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DOE OSTI2023

PCAfold 2.0—Novel tools and algorithms for low-dimensional manifold assessment and optimization

We describe an update to our open-source Python package, PCAfold, designed to help researchers generate, analyze and improve low-dimensional data manifolds. In the current version, PCAfold 2.0, we introduce novel tools and algorithms for assessing and optimizing low-dimensional manifolds. This includes a method that generates a “map” of local feature sizes that can help pinpoint researchers to problematic regions on a manifold. We introduce a novel cost function that characterizes the quality of a manifold topology with a single number. We develop two algorithms for feature selection based on principal component analysis (PCA) that use the cost function as an objective function to minimize. We introduce a quantity of interest (QoI)-aware dimensionality reduction strategy where data projections are computed using an artificial neural network and are directly optimized towards representing various projection-independent and projection-dependent QoIs. We also introduce an implementation of partition of unity networks (POUnets) for efficient reconstruction of QoIs from low-dimensional manifolds based on combining neural network classification with localized polynomial regression. Our software can be broadly applicable in all domains of science and engineering that aim to reduce data dimensionality, as well as in the fundamental research on representation learning.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2011

A parametrization of the growth index of matter perturbations in various Dark Energy models and observational prospects using a Euclid-like survey

We provide exact solutions to the cosmological matter perturbation equation in a homogeneous FLRW universe with a vacuum energy that can be parametrized by a constant equation of state parameter w and a very accurate approximation for the Ansatz w(a) = w{sub 0}+w{sub a}(1−a). We compute the growth index γ = log f(a)/log Ω{sub m}(a), and its redshift dependence, using the exact and approximate solutions in terms of Legendre polynomials and show that it can be parametrized as γ(a) = γ{sub 0}+γ{sub a}(1−a) in most cases. We then compare four different types of dark energy (DE) models: wΛCDM, DGP, f(R) and a LTB-large-void model, which have very different behaviors at z∼>1. This allows us to study the possibility to differentiate between different DE alternatives using wide and deep surveys like Euclid, which will measure both photometric and spectroscopic redshifts for several hundreds of millions of galaxies up to redshift z ≅ 2. We do a Fisher matrix analysis for the prospects of differentiating among the different DE models in terms of the growth index, taken as a given function of redshift or with a principal component analysis, with a value for each redshift bin for a Euclid-like survey. We use as observables the complete and marginalized power spectrum of galaxies P(k) and the Weak Lensing (WL) power spectrum. We find that, using P(k), one can reach (2%, 5%) errors in (w{sub 0},w{sub a}), and (4%, 12%) errors in (γ{sub 0},γ{sub a}), while using WL we get errors at least twice as large. These estimates allow us to differentiate easily between DGP, f(R) models and ΛCDM, while it would be more difficult to distinguish the latter from a variable equation of state parameter or LTB models using only the growth index.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2013

Application of Spectral Analysis Techniques in the Intercomparison of Aerosol Data: 1. an EOF Approach to the Spatial-Temporal Variability of Aerosol Optical Depth Using Multiple Remote Sensing Data Sets

Many remote sensing techniques and passive sensors have been developed to measure global aerosol properties. While instantaneous comparisons between pixel-level data often reveal quantitative differences, here we use Empirical Orthogonal Function (EOF) analysis, also known as Principal Component Analysis, to demonstrate that satellite-derived aerosol optical depth (AOD) data sets exhibit essentially the same spatial and temporal variability and are thus suitable for large-scale studies. Analysis results show that the first four EOF modes of AOD account for the bulk of the variance and agree well across the four data sets used in this study (i.e., Aqua MODIS, Terra MODIS, MISR, and SeaWiFS). Only SeaWiFS data over land have slightly different EOF patterns. Globally, the first two EOF modes show annual cycles and are mainly related to Sahara dust in the northern hemisphere and biomass burning in the southern hemisphere, respectively. After removing the mean seasonal cycle from the data, major aerosol sources, including biomass burning in South America and dust in West Africa, are revealed in the dominant modes due to the different interannual variability of aerosol emissions. The enhancement of biomass burning associated with El Niño over Indonesia and central South America is also captured with the EOF technique.

variability↗

DOE OSTI2017

Application of visible and near-infrared spectroscopy to classification of Miscanthus species

Here, the feasibility of visible and near infrared (NIR) spectroscopy as tool to classify Miscanthus samples was explored in this study. Three types of Miscanthus plants, namely, M. sinensis , M. sacchariflorus and M. fIoridulus , were analyzed using a NIR spectrophotometer. Several classification models based on the NIR spectra data were developed using line discriminated analysis (LDA), partial least squares (PLS), least squares support vector machine regression (LSSVR), radial basis function (RBF) and neural network (NN). The principal component analysis (PCA) presented rough classification with overlapping samples, while the models of Line_LSSVR, RBF_LSSVR and RBF_NN presented almost same calibration and validation results. Due to the higher speed of Line_LSSVR than RBF_LSSVR and RBF_NN, we selected the line_LSSVR model as a representative. In our study, the model based on line_LSSVR showed higher accuracy than LDA and PLS models. The total correct classification rates of 87.79 and 96.51% were observed based on LDA and PLS model in the testing set, respectively, while the line_LSSVR showed 99.42% of total correct classification rate. Meanwhile, the lin_LSSVR model in the testing set showed correct classification rate of 100, 100 and 96.77% for M. sinensis , M. sacchariflorus and M. fIoridulus , respectively. The lin_LSSVR model assigned 99.42% of samples to the right groups, except one M. fIoridulus sample. The results demonstrated that NIR spectra combined with a preliminary morphological classification could be an effective and reliable procedure for the classification of Miscanthus species.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2012

A DATA-DRIVEN MODEL FOR SPECTRA: FINDING DOUBLE REDSHIFTS IN THE SLOAN DIGITAL SKY SURVEY

We present a data-driven method-heteroscedastic matrix factorization, a kind of probabilistic factor analysis-for modeling or performing dimensionality reduction on observed spectra or other high-dimensional data with known but non-uniform observational uncertainties. The method uses an iterative inverse-variance-weighted least-squares minimization procedure to generate a best set of basis functions. The method is similar to principal components analysis (PCA), but with the substantial advantage that it uses measurement uncertainties in a responsible way and accounts naturally for poorly measured and missing data; it models the variance in the noise-deconvolved data space. A regularization can be applied, in the form of a smoothness prior (inspired by Gaussian processes) or a non-negative constraint, without making the method prohibitively slow. Because the method optimizes a justified scalar (related to the likelihood), the basis provides a better fit to the data in a probabilistic sense than any PCA basis. We test the method on Sloan Digital Sky Survey (SDSS) spectra, concentrating on spectra known to contain two redshift components: these are spectra of gravitational lens candidates and massive black hole binaries. We apply a hypothesis test to compare one-redshift and two-redshift models for these spectra, utilizing the data-driven model trained on a random subset of all SDSS spectra. This test confirms 129 of the 131 lens candidates in our sample and all of the known binary candidates, and turns up very few false positives.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2012

Constraining scale-dependent non-Gaussianity with future large-scale structure and the CMB

We forecast combined future constraints from the cosmic microwave background and large-scale structure on the models of primordial non-Gaussianity. We study the generalized local model of non-Gaussianity, where the parameter f{sub NL} is promoted to a function of scale, and present the principal component analysis applicable to an arbitrary form of f{sub NL}(k). We emphasize the complementarity between the CMB and LSS by using Planck, DES and BigBOSS surveys as examples, forecast constraints on the power-law f{sub NL}(k) model, and introduce the figure of merit for measurements of scale-dependent non-Gaussianity.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1984

Applications of array processors in the analysis of remote sensing images

The architectures, programming characteristics, and ranges of application of past, present, and planned array processors for the digital processing of remote-sensing images are compared. Such functions as radiometric and geometric corrections, principal-components analysis, cluster coding, histogram generation, grey-level mapping, convolution, classification, and mensuration and modeling operations are considered, and both pipeline-type and single-instruction/multiple-data-stream (SIMD) arrays are evaluated. Numerical results are presented in a table, and it is found that the pipeline-type arrays normally used with minicomputers increase their speed significantly at low cost, while even further gains are provided by the more expensive SIMD arrays. Most image-processing operations become I/O-limited when SIMD arrays are used with current I/O devices.

Ramapriyan, H. K.↗

NASA NTRS2000

Sea Ice Motion from Wavelet Analysis of Satellite Data

Wavelet analysis of NASA scatterometer (NSCAT) backscatter and Defense Meteorological Satellite Program (DMSP) Special Sensor Microwave/Imager (SSM/I) radiance data can be used to obtain daily sea ice drift information for the Arctic region. This technique provides improved spatial coverage over the existing array of Arctic Ocean buoys and better temporal resolution over techniques utilizing data from satellite synthetic aperture radars. Comparisons with ice motion derived from ocean buoys give good quantitative agreement. Both comparison results from NSCAT and SSM/I are compatible, and the results from NSCAT can definitely complement that from SSM/I when there are cloud or surface effects. Then three sea-ice drift daily results from NSCAT, SSM/I, and buoy data can be merged as a composite map by some data fusion techniques. The ice flow streamlines are highly correlated with surface air pressure contours. Examples of derived ice-drift maps in December 1996 illustrate large-scale circulation reversals over a period of four days. A method for deriving divergence and shear at the large-scale has been developed and comparison between buoys and satellite results shows a good agreement. These calibrated/validated results indicate that NSCAT, SSM/I merged daily ice motion are suitably accurate to identify and closely locate sea ice processes, and to improve our current knowledge of sea ice drift and related processes through the data assimilation of ocean-ice numerical model. For demonstration purpose, the ice velocities derived from satellite data are compared with the ice velocities derived from a coupled ice-ocean interaction model. The comparison reveals that the general circulation patterns of the two are quite similar but the ice velocity differences between the two are quite significant. In order to quantify the wind effects on ice motion, empirical orthogonal functions (EOF) are used in the principal component analysis for both ice motion and pressure field. Some preliminary results of sea-ice motion from QuikScat will also be presented.

Liu, Antony K.↗

DOE OSTI2018

Autoencoder node saliency: Selecting relevant latent representations

The autoencoder is an artificial neural network that performs nonlinear dimension reduction and learns hidden representations of unlabeled data. With a linear transfer function it is similar to the principal component analysis (PCA). While both methods use weight vectors for linear transformations, the autoencoder does not come with any indication similar to the eigenvalues in PCA that are paired with eigenvectors. In this work, we propose a novel autoencoder node saliency method that examines whether the features constructed by autoencoders exhibit properties related to known class labels. The supervised node saliency ranks the nodes based on their capability of performing a learning task. It is coupled with the normalized entropy difference (NED). We establish a property for NED values to verify classifying behaviors among the top ranked nodes. Lastly, by applying our methods to real datasets, we demonstrate their ability to provide indications on the performing nodes and explain the learned tasks in autoencoders.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1991

Intraseasonal oscillations in the global atmosphere. I - Northern Hemisphere and tropics

Oscillatory modes in the Northern Hemisphere and in the tropics were examined systematically. The 700 mb heights were used to analyze extratropical oscillations, and the outgoing longwave radiation to study tropical oscillations in convection. All datasets were band-pass filtered to focus on the intraseasonal (IS) band of 10-120 days. Leading spatial patterns of variability were obtained by applying empirical orthogonal function analysis to these IS data. The leading principal components were subjected to singular spectrum analysis. In the Northern Hemisphere, there are two important modes of oscillation with periods near 48 and 23 days, respectively. The 48-day mode is the most important of the two. It has both traveling and standing components, and is dominated by a zonal wavenumber two. The 23-day mode has the spatial structure and propagation properties described by Branstator and by Kushnir (1987). In the tropics, the 40-50 day oscillation documented by Madden and Julian (1972), Weickmann (1983), Lau, and their colleagues, dominates the Indian and Pacific oceans from 60 deg E to the date line. From 170 deg W to 90 deg W, however, a 24-28 day oscillation is equally strong. The extratropical modes are often independent of, and sometimes lead, the tropical modes.

Ghil, Michael↗

DOE OSTI2018

Discrete Regularization for Calibration of Geologic Facies Against Dynamic Flow Data

Abstract Subsurface flow model calibration involves many more unknowns than measurements, leading to ill‐posed problems with nonunique solutions. To alleviate nonuniqueness, the problem is regularized by constraining the solution space using prior knowledge. In certain sedimentary environments, such as fluvial systems, the contrast in hydraulic properties of different facies types tends to dominate the flow and transport behavior, making the effect of within facies heterogeneity less significant. Hence, flow model calibration in those formations reduces to delineating the spatial structure and connectivity of different lithofacies types and their boundaries. A major difficulty in calibrating such models is honoring the discrete, or piecewise constant, nature of facies distribution. The problem becomes more challenging when complex spatial connectivity patterns with higher‐order statistics are involved. This paper introduces a novel formulation for calibration of complex geologic facies by imposing appropriate constraints to recover plausible solutions that honor the spatial connectivity and discreteness of facies models. To incorporate prior connectivity patterns, plausible geologic features are learned from available training models. This is achieved by learning spatial patterns from training data, e.g., ‐SVD sparse learning or the traditional Principal Component Analysis. Discrete regularization is introduced as a penalty functions to impose solution discreteness while minimizing the mismatch between observed and predicted data. An efficient gradient‐based alternating directions algorithm is combined with variable splitting to minimize the resulting regularized nonlinear least squares objective function. Numerical results show that imposing learned facies connectivity and discreteness as regularization functions leads to geologically consistent solutions that improve facies calibration quality.

Khaninezhad, Mohammad‐Reza↗

DOE OSTI2023

The influence of physical and algorithmic factors on simulated far-field waveforms and source–time functions of underground explosions using unsupervised machine learning

SUMMARY Characterizing explosion sources and differentiating between earthquake and underground explosions using distributed seismic networks becomes non-trivial when explosions are detonated in cavities or heterogeneous ground material. Moreover, there is little understanding of how changes in subsurface physical properties affect the far-field waveforms we record and use to infer information about the source. Simulations of underground explosions and the resultant ground motions can be a powerful tool to systematically explore how different subsurface properties affect far-field waveform features, but there are added variables that arise from how we choose to model the explosions that can confound interpretation. To assess how both subsurface properties and algorithmic choices affect the seismic wavefield and the estimated source functions, we ran a series of 2-D axisymmetric non-linear numerical explosion experiments and wave propagation simulations that explore a wide array of parameters. We then inverted the synthetic far-field waveform data using a linear inversion scheme to estimate source–time functions (STFs) for each simulation case. We applied principal component analysis (PCA), an unsupervised machine learning method, to both the far-field waveforms and STFs to identify the most important factors that control variance in the waveform data and differences between cases. For the far-field waveforms, the largest variance occurs in the shallower radial receiver channels in the 0–50 Hz frequency band. For the STFs, both peak amplitude and rise times across different frequencies contribute to the variance. We find that the ground equation of state (i.e. lithology and rheology) and the explosion emplacement conditions (i.e. tamped versus cavity) have the greatest effect on the variance of the far-field waveforms and STFs, with the ground yield strength and fracture pressure being secondary factors. Differences in the PCA results between the far-field waveforms and STFs could possibly be due to near-field non-linearities of the source that are not accounted for in the estimation of STFs and could be associated with yield strength, fracture pressure, cavity radius and cavity shape parameters. Other algorithmic parameters are found to be less important and cause less variance in both the far-field waveforms and STFs, meaning algorithmic choices in how we model explosions are less important, which is encouraging for the further use of explosion simulations to study how physical Earth properties affect seismic waveform features and estimated STFs.

58 GEOSCIENCES↗

NASA NTRS2017

Large-Scale Circulation and Climate Variability

The causes of regional climate trends cannot be understood without considering the impact of variations in large-scale atmospheric circulation and an assessment of the role of internally generated climate variability. There are contributions to regional climate trends from changes in large-scale latitudinal circulation, which is generally organized into three cells in each hemisphere-Hadley cell, Ferrell cell and Polar cell-and which determines the location of subtropical dry zones and midlatitude jet streams. These circulation cells are expected to shift poleward during warmer periods, which could result in poleward shifts in precipitation patterns, affecting natural ecosystems, agriculture, and water resources. In addition, regional climate can be strongly affected by non-local responses to recurring patterns (or modes) of variability of the atmospheric circulation or the coupled atmosphere-ocean system. These modes of variability represent preferred spatial patterns and their temporal variation. They account for gross features in variance and for teleconnections which describe climate links between geographically separated regions. Modes of variability are often described as a product of a spatial climate pattern and an associated climate index time series that are identified based on statistical methods like Principal Component Analysis (PC analysis), which is also called Empirical Orthogonal Function Analysis (EOF analysis), and cluster analysis.

Perlwitz, J.↗

DOE OSTI2025

Design Basis Document / Owner’s Technical Specification for Nitrate Salt Systems in CSP Projects: Volume 1 Specifications for Parabolic Trough Projects, Volume 2 - Specifications for Central Receiver Projects, Volume 3 - Narrative

Design Basis Documents / Owner’s Technical Specifications are developed for parabolic trough and central receiver power plants using nitrate salt as the heat transport fluid and the thermal storage medium. The goals were to 1) distill the successful experience with nitrate salt systems from as many commercial projects as possible, 2) provide technical bases for equipment design/selection that an owner can impose on an EPC contractor, 3) compile this information in one location to provide guidance on salt systems that is as broadly applicable to as many projects as possible, and 4) work toward an industry consensus on a Design Basis Document that reflects the lessons learned from earlier commercial projects. The document allows an owner to provide design guidance, and to impose a minimum set of requirements, above and beyond those in the normal Codes and Standards, on an EPC contractor in an effort to avoid a repeat of past mistakes. If successful, this would allow salt systems to achieve the same levels of reliability and availability as commercial parabolic trough plants using diphenyl oxide / biphenyl (i.e., Dowtherm A, Therminol VP-1) as the heat transfer fluid. The report consists of 3 volumes: • Volume 1 - Specifications for Parabolic Trough Projects • Volume 2 - Specifications for Central Receiver Projects • Volume 3 - Narrative Volumes 1 and 2 include discussions of the following topics: • Plant functional requirements for the salt systems • Plant operating states, and transitions between states, for the salt systems • Risk analysis of the principal salt components • Plant requirements for the salt systems to meet the functional and the operating requirements • Type of specification for the principal salt components: functional; or prescriptive • Current state of the art for salt systems. Volume 3 discusses a number of cases in which the salt equipment at commercial parabolic trough and central receiver projects has not met the projected levels of reliability and availability. Possible reasons for the sources of the problems are discussed, as is a range of possible alternate designs that could avoid the known problems.

14 SOLAR ENERGY↗

DOE OSTI2014

Effects of Morphology and Geometry of Inclusions on Two-Point Correlation Statistics in Two Phase Composites

A spectral form of the two-point correlation functions for two-phase composites is presented and the effects of secondary phase morphology, geometry and volume fraction on the coefficients of the corresponding series are studied. Initially, a principal component analysis is performed on the coefficients of the series and then, the effects of different morphological and geometrical parameters of the second phase inclusions on two-point correlation functions are examined. A direct linkage between the principal components of the coefficients with the morphological features (inclusion shape, aspect ratio and size) is established and the influence of preferred orientation of the anisotropic inclusions is also investigated. Finally a composite hull is constructed using the principal components of the coefficients in a three-dimensional space, which helps in determining the interrelation of properties and microstructures of any composite containing these types of inclusions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Accurate Thermochemistry of Complex Lignin Structures via Density Functional Theory, Group Additivity, and Machine Learning

A molecular-level understanding of lignin structures and bond dissociation energies could facilitate depolymerization technologies. Still, this information is currently limited due to the lack of databases and the simplification of surrogate models. Here, substitution effects on seven common linkages in lignin polymers are systematically investigated. An automated reaction network generator is employed to create a database of structures. A new group additivity (GA) model based on principal component analysis (PCA) descriptors is introduced and trained on gas-phase density functional theory data of 4100 species at the M06-2X/6-311++G(d,p) level. Hydrogen bonds, local steric, and nonaromatic ring contributions are also incorporated. Lastly, we improve the accuracy of the group additivity model to reach the G4 theory by computing a data set of 770 species at this level and using a data fusion approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1991

Psychophysical evaluation of three-dimensional auditory displays

Work during this reporting period included the completion of our research on the use of principal components analysis (PCA) to model the acoustical head related transfer functions (HRTFs) that are used to synthesize virtual sources for three dimensional auditory displays. In addition, a series of studies was initiated on the perceptual errors made by listeners when localizing free-field and virtual sources. Previous research has revealed that under certain conditions these perceptual errors, often called 'confusions' or 'reversals', are both large and frequent, thus seriously comprising the utility of a 3-D virtual auditory display. The long-range goal of our work in this area is to elucidate the sources of the confusions and to develop signal-processing strategies to reduce or eliminate them.

Wightman, Frederic L.↗

NASA NTRS2002

Evidence of an Intrinsic Intraseasonal Oscillation over Tropical South America During Austral Summer

The intraseasonal variation (ISV) in the 30-60 day band, also known as Madden-Julian oscillation (MJO), has been studied for decades. Madden and Julian showed that the oscillation originated from the western Indian Ocean, propagated eastward, got enhanced over the maritime continent and weakened after passing over the dateline. Composite studies showed evidences of a signal in upper and lower level zonal wind propagating around the globe during an oscillation. Theoretical studies pointed out that the interaction with the warm ocean surface and the coupling with the convective and radiative processes in the atmosphere could manifest the oscillation, which propagates eastward via mutual feedbacks between the wave motions and the cumulus heating. Over tropical South America, no independent 30-60 day oscillation has been reported so far, despite that Amazon is the most distinct tropical convection center over the western hemisphere and the fluxes from its surface of tropical rainforests are close to that from the warm tropical ocean. Liebmann et al. showed a distinct spectral peak of 40-50 day oscillation in outgoing longwave radiation (OLR) over tropical South America and considered that was manifested by the MJO propagation. Nogues-Paegle et al. (2000) focused on a dipole pattern of the OLR anomaly with centers of action over the South Atlantic Convergence Zone (SACZ) and the subtropical plain. They used the regional 10-90 day filtered data and demonstrated this pattern could be represented by the fifth mode of the rotated empirical orthogonal function. Its principal component was further analyzed using the singular spectrum analysis. Their result showed two oscillatory modes with periods of 36-40 days and 22-28 days, of which the former was related to the MJO influence and the latter linked to the remote forcing over southwest of Australia, which produced a wave train propagating southeastward, rounding the southern tip of South America and returning back toward the northeast. The 22-28 day mode has distinct impact on SACZ, responsible for the regional seesaw pattern of alternating dry and wet conditions. In this study we will focus on the 30-60-day spectral band and investigate whether the independent oscillation source over tropical South America is existed. First, we will show the seasonal dependence of the tropical South American ISV in Section 3. Then, the leading principal modes of 30-60 day bandpass filtered 850-hPa velocity potential (VP850) will be computed to distinguish the stationary ISV over tropical South America (SISA) from the propagating MJO in the austral summertime in Section 4. The importance of SISA in representing the regional ISV over South America will be discussed. In Section 5, we will demonstrate the mass oscillation regime of SISA, which is well separated from that of MJO by the Andes, and the convective coupling with rainfall. The dynamical response of SISA and the impact on the South American summer monsoon (SASM) will be presented. Finally, we will give the concluding remarks.

Zhou, Jiayu↗