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SO(3)-invariant PCA with application to molecular data
Principal component analysis (PCA) is a fundamental technique for dimensionality reduction and denoising; however, its application to three-dimensional data with arbitrary orientations -- common in structural biology -- presents significant challenges. A naive approach requires augmenting the dataset with many rotated copies of each sample, incurring prohibitive computational costs. In this paper, we extend PCA to 3D volumetric datasets with unknown orientations by developing an efficient and principled framework for SO(3)-invariant PCA that implicitly accounts for all rotations without explicit data augmentation. By exploiting underlying algebraic structure, we demonstrate that the computation involves only the square root of the total number of covariance entries, resulting in a substantial reduction in complexity. We validate the method on real-world molecular datasets, demonstrating its effectiveness and opening up new possibilities for large-scale, high-dimensional reconstruction problems.
What drives the variance of galaxy spectra?
We present a study aimed at understanding the physical phenomena underlying the formation and evolution of galaxies following a data-driven analysis of spectroscopic data based on the variance in a carefully selected sample. We apply principal component analysis (PCA) independently to three subsets of continuum-subtracted optical spectra, segregated into their nebular emission activity as quiescent, star-forming, and active galactic nuclei (AGNs). We emphasize that the variance of the input data in this work only relates to the absorption lines in the photospheres of the stellar populations. The sample is taken from the Sloan Digital Sky Survey (SDSS) in the stellar velocity dispersion range 100–150 km s −1 , to minimize the ‘blurring’ effect of the stellar motion. We restrict the analysis to the first three principal components (PCs) and find that PCA segregates the three types with the highest variance mapping SSP-equivalent age, along with an inextricable degeneracy with metallicity, even when all three PCs are included. Spectral fitting shows that stellar age dominates PC1, whereas PC2 and PC3 have a mixed dependence of age and metallicity. The trends support – independently of any model fitting – the hypothesis of an evolutionary sequence from star formation to AGN to quiescence. As a further test of the consistency of the analysis, we apply the same methodology in different spectral windows, finding similar trends, but the variance is maximal in the blue wavelength range, roughly around the 4000 Å break.
Mapping Rare Earths and Toxics in E-Waste via Hyperspectral Imaging and Machine Learning
Electronic waste (e-waste) presents a mounting challenge to environmental sustainability due to its complex composition, which includes high-value rare earth elements, hazardous organic compounds, and non-recyclable plastics. Accurate and scalable material classification is essential for enabling efficient resource recovery and safe recycling practices. This study introduces a confidence-aware classification pipeline that combines mid-infrared hyperspectral imaging (HSI), spectral angle mapping (SAM), and iterative machine learning to perform pixel-level material identification across e-waste devices. A curated spectral library encompassing artificial materials (e.g., plastic iron oxide, galvanized metals), minerals (e.g., allanite, hematite), and organic compounds (e.g., benzanthracene, toluene) was used to generate pseudo-labels, each assigned a confidence score based on SAM-derived spectral similarity. High-confidence samples from seven consumer electronics—digital cameras, keyboards, laptop fans, modems, motherboards, TV remotes, and speakers—were iteratively expanded and classified using models such as Support Vector Machine (SVM), Random Forest, Gradient Boosting Classifier, Partial Least Squares Discriminant Analysis (PLSDA) and Logistic Regression. The best-performing classifiers achieved macro F1 scores approaching 1.0. Results revealed widespread plastic content (dominated by plastic iron oxide), the presence of rare earth-bearing minerals like cerium-containing allanite, and pervasive detection of hazardous organics such as benzanthracene. Principal Component Analysis (PCA) visualizations and confusion matrices confirmed high separability and robust classification performance. This methodology enables precise, non-destructive, and scalable classification of heterogeneous e-waste streams. It supports automated, hazard-aware sorting in recycling workflows, facilitating selective recovery of critical materials and compliance with circular economy goals. The confidence-aware framework provides a foundation for real-time deployment in industrial settings, offering significant implications for smart e-recycling infrastructure and policy-driven material stewardship.
Structuring Nutrient Yields throughout Mississippi/Atchafalaya River Basin Using Machine Learning Approaches
To minimize the eutrophication pressure along the Gulf of Mexico or reduce the size of the hypoxic zone in the Gulf of Mexico, it is important to understand the underlying temporal and spatial variations and correlations in excess nutrient loads, which are strongly associated with the formation of hypoxia. This study’s objective was to reveal and visualize structures in high-dimensional datasets of nutrient yield distributions throughout the Mississippi/Atchafalaya River Basin (MARB). For this purpose, the annual mean nutrient concentrations were collected from thirty-three US Geological Survey (USGS) water stations scattered in the upper and lower MARB from 1996 to 2020. Eight surface water quality indicators were selected to make comparisons among water stations along the MARB over the past two decades. Principal component analysis (PCA) was used to comprehensively evaluate the nutrient yields across thirty-three USGS monitoring stations and identify the major contributing nutrient loads. The results showed that all samples could be analyzed using two main components, which accounted for 81.6% of the total variance. The PCA results showed that yields of orthophosphate (OP), silica (SI), nitrate–nitrites (NO 3 -NO 2 ), and total suspended sediment (TSS) are major contributors to nutrient yields. It also showed that land-planted crops, density of population, domestic and industrial discharges, and precipitation are fundamental causes of excess nutrient loads in MARB. These factors are of great significance for the excess nutrient load management and pollution control of the Mississippi River. It was found that the average nutrient yields were stable within the sub-MARB area, but the large nitrogen yields in the upper MARB and the large phosphorus yields in the lower MARB were of great concern. t-distributed stochastic neighbor embedding (t-SNE) revealed interesting nonlinear and local structures in nutrient yield distributions. Clustering analysis (CA) showed the detailed development of similarities in the nutrient yield distribution. Moreover, PCA, t-SNE, and CA showed consistent clustering results. This study demonstrated that the integration of dimension reduction techniques, PCA, and t-SNE with CA techniques in machine learning are effective tools for the visualization of the structures of the correlations in high-dimensional datasets of nutrient yields and provide a comprehensive understanding of the correlations in the distributions of nutrient loads across the MARB.
Reducing the matrix effect in mass spectral imaging of biofilms using flow-cell culture
The interactions between soil microorganisms and soil minerals play a crucial role in the formation and evolution of minerals and the stability of soil aggregates. Due to the heterogeneity and diversity of the soil environment, the under-standing of the functions of bacterial biofilms in soil minerals at the microscale is limited. A soil mineral-bacterial biofilm system was used as a model in this study, and it was analyzed by time-of-flight secondary ion mass spectrometry (ToF-SIMS) to acquire molecular level information. Static culture in multi-wells and dynamic flow-cell culture in microfluidics of biofilms were investigated. Our results show that more characteristic molecules of biofilms can be observed in SIMS spectra of the flow-cell culture. In contrast, biofilm signature peaks are buried under the mineral components in SIMS spectra in the static culture case. Spectral overlay was used in peak selection prior to performing Principal component analysis (PCA). Comparisons of the PCA results between the static and flow-cell culture show more pronounced molecular features and higher loadings of organic peaks of the dynamic cultured specimens. For example, fatty acids secreted from bacterial biofilm extracellular polymeric substance are likely to be responsible for biofilm dispersal due to mineral treatment up to 48 h. Such findings suggest that the use of microfluidic cells to dynamically culture biofilms be a more suitable method for reducing the matrix effect arisen from the growth medium and minerals as a perturbation fac-tor for improved spectral and multivariate analysis of complex mass spectral data in ToF-SIMS. These results show that the interaction mechanism between biofilms and soil minerals at the molecular level can be better studied using the flow-cell culture and advanced mass spectral imaging techniques like ToF-SIMS.
Predicting non-linear stress–strain response of mesostructured cellular materials using supervised autoencoder
Recent breakthroughs in advanced manufacturing capabilities have made it possible to design and print sophisticated topologies of cellular structures using diverse engineering materials such as metals, polymers, and ceramics. In these architectured materials, it is often desirable to tailor the mechanical properties by altering the unit cell topology. This necessitates an in-depth understanding of how the topology of the unit cell structure affects the macroscopic behavior of the material in both the linear and the non-linear regimes encountered under large compression. Here, we have developed a machine learning (ML) approach capable of accelerating the prediction of the stress–strain response of a polymer-based cellular structure under uniaxial confined compression. As part of generating the training data for ML, 60,000 mesostructures were generated using a relatively novel approach based on cellular automata, and their corresponding stress–strain responses were obtained from the finite element simulations. Principal component analysis (PCA) was used to reduce the dimensionality of the stress–strain curves. With only 20 principal components, PCA captured 99.89% of the variance in the stress–strain curves while reducing the dimensionality by 5X. ML using supervised autoencoder was able to successfully speed up the prediction of the non-linear stress–strain response of a unit cell by up to 4600X. The proposed method can serve as an efficient data generation tool and a rapid means for predicting the structure–property relationship through accelerated forward modeling of cellular materials under compaction, in cases where the macroscopic stress–strain response is governed by the unit-cell topology.
DEEPEN Global Standardized Categorical Exploration Datasets for Magmatic Plays
DEEPEN stands for DE-risking Exploration of geothermal Plays in magmatic ENvironments. As part of the development of the DEEPEN 3D play fairway analysis (PFA) methodology for magmatic plays (conventional hydrothermal, superhot EGS, and supercritical), weights needed to be developed for use in the weighted sum of the different favorability index models produced from geoscientific exploration datasets. This was done using two different approaches: one based on expert opinions, and one based on statistical learning. This GDR submission includes the datasets used to produce the statistical learning-based weights. While expert opinions allow us to include more nuanced information in the weights, expert opinions are subject to human bias. Data-centric or statistical approaches help to overcome these potential human biases by focusing on and drawing conclusions from the data alone. The drawback is that, to apply these types of approaches, a dataset is needed. Therefore, we attempted to build comprehensive standardized datasets mapping anomalies in each exploration dataset to each component of each play. This data was gathered through a literature review focused on magmatic hydrothermal plays along with well-characterized areas where superhot or supercritical conditions are thought to exist. Datasets were assembled for all three play types, but the hydrothermal dataset is the least complete due to its relatively low priority. For each known or assumed resource, the dataset states what anomaly in each exploration dataset is associated with each component of the system. The data is only a semi-quantitative, where values are either high, medium, or low, relative to background levels. In addition, the dataset has significant gaps, as not every possible exploration dataset has been collected and analyzed at every known or suspected geothermal resource area, in the context of all possible play types. The following training sites were used to assemble this dataset: - Conventional magmatic hydrothermal: Akutan (from AK PFA), Oregon Cascades PFA, Glass Buttes OR, Mauna Kea (from HI PFA), Lanai (from HI PFA), Mt St Helens Shear Zone (from WA PFA), Wind River Valley (From WA PFA), Mount Baker (from WA PFA). - Superhot EGS: Newberry (EGS demonstration project), Coso (EGS demonstration project), Geysers (EGS demonstration project), Eastern Snake River Plain (EGS demonstration project), Utah FORGE, Larderello, Kakkonda, Taupo Volcanic Zone, Acoculco, Krafla. - Supercritical: Coso, Geysers, Salton Sea, Larderello, Los Humeros, Taupo Volcanic Zone, Krafla, Reyjanes, Hengill. **Disclaimer: Treat the supercritical fluid anomalies with skepticism. They are based on assumptions due to the general lack of confirmed supercritical fluid encounters and samples at the sites included in this dataset, at the time of assembling the dataset. The main assumption was that the supercritical fluid in a given geothermal system has shared properties with the hydrothermal fluid, which may not be the case in reality. Once the datasets were assembled, principal component analysis (PCA) was applied to each. PCA is an unsupervised statistical learning technique, meaning that labels are not required on the data, that summarized the directions of variance in the data. This approach was chosen because our labels are not certain, i.e., we do not know with 100% confidence that superhot resources exist at all the assumed positive areas. We also do not have data for any known non-geothermal areas, meaning that it would be challenging to apply a supervised learning technique. In order to generate weights from the PCA, an analysis of the PCA loading values was conducted. PCA loading values represent how much a feature is contributing to each principal component, and therefore the overall variance in the data.
PCA -BASED COMPRESSOR HARDWARE DESIGN GENERATOR IN CHISEL
SF-25-077 This repository includes a hardware generator written in Chisel that generates lossy compression hardware designs based on principal component analysis (PCA), along with a flexible testbench. It also includes a Python tool for evaluating the accuracy loss of integer quantization.
A co-kurtosis PCA based dimensionality reduction with nonlinear reconstruction using neural networks
For turbulent reacting flow systems, identification of low-dimensional representations of the thermo-chemical state space is vitally important, primarily to significantly reduce the computational cost of device-scale simulations. Principal component analysis (PCA), and its variants, are a widely employed class of methods. Recently, an alternative technique that focuses on higher-order statistical interactions, co-kurtosis PCA (CoK-PCA), has been shown to effectively provide a low-dimensional representation by capturing the stiff chemical dynamics associated with spatiotemporally localized reaction zones. While its effectiveness has only been demonstrated based on a priori analyses with linear reconstruction, in this work, we employ nonlinear techniques to reconstruct the full thermo-chemical state and evaluate the efficacy of CoK-PCA compared to PCA. Specifically, we combine a CoK-PCA-/PCA-based dimensionality reduction (encoding) with an artificial neural network (ANN) based reconstruction (decoding) and examine, a priori, the reconstruction errors of the thermo-chemical state. In addition, we evaluate the errors in species production rates and heat release rates, which are nonlinear functions of the reconstructed state, as a measure of the overall accuracy of the dimensionality reduction technique. We employ four datasets to assess CoK-PCA/PCA coupled with ANN-based reconstruction: zero-dimensional (homogeneous) reactor for autoignition of an ethylene/air mixture that has conventional single-stage ignition kinetics, a dimethyl ether (DME)/air mixture which has two-stage (low and high temperature) ignition kinetics, a one-dimensional freely propagating premixed ethylene/air laminar flame, and a two-dimensional dataset representing turbulent autoignition of ethanol in a homogeneous charge compression ignition (HCCI) engine. Finally, results from the analyses demonstrate the robustness of the CoK-PCA based low-dimensional manifold with ANN reconstruction in accurately capturing the data, specifically from the reaction zones.
Using the optimal combined index weight ratio to improve the probability of anomaly detection in big area additive manufacturing
Big Area Additive Manufacturing (BAAM) of composites requires significant time, energy, and material, so it is critical to reduce production inefficiencies to make functional parts without multiple iterations. Statistical process control coupled with Principal Component Analysis (PCA) is a powerful technique that provides a quick, computationally inexpensive, and intuitive way for operators to detect defects that form in a manufacturing process without massive datasets. Recently, a combined index that is a weighted sum of the Hotelling's T 2 and squared residual error statistics has been proposed that can be monitored in one chart, improving interpretation accuracy and simplicity. However, the literature does not offer a formal method to optimise the weights. Here, we introduce two new approaches to the traditional weight selection approach using simulated and BAAM image data. Approach 1 uses a theoretically motivated optimum inspired by probabilistic principal component analysis. Approach 2 systematically varies the ratio of the weights to find the optimum. We show that approach 1 delivers optimal anomaly detection performance in select cases while approach 2 fares better in practice. Surprisingly, we also show that choosing a more complex PCA model has a minimal negative impact on anomaly detection performance compared to a more simplistic model.
Fault Detection via Occupation Kernel Principal Component Analysis
Reliable operation of automatic systems is heavily dependent on the ability to detect faults in the underlying dynamics. While traditional model-based methods have been widely used for fault detection, data-driven approaches have garnered increasing attention due to their ease of deployment and minimal need for expert knowledge. In this letter, we present a novel principal component analysis (PCA) method that uses occupation kernels. Occupation kernels result in feature maps that are tailored to the measured data, have inherent noise-robustness due to the use of integration, and can utilize irregularly sampled system trajectories of variable lengths for PCA. The occupation kernel PCA method is used to develop a reconstruction error approach to fault detection and its efficacy is validated using numerical simulations.
Effects of 9.5 years warming on SOC concentration and composition in bulk soil and density fractions
Original data of whole-soil warming experiment after 9.5 years at Blodgett Forest Research Station. The Blodgett Forest is a mixed coniferous temperate forest with Mediterranean climate. The annual air temperature is 12.5℃ and the annual precipitation is 1774 mm yr-1- The soil is mesic ultic Alfisol of granitic origin, equivalent to Dystric Cambisol according to The World Reference Base for Soil Resources (WRB) system. The soil is warmed down to 1 m at + 4℃ by vertically installed heating cables. At the time of soil sampling on 1 May 2023, the whole-soil warming experiment had been running for approximately 9.5 years, from January 2014 to May 2023. The dataset includes: - Bulk_EA: C, N content, δ13C, and CN ratio of bulk soil; - Density_fractionation: organic carbon concentration, δ13C, and C/N ratio of free light fraction (fLF), occluded ligh fraction (oLF), and heavy fraction (HF); - PCA_DRIFT_AUC: original data of area under the curve (AUC) values of eight carbon bond types integrated on diffuse reflectance infrared fourier transform spectroscopy for each soil sample and soil fraction, which are consequently used for principal component analysis (PCA); - DRIFTS_stability_index: the calculation of aliphatic C–H (3000–2800 cm-1) to aromatic C=C (1670–1600 cm-1) ratios for each bulk soil sample and soil fraction. All data are provided in CSV format and can be viewed using Microsoft Excel.
Data-driven analysis and prediction of wastewater treatment plant performance: Insights and forecasting for sustainable operations
Here this study presents a comprehensive performance and forecasting analysis of the As-Samra wastewater treatment plant (WWTP) in Jordan, with two main objectives. Firstly, a thorough evaluation of the plant's performance is conducted. The analysis involves independently assessing historical operational conditions, plant production, and their statistical correlations using various statistical techniques. The second objective focuses on developing a data-driven forecasting approach to predict the plant's production one month in advance, using multiple machine learning models. The results highlight the effectiveness of principal component analysis (PCA) in simplifying operational data, revealing distinct operational clusters, and identifying seasonal production patterns while showing correlations between operational conditions and overall power production. The support vector machine (SVM) forecasting model emerged as the top performer, showcasing the potential of a hybrid forecasting approach. The findings offer valuable perspectives for enhancing operational efficiency, refining production planning, and ultimately improving the environmental impact of the plant.
Beyond PCA: Additional Dimension Reduction Techniques to Consider in the Development of Climate Fingerprints
Abstract Dimension reduction techniques are an essential part of the climate analyst’s toolkit. Due to the enormous scale of climate data, dimension reduction methods are used to identify major patterns of variability within climate dynamics, to create compelling and informative visualizations, and to quantify major named modes such as El Niño–Southern Oscillation. Principal components analysis (PCA), also known as the method of empirical orthogonal functions (EOFs), is the most commonly used form of dimension reduction, characterized by a remarkable confluence of attractive mathematical, statistical, and computational properties. Despite its ubiquity, PCA suffers from several difficulties relevant to climate science: high computational burden with large datasets, decreased statistical accuracy in high dimensions, and difficulties comparing across multiple datasets. In this paper, we introduce several variants of PCA that are likely to be of use in climate sciences and address these problems. Specifically, we introduce non-negative , sparse , and tensor PCA and demonstrate how each approach provides superior pattern recognition in climate data. We also discuss approaches to comparing PCA-family results within and across datasets in a domain-relevant manner. We demonstrate these approaches through an analysis of several runs of the E3SM climate model from 1991 to 1995, focusing on the simulated response to the Mt. Pinatubo eruption; our findings are consistent with a recently identified stratospheric warming fingerprint associated with this type of stratospheric aerosol injection.
Uncertainty Quantification for Smooth Functional Data with Application to Material Properties
This document outlines a method for processing functional output (i.e., curves) for the ultimate purpose of sampling curves under specified input conditions for use in modeling and simulation uncertainty quantification (UQ) studies. A set of benchmark curves sufficiently representative of the relevant scenario(s) being simulated are provided to the process and formatted as described in Section 1. Principal Component Analysis (PCA) is utilized to discover the components of uncertainty in the benchmark curves and is outlined in Section 2. Section 3 describes the application of uncertainty quantification to the PCA results for the purpose of sampling curves to be used in UQ analysis. Section 4 applies these techniques to an example benchmark dataset. Concluding remarks are provided in the final section.
Elemental and isotopic signatures of Asteroid Ryugu support three early Solar System reservoirs
Understanding the number and locations of different reservoirs present in the early Solar System is crucial to understanding the Solar System’s origin and evolution. Previous work has suggested that three unique isotopic reservoirs existed in the early Solar System but subsequent works have challenged that idea. Here we present elemental abundances along with Ca, Ti, Cr, Fe, Ni, and Zn isotopic data from primitive material returned by the Japan Aerospace Exploration Agency’s (JAXA) Hayabusa2 mission to asteroid (162173) Ryugu to make inferences on the Solar System’s early architecture. Data from Ryugu particle A0208 are consistent with a close genetic heritage between Ryugu and CI chondrites. Here, we employ principal component analysis (PCA) on these Ryugu and published meteorite data to demonstrate that Ryugu and CI chondrites are distinct from other known astromaterials, strongly supporting the existence of a third major isotopic reservoir in the early Solar System.
Modeling MTS pyrolysis and SiC deposition kinetics using principal component analysis and neural networks
Accurate chemical kinetics modeling is crucial for improving the efficiency of chemical processing and synthesis of ceramic matrix composites. Detailed kinetic models are computationally expensive due to the large number of transported chemical species, while the simplified physics-based models, such as single-step global mechanisms, are efficient but often overlook key chemical intermediates and pathways. Recent deep learning approaches promise accurate and cost-effective models. Yet, they require additional closures for the transported nonlinear latent variables, complicating integration with existing solvers. In this work, we develop a hybrid linear—nonlinear reduced model for silicon carbide deposition from methyltrichlorosilane precursor by combining principal component analysis (PCA) and autoencoder (AE) neural network (NN) approaches. PCA is used to identify a smaller set of linear transport variables, enabling direct reuse of conventional transport solvers. NNs then reconstruct the full chemical state from these reduced variables. We demonstrate the method on a chemical vapor deposition reactor—comprising a gas-phase pyrolysis plug flow reactor and a heterogeneous surface reactor—over a wide range of temperatures, pressures, and residence times. Our PCA–AE model achieves high accuracy with only five transported scalars, achieving an eightfold cost reduction compared to detailed mechanisms, in both a priori (using data from the test set only) and a posteriori (coupled with a differential equation solver). In conclusion, notable errors arise primarily near training domain boundaries and for long residence times, indicating the need for domain shift indicators and better long-horizon predictions in future reduced chemistry model development.