Search NASA⌕ Search

SEARCH · Search NASA

Results for “Dimensionality reduction”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

From microbial diversity to functional potential using dimensionality reduction

The high dimensionality of microbial diversity data from ‘omics observations can be reduced using Machine Learning, with many recent studies showcasing ML utility for exploratory ecological feature finding and process prediction. Here, we compare the Self Organizing Map (SOM) dimensionality reduction method to the well-documented sample-based Principal Coordinate Analysis (PCoA) and taxa-based Weighted Gene Correlation Network Analysis (WGCNA) using near daily 16S rRNA gene amplicon sequencing data from the 2019 to 2020 MOSAiC International Arctic Drift Expedition. We then map k-means clustering outputs from each method to available metagenomes, extracting functionally distinct seasonal microbial ecotypes in the surface Arctic Ocean. Our results indicate the SOM method better represented expected seasonal transitions and identified a greater number of metabolically distinct functional groups than the more traditional PCoA ordination. Ultimately, we identified four community ecotypes with distinct taxonomic and functional cut-offs driven by seasonality, water mass, and substrate turnover, highlighting the importance of succession in functional diversity for the central Arctic Ocean. These results reinforce ML dimensionality reduction as a meaningful translator in the mining of historical amplicon datasets to address modern mechanistic questions and potentially provide ’omics informed ecotype diversity to leverage in mechanistic biogeochemical models.

Arctic Ocean↗
DOE OSTI2025

Neural Active Manifolds: Nonlinear Dimensionality Reduction for Uncertainty Quantification

We present a new approach for nonlinear dimensionality reduction, specifically designed for computationally expensive mathematical models. We leverage autoencoders to discover a one-dimensional neural active manifold (NeurAM) capturing the model output variability, through the aid of a simultaneously learnt surrogate model with inputs on this manifold. Our method only relies on model evaluations and does not require the knowledge of gradients. The proposed dimensionality reduction framework can then be applied to assist outer loop many-query tasks in scientific computing, like sensitivity analysis and multifidelity uncertainty propagation. In particular, we prove, both theoretically under idealized conditions, and numerically in challenging test cases, how NeurAM can be used to obtain multifidelity sampling estimators with reduced variance by sampling the models on the discovered low-dimensional and shared manifold among models. Several numerical examples illustrate the main features of the proposed dimensionality reduction strategy and highlight its advantages with respect to existing approaches in the literature.

Autoencoders↗
DOE OSTI2025

Kernel Manifolds: Nonlinear‐Augmentation Dimensionality Reduction Using Reproducing Kernel Hilbert Spaces

This paper generalizes recent advances on quadratic manifold (QM) dimensionality reduction by developing kernel methods-based nonlinear-augmentation dimensionality reduction. QMs, and more generally feature map-based nonlinear corrections, augment linear dimensionality reduction with a nonlinear correction term in the reconstruction map to overcome approximation accuracy limitations of purely linear approaches. While feature map-based approaches typically learn a least squares optimal polynomial correction term, we generalize this approach by learning an optimal nonlinear correction from a user-defined reproducing kernel Hilbert space. Our approach allows one to impose arbitrary nonlinear structure on the correction term, including polynomial structure, and includes feature map and radial basis function-based corrections as special cases. Furthermore, our method has relatively low training cost and has monotonically decreasing error as the latent space dimension increases. In conclusion, we compare our approach to proper orthogonal decomposition and several recent QM approaches on data from several example problems.

kernel methods↗
DOE OSTI2025

Dimensional Reduction Guides Electronic Structure Evolution in the A n Cu 4–n SnS 4 Semiconductor Series

The search for new functional materials with tunable properties remains a central challenge in chemistry, particularly for applications in energy and electronics. In this work, we present a framework for predictive crystal design in alkali metal chalcogenides that enables controlled dimensional reduction of a parent covalent motif, yielding a broad range of electronic structures, which systematically evolve from one parent to the other. We present 11 new members of the A n Cu 4–n SnS 4 family (A = alkali metal; n = 0–4), which reduce the three-dimensional (3D) covalent network of Cu 4 SnS 4 into various 3D, 2D, 1D, and 0D [Cu 4–n SnS 4 ] n− motifs through the substitution of Cu with alkali metals of various radii. The end members of the family set the range in achievable band gaps at 0.99 eV for fully covalent Cu 4 SnS 4 (n = 0) and 3.38 eV for K 4 SnS 4 (n = 4) with 0D [SnS 4 ] n− tetrahedra. As the dimensionality of [Cu 4–n SnS 4 ] n− systematically reduces within A n Cu 4–n SnS 4 (n = 1–3), a stepwise increase in band gap energy occurs through a gradual decrease in the energy of the valence band maximum and an increase in the conduction band minimum, with an increase in the effective masses of charge carriers. Furthermore, irrespective of the alkali metal, the thermal stability decreases with decreasing [Cu 4–n SnS 4 ] n− dimensionality within the quaternary members. Most importantly, we demonstrate that predictable crystal structure and property evolution for a given composition space is possible by deriving a general formula based on substituting the covalent metals of a parent structure with alkali metals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Systematic characterization of unknown compounds via dimensionality reduction of time series

Analysis of ambient aerosols provides valuable insight into particle sources and formation chemistry. However, due to the complexity of atmospheric data and the dynamic nature of aerosol composition, a substantial fraction of data often become discarded by conventional analysis methods. Furthermore, a large fraction of chemical species within those data are unidentifiable due to a lack of matching spectral information, resulting in suboptimal characterization of chemical composition. Previous work has demonstrated techniques for cataloging analytes in a chromatographic dataset by deconvolution of mass spectra, but integration of these analytes throughout a large dataset remains time consuming. Here, we present a method to automatically identify an ion for quantitation for single-ion chromatogram based peak fitting and integration, enabling comprehensive integration of analytes with minimal user interaction. The resulting time series are clustered with a machine-learning based dimensionality reduction technique to systematically investigate the underlying characteristics of the categorized analytes and gain new insights into the chemical composition and physicochemical properties of the unidentifiable analytes. We apply these methods to existing atmospheric datasets collected in Manacapuru, Brazil during the GoAmazon2014/5 campaign to identify new analytes and interpret their variability and transformations in the atmosphere. The analysis results generate 408 time series from cataloged analytes of interest, and the clustering of those time series with spherical k-means results in 8 distinct clusters. We find the analytes form clusters based on their distinct physicochemical properties, demonstrating the method’s ability to systematically identify and selectively filter contaminants and instrumental analytes and characterize the unidentifiable analytes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Dimensional Reduction for Sampled Priors and Application to Photometric Redshift Distributions

A typical Bayesian inference on the values of some parameters of interest q from some data D involves running a Markov Chain (MC) to sample from the posterior $p$($q$,$n$|$D$) $\propto$ $\mathcal{L}$($D$|$q$,$n$)$p$(q)$p$($n$), where n are some nuisance parameters with a separable prior. In some cases, the nuisance parameters are high-dimensional, and their prior p(n) is itself defined only by a set of samples that have been drawn from some other MC. The MC for the posterior will typically require evaluation of p(n) at arbitrary values of n, i.e., one needs to provide a density estimator over the full n space from the provided samples. But the high dimensionality of n hinders both the density estimation and the efficiency of the MC for the posterior. We describe a solution to this problem: a linear compression of the n space into a much lower-dimensional space u, which projects away directions in n space that cannot appreciably alter $\mathcal{L}$. The algorithm for doing so is a slight modification to principal components analysis, and is less restrictive on p(n) than other proposed solutions to this issue. We demonstrate this “mode projection” technique using the analysis of 2-point correlation functions of weak lensing fields and galaxy density in the Dark Energy Survey, where n is a binned representation of the redshift distribution n(z) of the galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Online learning of quadratic manifolds from streaming data for nonlinear dimensionality reduction and nonlinear model reduction

Here, this work introduces an online greedy method for constructing quadratic manifolds from streaming data, designed to enable in situ analysis of numerical simulation data on the Petabyte scale. Unlike traditional batch methods, which require all data to be available upfront and take multiple passes over the data, the proposed online greedy method incrementally updates quadratic manifolds in one pass as data points are received, eliminating the need for expensive disk input/output operations as well as storing and loading data points once they have been processed. A range of numerical examples demonstrate that the online greedy method learns accurate quadratic manifold embeddings while being capable of processing data that far exceed common disk input/output capabilities and volumes as well as main-memory sizes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Hierarchical Gaussian Random Field Sampling for Multilevel Markov Chain Monte Carlo: Coupling Stochastic Partial Differential Equation and the Karhunen–Loève Decomposition

This work introduces structure preserving hierarchical decompositions for sampling Gaussian random fields (GRFs) within the context of multilevel Bayesian inference in high-dimensional space. Existing scalable hierarchical sampling methods, such as those based on stochastic partial differential equations (SPDEs), often reduce the dimensionality of the sample space at the cost of accuracy of inference. Other approaches, such that those based on Karhunen-Loève (KL) expansions, offer sample space dimensionality reduction but sacrifice GRF representation accuracy and ergodicity of the Markov chain Monte Carlo (MCMC) sampler and are computationally expensive for high-dimensional problems. The proposed method integrates the dimensionality reduction capabilities of KL expansions with the scalability of SPDE-based sampling, thereby providing a robust, unified framework for high-dimensional uncertainty quantification (UQ) that is scalable and accurate, preserves ergodicity, and offers dimensionality reduction of the sample space. The hierarchy in our multilevel algorithm is derived from the geometric multigrid hierarchy. By constructing a hierarchical decomposition that maintains the covariance structure across the levels in the hierarchy, the approach enables efficient coarse-to-fine sampling while ensuring that all samples are drawn from the desired distribution. The effectiveness of the proposed method is demonstrated on a benchmark subsurface flow problem, demonstrating its effectiveness in improving computational efficiency and statistical accuracy. Furthermore, our proposed technique is more efficient and accurate and displays better convergence properties than existing methods for high-dimensional Bayesian inference problems.

Gaussian random fields↗
DOE OSTI2025

Randomized Algorithms for Low-Rank Matrix and Tensor Decompositions

This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimensionality reduction, such as the singular value decomposition (SVD) or interpolative (ID) and CUR decompositions. Recent advances in randomized dimensionality reduction are discussed, including new methods of fast matrix sketching and sampling techniques, which are incorporated into classical matrix algorithms for fast low-rank matrix approximations. The extension of randomized matrix algorithms to tensors is then explored for several low-rank tensor decompositions in the CP and Tucker formats, including the higher-order SVD, ID, and CUR decomposition.

Pearce, Katherine J. [The University of Texas at A↗
DOE OSTI2026

Multidimensional scaling informed by F -statistic: Visualizing grouped microbiome data with inference

Multidimensional scaling (MDS) is a widely used dimensionality reduction technique in microbial ecology data analysis that captures the multivariate structure of the data while preserving pairwise distances between samples. While improvements in MDS have enhanced the ability to reveal group-specific data patterns, these MDS-based methods require prior assumptions for inference, limiting their application in general microbiome analysis. Here, in this study, we introduce a new MDS-based ordination method, “F-informed MDS,” which configures the data distribution based on the F-statistic, the ratio of dispersion between groups sharing common and different characteristics. Using semisynthetic datasets, we demonstrate that the proposed method is robust to hyperparameter selection while maintaining statistical significance throughout the ordination process. Various quality metrics for evaluating dimensionality reduction confirm that F-informed MDS is comparable to state-of-the-art methods in preserving both local and global data structures. Its application to a diatom-associated bacterial community suggests the role of this new method in interpreting the community’s response to the host. Our approach offers a well-founded refinement of MDS that aligns with statistical test results, which can be beneficial for broader multidimensional data analyses in microbiology and ecology. This new visualization tool can be incorporated into standard microbiome data analyses.

Biological and medical sciences↗
DOE OSTI2025

Nonintrusive projection-based reduced order modeling using stable learned differential operators

Nonintrusive projection-based reduced order models (ROMs) are essential for dynamics prediction in multi-query applications where underlying governing equations are known but the access to the source of the underlying full order model (FOM) is unavailable; that is, FOM is a glass-box. This article proposes a learn-then-project approach for nonintrusive model reduction. In the first step of this approach, high-dimensional stable sparse learned differential operators (S-LDOs) are determined using the generated data. In the second step, the ordinary differential equations, comprising these S-LDOs, are used with suitable dimensionality reduction and low-dimensional subspace projection methods to provide equations for the evolution of reduced states. This approach allows easy integration into the existing intrusive ROM framework to enable nonintrusive model reduction while allowing the use of Petrov–Galerkin projections. The applicability of the proposed approach is demonstrated for Galerkin and LSPG projection-based ROMs through four numerical experiments: 1-D scalar advection, 1-D Burgers, 2-D scalar advection and 1-D scalar advection–diffusion–reaction equations. In conclusion, the results indicate that the proposed nonintrusive ROM strategy provides accurate and stable dynamics prediction.

42 ENGINEERING↗
DOE OSTI2025

Enhancing Interpretability in Generative Modeling: Statistically Disentangled Latent Spaces Guided by Generative Factors in Scientific Datasets

This study addresses the challenge of statistically extracting generative factors from complex, high-dimensional datasets in unsupervised or semi-supervised settings. We investigate encoder-decoder-based generative models for nonlinear dimensionality reduction, focusing on disentangling low-dimensional latent variables corresponding to independent physical factors. Introducing Aux-VAE, a novel architecture within the classical Variational Autoencoder framework, we achieve disentanglement with minimal modifications to the standard VAE loss function by leveraging prior statistical knowledge through auxiliary variables. These variables guide the shaping of the latent space by aligning latent factors with learned auxiliary variables. We validate the efficacy of Aux-VAE through comparative assessments on multiple datasets, including astronomical simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

An interactive machine learning platform for analyzing multi-particle coincidence data from cold target recoil ion momentum spectroscopy

We present SCULPT (Supervised Clustering and Uncovering Latent Patterns with Training), a comprehensive software platform for analyzing tabulated high-dimensional multi-particle coincidence data from Cold Target Recoil Ion Momentum Spectroscopy (COLTRIMS) experiments. The software addresses critical challenges in modern momentum spectroscopy by integrating advanced machine learning techniques with physics-informed analysis in an interactive web-based environment. SCULPT implements uniform manifold approximation and projection for non-linear dimensionality reduction to reveal correlations in high-dimensional data. We also discuss potential extensions to deep autoencoders for feature learning and genetic programming for automated discovery of physically meaningful observables. A novel adaptive confidence scoring system provides quantitative reliability assessments by evaluating user-selected clustering quality metrics with predefined weights that reflect each metric’s robustness. The platform features configurable molecular profiles for different experimental systems, interactive visualization with selection tools, and comprehensive data filtering capabilities. Utilizing a subset of SCULPT’s capabilities, we analyze photo-double-ionization data measured using the COLTRIMS method for three-body dissociation of the D 2 O molecule, revealing distinct fragmentation channels and their correlations with physics parameters. The software’s modular architecture and web-based implementation make it accessible to the broader atomic and molecular physics community, significantly reducing the time required for complex multi-dimensional analyses. This opens the door to finding and isolating rare events exhibiting non-linear correlations on the fly during experimental measurements, which can help steer exploration and improve the efficiency of experiments.

Artificial neural networks↗
DOE OSTI2025

MOOSE ProbML: Parallelized probabilistic machine learning and uncertainty quantification for computational energy applications

Here, this paper presents the development and demonstration of massively parallel probabilistic machine learning (ML) and uncertainty quantification (UQ) capabilities within the Multiphysics Object-Oriented Simulation Environment (MOOSE), an open-source computational platform for parallel finite element and finite volume analyses. In addressing the computational expense and uncertainties inherent in complex multiphysics simulations, this paper integrates Gaussian process (GP) variants, active learning, Bayesian inverse UQ, adaptive forward UQ, Bayesian optimization, evolutionary optimization, and Markov chain Monte Carlo (MCMC) within MOOSE. It also elaborates on the interaction among key MOOSE systems — Sampler, MultiApp, Reporter, and Surrogate — in enabling these capabilities. The modularity offered by these systems enables development of a multitude of probabilistic ML and UQ algorithms in MOOSE. Example code demonstrations include parallel active learning and parallel Bayesian inference via active learning. The impact of these developments is illustrated through five applications relevant to computational energy applications: UQ of nuclear fuel fission product release, using parallel active learning Bayesian inference; very rare events analysis in nuclear microreactors using active learning; advanced manufacturing process modeling using multi-output GPs (MOGPs) and dimensionality reduction; fluid flow using deep GPs (DGPs); and tritium transport model parameter optimization for fusion energy, using batch Bayesian optimization. These capabilities are part of the MOOSE framework.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2026

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.

Fraiman, Michael [Tel Aviv Univ., Tel Aviv (Israel↗