an end-to-end machine learn- ing (ML) workflow that can generate I/O traces for large-scale HPC applications. We leverage ML based feature selection and gener- ative models for I/O trace generation. The generative models are trained on I/O traces collected by the darshan I/O characterization tool over a period of one year. We present a two-step generation process consisting of two deep-learning models, called the feature generator and the trace generator. The combination of two-step generative models provides robustness by reducing the bias of the model and accounting for the stochastic nature of the I/O traces across different runs of an application. We evaluate the performance of the generative models and show that the two-step model can generate time-series I/O traces with less than 20% root mean square error.

Paul, Arnab↗
DOE OSTI2023

Skyrme-Hartree-Fock-Bogoliubov mass models on a 3D mesh: III. From atomic nuclei to neutron stars

Here, we present BSkG3, the latest entry in the Brussels-Skyrme-on-a-grid series of large-scale models of nuclear structure based on an energy density functional. Compared to its predecessors, the new model offers a more realistic description of nucleonic matter at the extreme densities relevant to neutron stars. This achievement is made possible by incorporating a constraint on the infinite nuclear matter properties at high densities in the parameter adjustment, ensuring in this way that the predictions of BSkG3 for the nuclear Equation of State are compatible with the observational evidence for heavy pulsars with M > 2M ⊙ . Instead of the usual phenomenological pairing terms, we also employ a more microscopically founded treatment of nucleon pairing, resulting in extrapolations to high densities that are in line with the predictions of advanced many-body methods and are hence more suited to the study of superfluidity in neutron stars. By adopting an extended form of the Skyrme functional, we are able to reconcile the description of matter at high densities and at saturation density: the new model further refines the description of atomic nuclei offered by its predecessors. A qualitative improvement is our inclusion of ground state reflection asymmetry, in addition to the spontaneous breaking of rotational, axial, and time-reversal symmetry. Quantitatively, the model offers lowered root-mean-square deviations on 2457 masses (0.631 MeV), 810 charge radii (0.0237 fm) and an unmatched accuracy with respect to 45 primary fission barriers of actinide nuclei (0.33 MeV). Reconciling the complexity of neutron stars with those of atomic nuclei establishes BSkG3 as a tool of choice for applications to nuclear structure, the nuclear equation of state and nuclear astrophysics in general.

Physics↗
NASA NTRS1993

Steady induction effects in geomagnetism. Part 1C: Geomagnetic estimation of steady surficial core motions: Application to the definitive geomagnetic reference field models

In the source-free mantle/frozen-flux core magnetic earth model, the non-linear inverse steady motional induction problem was solved using the method presented in Part 1B. How that method was applied to estimate steady, broad-scale fluid velocity fields near the top of Earth's core that induce the secular change indicated by the Definitive Geomagnetic Reference Field (DGRF) models from 1945 to 1980 are described. Special attention is given to the derivation of weight matrices for the DGRF models because the weights determine the apparent significance of the residual secular change. The derived weight matrices also enable estimation of the secular change signal-to-noise ratio characterizing the DGRF models. Two types of weights were derived in 1987-88: radial field weights for fitting the evolution of the broad-scale portion of the radial geomagnetic field component at Earth's surface implied by the DGRF's, and general weights for fitting the evolution of the broad-scale portion of the scalar potential specified by these models. The difference is non-trivial because not all the geomagnetic data represented by the DGRF's constrain the radial field component. For radial field weights (or general weights), a quantitatively acceptable explication of broad-scale secular change relative to the 1980 Magsat epoch must account for 99.94271 percent (or 99.98784 percent) of the total weighted variance accumulated therein. Tolerable normalized root-mean-square weighted residuals of 2.394 percent (or 1.103 percent) are less than the 7 percent errors expected in the source-free mantle/frozen-flux core approximation.

Voorhies, Coerte V.↗
DOE OSTI2021

Numerical solution of singular Lyapunov equations

We consider the numerical solution of large scale singular (continuous-time) Lyapunov equations of the form AX + XA T + BB T = 0, where A is semistable, that is, its spectrum is contained in the left half plane, with the exception of a few semisimple eigenvalues at zero. We also consider the case of a few semisimple eigenvalues on the imaginary axis. We assume that we know these few eigenvalues (zero or imaginary), and that we have or can compute the corresponding invariant subspaces. We use this information to build an appropriate newly proposed subspace on which to project the Lyapunov equations, and then compute a low-rank approximation to the least squares solution. Selected illustrative numerical examples are provided.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Gradient Coding With Iterative Block Leverage Score Sampling

Gradient coding is a method for mitigating straggling servers in a centralized computing network that uses erasure-coding techniques to distributively carry out first-order optimization methods. Randomized numerical linear algebra uses randomization to develop improved algorithms for large-scale linear algebra computations. In this study, we propose a method for distributed optimization that combines gradient coding and randomized numerical linear algebra. The proposed method uses a randomized ℓ 2 -subspace embedding and a gradient coding technique to distribute blocks of data to the computational nodes of a centralized network, and at each iteration the central server only requires a small number of computations to obtain the steepest descent update. The novelty of our approach is that the data is replicated according to importance scores, called block leverage scores, in contrast to most gradient coding approaches that uniformly replicate the data blocks. Furthermore, we do not require a decoding step at each iteration, avoiding a bottleneck in previous gradient coding schemes. We show that our approach results in a valid ℓ 2 -subspace embedding, and that our resulting approximation converges to the optimal solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Deep learning to estimate permeability using geophysical data

Time-lapse electrical resistivity tomography (ERT) is a popular geophysical method to estimate three-dimensional (3D) permeability fields from electrical potential difference measurements. Traditional inversion and data assimilation methods are used to ingest this ERT data into hydrogeophysical models to estimate permeability. Due to ill-posedness and the curse of dimensionality, existing inversion strategies provide poor estimates and low resolution of the 3D permeability field. Recent advances in deep learning provide us with powerful algorithms to overcome this challenge. This paper presents a deep learning (DL) framework to estimate the 3D subsurface permeability from time-lapse ERT data. To test the feasibility of the proposed framework, we train DL-enabled inverse models on simulation data. Each measurement in both synthetic and field data is standardized by removing the mean and scaling the time-series to unit variance. This pre-processing step is necessary to bring simulation data closer to field observations. Subsurface process models based on hydrogeophysics are used to generate this synthetic data. Training performed on limited simulation data resulted in the DL model over-fitting. An advanced data augmentation based on mixup is implemented to generate additional training samples to overcome this issue. This mixup technique creates weakly labeled (low-fidelity) samples from strongly labeled (high-fidelity) data. The weakly labeled training data is then used to develop DL-enabled inverse models and reduce over-fitting. As both time-lapse ERT (1133048 features/realization) and 3D permeability (585453 features/realization) data samples are from a high-dimensional space, principal component analysis (PCA) is employed to reduce dimensionality. Encoded ERT and encoded permeability are generated using the trained PCA estimators. A deep neural network is then trained to map the encoded ERT to encoded permeability. This mixup training and unsupervised learning allowed us to build a fast and reasonably accurate DL-based inverse model under limited simulation data. Results show that proposed weak supervised learning can capture salient spatial features in the 3D permeability field. Quantitatively, the average mean squared error (in terms of the natural log) on the strongly labeled training, validation, and test datasets is less than 0.5. The R 2 -score (global metric) is greater than 0.75, and the percent error in each cell (local metric) is less than 10%. Finally, an added benefit in terms of computational cost is that the proposed DL-based inverse model is at least O(10 4 ) times faster than running a forward model once it is trained. Data generation, DL model training, and hyperparameter tuning to identify optimal neural network architectures utilized high-performance computing resources while the DL inference is performed on a standard laptop. Approximately, O(10 5 ) processor hours are used for generating data and DL tuning and training. We acknowledge that the data generation and DL model development are expensive. But once a DL model is trained, it can be re-used for inversion rapidly for the given system, with set physics and domain. Note that traditional inversion may require multiple forward model simulations (e.g., in the order of 10 to 1000), which are very expensive. This computational savings ≈ O(10 5 ) – O(10 7 )) makes the proposed DL-based inverse model attractive for subsurface imaging and real-time ERT monitoring applications due to fast and yet reasonably accurate estimations of permeability field.

58 GEOSCIENCES↗
DOE OSTI2020

Explicitly correlated coupled cluster method for accurate treatment of open-shell molecules with hundreds of atoms

We present a near-linear scaling formulation of the explicitly correlated coupled-cluster singles and doubles with the perturbative triples method [CCSD(T)F12¯] for high-spin states of open-shell species. The approach is based on the conventional open-shell CCSD formalism [M. Saitow et al., J. Chem. Phys. 146, 164105 (2017)] utilizing the domain local pair-natural orbitals (DLPNO) framework. The use of spin-independent set of pair-natural orbitals ensures exact agreement with the closed-shell formalism reported previously, with only marginally impact on the cost (e.g., the open-shell formalism is only 1.5 times slower than the closed-shell counterpart for the C160H322 n-alkane, with the measured size complexity of ≈1.2). Evaluation of coupled-cluster energies near the complete-basis-set (CBS) limit for open-shell systems with more than 550 atoms and 5000 basis functions is feasible on a single multi-core computer in less than 3 days. The aug-cc-pVTZ DLPNO-CCSD(T)F12¯ contribution to the heat of formation for the 50 largest molecules among the 348 core combustion species benchmark set [J. Klippenstein et al., J. Phys. Chem. A 121, 6580–6602 (2017)] had root-mean-square deviation (RMSD) from the extrapolated CBS CCSD(T) reference values of 0.3 kcal/mol. For a more challenging set of 50 reactions involving small closed- and open-shell molecules [G. Knizia et al., J. Chem. Phys. 130, 054104 (2009)], the aug-cc-pVQ(+d)Z DLPNO-CCSD(T)F12¯ yielded a RMSD of ∼0.4 kcal/mol with respect to the CBS CCSD(T) estimate.

Kumar, Ashutosh (ORCID:0000000175896030)↗