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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 OSTI2020

The Langmuir probe system in the Wendelstein 7-X test divertor

Here, the design and evaluation of the Langmuir probe system used in the first divertor operation phase of Wendelstein 7-X is described. The probes are integrated into the target plates and have individually facetted surfaces to keep the angle of incidence of the magnetic field within an appropriate range for different magnetic configurations. Multiple models for the derivation of plasma parameters from current–voltage characteristics are introduced. These are analyzed with regard to their assumptions and limitations, generalized, and adapted to our use case. A detailed comparison is made to determine the most suitable model. It is found that the choice of model has a large impact, for example, resulting in a change in the inferred temperatures of up to a factor two. This evaluation is implemented in a Bayesian modeling framework and automated to allow for joint analysis with other diagnostics and a replacement of ad hoc assumptions. We rigorously treat parameter uncertainties, revealing strong correlations between them. General and flexible model formulations permit an expansion to additional effects.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Impact of genotype‐calling methodologies on genome‐wide association and genomic prediction in polyploids

Abstract Discovery and analysis of genetic variants underlying agriculturally important traits are key to molecular breeding of crops. Reduced representation approaches have provided cost‐efficient genotyping using next‐generation sequencing. However, accurate genotype calling from next‐generation sequencing data is challenging, particularly in polyploid species due to their genome complexity. Recently developed Bayesian statistical methods implemented in available software packages, polyRAD, EBG, and updog, incorporate error rates and population parameters to accurately estimate allelic dosage across any ploidy. We used empirical and simulated data to evaluate the three Bayesian algorithms and demonstrated their impact on the power of genome‐wide association study (GWAS) analysis and the accuracy of genomic prediction. We further incorporated uncertainty in allelic dosage estimation by testing continuous genotype calls and comparing their performance to discrete genotypes in GWAS and genomic prediction. We tested the genotype‐calling methods using data from two autotetraploid species, Miscanthus sacchariflorus and Vaccinium corymbosum , and performed GWAS and genomic prediction. In the empirical study, the tested Bayesian genotype‐calling algorithms differed in their downstream effects on GWAS and genomic prediction, with some showing advantages over others. Through subsequent simulation studies, we observed that at low read depth, polyRAD was advantageous in its effect on GWAS power and limit of false positives. Additionally, we found that continuous genotypes increased the accuracy of genomic prediction, by reducing genotyping error, particularly at low sequencing depth. Our results indicate that by using the Bayesian algorithm implemented in polyRAD and continuous genotypes, we can accurately and cost‐efficiently implement GWAS and genomic prediction in polyploid crops.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

BayFlux: A Bayesian method to quantify metabolic Fluxes and their uncertainty at the genome scale

Metabolic fluxes, the number of metabolites traversing each biochemical reaction in a cell per unit time, are crucial for assessing and understanding cell function. 13 C Metabolic Flux Analysis ( 13 C MFA) is considered to be the gold standard for measuring metabolic fluxes. 13 C MFA typically works by leveraging extracellular exchange fluxes as well as data from 13 C labeling experiments to calculate the flux profile which best fit the data for a small, central carbon, metabolic model. However, the nonlinear nature of the 13 C MFA fitting procedure means that several flux profiles fit the experimental data within the experimental error, and traditional optimization methods offer only a partial or skewed picture, especially in “non-gaussian” situations where multiple very distinct flux regions fit the data equally well. Here, we present a method for flux space sampling through Bayesian inference (BayFlux), that identifies the full distribution of fluxes compatible with experimental data for a comprehensive genome-scale model. This Bayesian approach allows us to accurately quantify uncertainty in calculated fluxes. We also find that, surprisingly, the genome-scale model of metabolism produces narrower flux distributions (reduced uncertainty) than the small core metabolic models traditionally used in 13 C MFA. The different results for some reactions when using genome-scale models vs core metabolic models advise caution in assuming strong inferences from 13 C MFA since the results may depend significantly on the completeness of the model used. Based on BayFlux, we developed and evaluated novel methods (P- 13 C MOMA and P- 13 C ROOM) to predict the biological results of a gene knockout, that improve on the traditional MOMA and ROOM methods by quantifying prediction uncertainty.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

New approaches to Bayesian uncertainty quantification for Nuclear Science (Final Technical Report)

Inverse problems play a central role in experimentation and theory/data comparisons for many areas of modern Nuclear Physics (NP) and High-Energy Physics (HEP). Bayes’s Theorem is a powerful tool for solving Inverse Problems, providing conceptually transparent and unbiased constraints on theoretical parameters and their uncertainties (“Bayesian Inference”) and enabling the quantification of agreement or tension between models and data. However, analyses based on Bayesian Inference are often challenging for NP and HEP applications, either because of the large number of parameters in the problem, the high computational cost, or both. We propose a multi-institutional collaboration to develop and deploy novel Bayesian analysis tools that advance the scientific scope of a broad range of current and future NP experiments. This project brings together NP domain scientists working on several high-profile NP projects for which new, high-performance Bayesian Uncertainty Quantification (“Bayesian UQ”) methods are essential to carry out the science, and data scientists who are developing state-of-the-art methods applicable to these problems. The NP projects in this proposal comprise measurements of the mass and fundamental nature of the neutrino; study of the Quark-Gluon Plasma that filled the early universe; and mapping of natural and anthropogenic radiation environments. While these NP projects have very different scientific goals, with datasets and analysis approaches that differ significantly, they share common requirements for improving computationally intensive Bayesian analyses using advanced Machine Learning algorithms and will benefit strongly from a coherent effort to develop general solutions. This proposal brings together these projects and forefront ML-based data science algorithms to develop such general solutions. The methods developed in this project will also be more widely applicable, thereby advancing science in the larger Nuclear Physics portfolio.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

A probabilistic inverse prediction method for predicting plutonium processing conditions

In the past decade, nuclear chemists and physicists have been conducting studies to investigate the signatures associated with the production of special nuclear material (SNM). In particular, these studies aim to determine how various processing parameters impact the physical, chemical, and morphological properties of the resulting special nuclear material. By better understanding how these properties relate to the processing parameters, scientists can better contribute to nuclear forensics investigations by quantifying their results and ultimately shortening the forensic timeline. This paper aims to statistically analyze and quantify the relationships that exist between the processing conditions used in these experiments and the various properties of the nuclear end-product by invoking inverse methods. In particular, these methods make use of Bayesian Adaptive Spline Surface models in conjunction with Bayesian model calibration techniques to probabilistically determine processing conditions as an inverse function of morphological characteristics. Not only does the model presented in this paper allow for providing point estimates of a sample of special nuclear material, but it also incorporates uncertainty into these predictions. This model proves sufficient for predicting processing conditions within a standard deviation of the observed processing conditions, on average, provides a solid foundation for future work in predicting processing conditions of particles of special nuclear material using only their observed morphological characteristics, and is generalizable to the field of chemometrics for applicability across different materials.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Bayesian Tensor Decompositions for Scalable Supervised Learning of Scientific Data (Final Report)

In this document we highlight the detailed accomplishments and progress that we have made in this period. This progress seeks to address the three main objectives to provide new algorithms for quantifying uncertainty in low-multilinear-rank models and to leverage them for data analysis. These include: (1) develop probabilistic models for low-multilinear-rank functions; (2) develop a suite of Bayesian learning approaches to learn the probabilistic models from data; (3) apply the techniques on challenging problems arising in DOE-relevant applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Understanding Model Inadequacy in TRISO Nuclear Fuel Fission Products Release Models: Empirical and Mechanistic Approaches

The increasing use of tristructural isotropic (TRISO) particle fuel in both advanced and existing reactors necessitates a thorough evaluation of uncertainties and shortcomings in TRISO fission product release models. These inadequacies arise from the simplifications made in computational models compared to experimental data. Utilizing the BISON fuel performance code and experimental data from the Advanced Gas Reactor (AGR) program provides a unique chance to rigorously assess these inadequacies within a Bayesian uncertainty quantification (UQ) framework. This study contrasts the standard Bayesian framework with the Kennedy-O'Hagan (KOH) framework, which explicitly accounts for modeling inadequacies, in the context of UQ for TRISO silver release models. It examines both the traditional Arrhenius equation and a more advanced lower-length-scale (LLS)-informed model that incorporates microstructure information. The inverse UQ process applied to AGR-2 and AGR-3/4 datasets identified modeling inadequacy as the primary source of uncertainty, with experimental noise also being significant, while model parameter uncertainty was minimal. Both the Arrhenius and LLS-informed models showed similar levels of modeling inadequacy. For forward predictive UQ using the AGR-1 dataset, the KOH framework enhanced the accuracy and quality of quantified uncertainties by approximately 30% and 40%, respectively, compared to the standard Bayesian framework. This improvement was observed for both the Arrhenius and LLS-informed models. At the engineering scale, both models performed similarly, but the LLS-informed model outperformed the Arrhenius equation at the mesoscale. These findings underscore the importance of explicitly considering modeling inadequacy in the UQ process and highlight the need for ongoing refinement of physics-based models to address these shortcomings.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Accurate and Rapid Forecasts for Geologic Carbon Storage via Learning-Based Inversion-Free Prediction

Carbon capture and storage (CCS) is one approach being studied by the U.S. Department of Energy to help mitigate global warming. The process involves capturing CO 2 emissions from industrial sources and permanently storing them in deep geologic formations (storage reservoirs). However, CCS projects generally target “green field sites,” where there is often little characterization data and therefore large uncertainty about the petrophysical properties and other geologic attributes of the storage reservoir. Consequently, ensemble-based approaches are often used to forecast multiple realizations prior to CO 2 injection to visualize a range of potential outcomes. In addition, monitoring data during injection operations are used to update the pre-injection forecasts and thereby improve agreement between forecasted and observed behavior. Thus, a system for generating accurate, timely forecasts of pressure buildup and CO 2 movement and distribution within the storage reservoir and for updating those forecasts via monitoring measurements becomes crucial. This study proposes a learning-based prediction method that can accurately and rapidly forecast spatial distribution of CO 2 concentration and pressure with uncertainty quantification without relying on traditional inverse modeling. The machine learning techniques include dimension reduction, multivariate data analysis, and Bayesian learning. The outcome is expected to provide CO 2 storage site operators with an effective tool for timely and informative decision making based on limited simulation and monitoring data.

58 GEOSCIENCES↗
DOE OSTI2021

Overview of Algorithms for Using Particle Morphology in Pre-Detonation Nuclear Forensics

A major goal in pre-detonation nuclear forensics is to infer the processing conditions and/or facility type that produced radiological material. This review paper focuses on analyses of particle size, shape, texture (“morphology”) signatures that could provide information on the provenance of interdicted materials. For example, uranium ore concentrates (UOC or yellowcake) include ammonium diuranate (ADU), ammonium uranyl carbonate (AUC), sodium diuranate (SDU), magnesium diuranate (MDU), and others, each prepared using different salts to precipitate U from solution. Once precipitated, UOCs are often dried and calcined to remove adsorbed water. The products can be allowed to react further, forming uranium oxides UO3, U3O8, or UO2 powders, whose surface morphology can be indicative of precipitation and/or calcination conditions used in their production. This review paper describes statistical issues and approaches in using quantitative analyses of measurements such as particle size and shape to infer production conditions. Statistical topics include multivariate t tests (Hotelling’s T 2 ), design of experiments, and several machine learning (ML) options including decision trees, learning vector quantization neural networks, mixture discriminant analysis, and approximate Bayesian computation (ABC). ABC is emphasized as an attractive option to include the effects of model uncertainty in the selected and fitted forward model used for inferring processing conditions.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2021

Combining Astrometry and Elemental Abundances: The Case of the Candidate Pre-Gaia Halo Moving Groups G03-37, G18-39, and G21-22

While most moving groups are young and nearby, a small number have been identified in the Galactic halo. Understanding the origin and evolution of these groups is an important piece of reconstructing the formation history of the halo. Here we report on our analysis of three putative halo moving groups: G03-37, G18-39, and G21-22. Based on Gaia EDR3 data, the stars associated with each group show some scatter in velocity (e.g., Toomre diagram) and integrals of motion (energy, angular momentum) spaces, counter to expectations of moving-group stars. We choose the best candidate of the three groups, G21-22, for follow-up chemical analysis based on high-resolution spectroscopy of six presumptive members. Using a new Python code that uses a Bayesian method to self-consistently propagate uncertainties from stellar atmosphere solutions in calculating individual abundances and spectral synthesis, we derive the abundances of α- (Mg, Si, Ca, Ti), Fe-peak (Cr, Sc, Mn, Fe, Ni), odd-Z (Na, Al, V), and neutron-capture (Ba, Eu) elements for each star. We find that the G21-22 stars are not chemically homogeneous. Based on the kinematic analysis for all three groups and the chemical analysis for G21-22, we conclude the three are not genuine moving groups. The case for G21-22 demonstrates the benefit of combining kinematic and chemical information in identifying conatal populations when either alone may be insufficient. Comparing the integrals of motion and velocities of the six G21-22 stars with those of known structures in the halo, we tentatively associate them with the Gaia-Enceladus accretion event.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

An entropy-based debiasing approach to quantifying experimental coverage for novel applications of interest in the nuclear community

This manuscript proposes a novel information-theoretic approach to the quantification of experimental relevance, i.e., coverage, to achieve optimal data assimilation results for nuclear engineering applications. Specifically, this work posits the need for a new metric, called coverage (q C ) of an application’s quantity of interest, i.e., eigenvalue or power peaking for an advanced reactor concept, defined herein as the theoretically maximum achievable reduction in the quantity’s uncertainty given measurements from a pool of experiments in a manner that is independent of the data assimilation procedure employed. Currently, reduction in a quantity’s uncertainty is strongly biased by the underlying assumptions of the assimilation procedure to account for the under-determined nature of such problems and the similarity criterion employed to identify relevant experiments. To address this challenge, this work has developed a coverage metric, q C , based on mutual information, which establishes a new conceptual framework for assessing coverage, one that is independent of the model parameters and responses degree of variations in both the experimental and application domains, i.e., linear vs non-linear, and their prior uncertainty distributions, i.e., Gaussian vs. non-Gaussian. The q C is an entropic measure capable of addressing coverage for general nonlinear problems with non-Gaussian uncertainties and inclusive of the measurement uncertainties from multiple experiments. Numerical experiments from manufactured analytical problems as well as a set of benchmarks from the ICSBEP handbook are employed to demonstrate its theoretical and practical performance as compared to the c k -based experiment selection methodology, commonly employed in the neutronic community. The manuscript then employs other well-known adaptations to existing data assimilation methodologies for nonlinear and non-Gaussian problems capable of achieving the coverage posited by q C .

Bayesian data assimilation↗
DOE OSTI2020

Detection of atmospheric rivers with inline uncertainty quantification: TECA-BARD v1.0.1

It has become increasingly common for researchers to utilize methods that identify weather features in climate models. There is an increasing recognition that the uncertainty associated with choice of detection method may affect our scientific understanding. For example, results from the Atmospheric River Tracking Method Intercomparison Project (ARTMIP) indicate that there are a broad range of plausible atmospheric river (AR) detectors and that scientific results can depend on the algorithm used. There are similar examples from the literature on extratropical cyclones and tropical cyclones. It is therefore imperative to develop detection techniques that explicitly quantify the uncertainty associated with the detection of events. We seek to answer the following question: given a “plausible” AR detector, how does uncertainty in the detector quantitatively impact scientific results? We develop a large dataset of global AR counts, manually identified by a set of eight researchers with expertise in atmospheric science, which we use to constrain parameters in a novel AR detection method. We use a Bayesian framework to sample from the set of AR detector parameters that yield AR counts similar to the expert database of AR counts; this yields a set of “plausible” AR detectors from which we can assess quantitative uncertainty. This probabilistic AR detector has been implemented in the Toolkit for Extreme Climate Analysis (TECA), which allows for efficient processing of petabyte-scale datasets. We apply the TECA Bayesian AR Detector, TECA-BARD v1.0.1, to the MERRA-2 reanalysis and show that the sign of the correlation between global AR count and El Niño–Southern Oscillation depends on the set of parameters used.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Unpacking model inadequacy: The quantification of silver release from TRISO fuel by considering empirical and mechanistic approaches

Increasing adoption of the proposed tristructural isotropic (TRISO) particle fuel for both advanced and existing reactors makes it critical to assess and address any uncertainties and inadequacies of TRISO fission product release models. Model inadequacy stems from simplifications made to the computational model when compared to the experiments. The modeling and simulation efforts conducted using the BISON fuel performance code, along with the experimental campaigns carried out under the Advanced Gas Reactor Fuel Development and Qualification Program, afford a unique opportunity to conduct a rigorous modeling inadequacy assessment within the Bayesian uncertainty quantification (UQ) framework. Here, this study compares the standard Bayesian framework against the Kennedy-O'Hagan (KOH) framework, which explicitly represents modeling inadequacy, in regard to UQ for TRISO silver release models. For this purpose, both the traditional Arrhenius equation fitted to experimental data and the more advanced lower-length-scale (LLS)-informed model, which considers microstructure information, are independently considered. Applying the inverse UQ process on the AGR-2 and -3/4 datasets revealed modeling inadequacy to be the most dominant source of uncertainty. Experimental noise uncertainty is also significant; however, model parameter uncertainty can be considered negligible. Interestingly, both the Arrhenius equation and the LLS-informed model demonstrated similar levels of modeling inadequacy. For the forward predictive UQ, the KOH framework improved both the accuracy and quality of quantified uncertainties in comparison to the standard Bayesian framework. This is true for both the Arrhenius equation and the LLS-informed model. In comparing these modeling approaches, both demonstrated similar performance at the engineering scale, while the LLS-informed model expectedly outperformed the Arrhenius equation at the mesoscale. These conclusions highlight the importance of explicitly accounting for modeling inadequacy in the UQ process, and reinforce the need for continuous refinement of physics-based models in order to address the modeling inadequacy.

Advanced reactors↗
DOE OSTI2024

Assay-based background projection for the Majorana Demonstrator using Monte Carlo uncertainty propagation

The background index (BI) is an important quantity to project and calculate the half-life sensitivity of neutrinoless double-𝛽 decay (0⁢𝜈⁢𝛽⁢𝛽) experiments. An analysis framework is presented to calculate the BI using the specific activities, masses, and simulated efficiencies of an experiments components as distributions. This Bayesian framework includes a unified approach to combine specific activities from assay. Monte Carlo uncertainty propagation is used to build a BI distribution from the specific activity, mass, and efficiency distributions. This method is applied to the M AJORANA D EMONSTRATOR , which deployed arrays of high-purity Ge detectors enriched in 76 Ge to search for 0⁢𝜈⁢𝛽⁢𝛽. The original assay-based projection is requantified in the new framework, using the as-built geometry of the Demonstrator and additional assay information. While 47% higher than the original projection, the resulting BI of [8.95±0.36]×10 −4 cts/(keVkgyr) from the 232 Th and 238 U decay chains does not account for the higher-than-expected BI observed by the D EMONSTRATOR . Finally, this method enables us to demonstrate the statistical incompatibility between the D EMONSTRATOR 's observed background and the assay results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Accurate and Timely Forecasts of Geologic Carbon Storage using Machine Learning Methods

Carbon capture and storage is one strategy to reduce greenhouse gas emissions. One approach to storing the captured CO2 is to inject it into deep saline aquifers. However, dynamics of the injected CO2 plume is uncertain and the potential for leakage back to the atmosphere must be assessed. Thus, accurate and timely forecasts of CO2 storage via real-time measurements integration becomes very crucial. This study proposes a learning-based, inverse-free prediction method that can accurately and rapidly forecast CO2 movement and distribution with uncertainty quantification based on limited simulation and observation data. The machine learning techniques include dimension reduction, multivariate data analysis, and Bayesian learning. The outcome is expected to provide CO2 storage site operators with an effective tool for real-time decision making.

Lu, Dan↗
DOE OSTI2023

Massively Parallel Bayesian Model Calibration and Uncertainty Quantification with Applications to Nuclear Fuels and Materials

The U.S. Department of Energy (DOE)’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel cycle systems. This program has been providing engineering-scale support for the development of BISON, a high-fidelity and high-resolution fuel performance tool. Fuel behavior in a nuclear reactor is governed by a complex network of mechanisms interacting with various other physics aspects in the reactor system. Any model developed to represent the fuel behavior will likely be idealized resulting in uncertainties in their predictions compared to the observed data. As such, this report was motivated by the need to identify the sources of uncertainties and quantify and propagate them through the fuel model outputs. Such quantification of uncertainties will establish a level of model trustworthiness, identify approaches to improve the model trustworthiness, and even guide optimal experiment design for maximal information gain. To accomplish the uncertainty quantification for computational models, this report has relied on the Bayesian framework which provides probabilistic treatment of models their inputs and outputs. The current state-of-the-art on performing Bayesian Uncertainty Quantification (UQ) for nuclear engineering models using High Performance Computing (HPC) resources have been reviewed. Implementation of capabilities for massively parallel Bayesian UQ in Multiphysics Object-Oriented Simulation Environment (MOOSE) is discussed. Several verification cases are discussed to verify the accuracy of the quantified uncertainties using the developed computational capabilities in MOOSE. Then, the problem of quantifying the uncertainties in TRI-Structural isOtropic (TRISO) fuel silver release is addressed. For the first time, the uncertainties arising from the TRISO Fission Gas Release (FGR) model due to model inadequacy and experimental noise are quantified. Also, the Bayesian capabilities are applied to the calibration of the MATPRO creep model, a widely used model in several fuel assessment cases. The impact of the prediction uncertainties in the MATPRO model on the fuel cladding behavior as part of the TRIBULATION assessment case (which is an integral effects case) is investigated. This report concludes with a discussion on the future work for the UQ for computational models.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Reduced scale stripline platform to extend accessible pressures on the Z machine: Shockless compression of platinum to 650 GPa

Reaching astrophysically relevant high energy density (HED) material states in the laboratory is an ongoing effort at multiple experimental facilities. We have developed a new dynamic compression platform for the Z Pulsed Power Facility that allows for sample sizes 100s of [Formula: see text]m in thickness that accommodate multiple grains in order to fully capture bulk properties, such as material strength. A pair of experiments compressed platinum (Pt) to HED conditions and conventional inverse Lagrangian analysis as well as a recent Bayesian calibration technique were used to determine the principal isentrope to 650 GPa with density uncertainties of <2%. These low uncertainties are calculated for single sample experiments, presenting the possibility of even smaller experimental uncertainties with multiple samples the platform allows. Our new platform extends the accessible Pt ramp pressures achievable on the Z machine to over 80% of the pressure recently achieved using the National Ignition Facility planar Hohlraum platform. This new capability, the next generation evolution of the stripline platform, was made possible by advancements in both our understanding of the Z pulsed power driver and our overall magnetohydrodynamic modeling capabilities.

Porwitzky, Andrew↗
DOE OSTI2022

Baycal

Bayesian Model Calibration (BayCal) toolkit is a software plugin for Risk Analysis Virtual Environment (RAVEN) framework, arming at inversely quantifying the uncertainties associated with simulation model parameters based on available experiment data. BayCal seeks statistical inference of the uncertain input parameters that are consistent with the available measurement data or observed data. The unique feature of BayCal is the capability to be linked with RAVEN to build corresponding calibration workflows for complex multi-physics simulations. In addition to be able to use the machine learning capability of RAVEN to significantly reduce the computational cost of expensive simulation models, another distinctive feature of BayCal is the capability to deal with high-dimensional correlated model outputs, such as time series observations at multiple locations, via principal component analysis (PCA) technique.

Wang, Congjian↗