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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.

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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 OSTI2023

Understanding the evolution of double perovskite band structure upon dimensional reduction

Recent investigations into the effects of dimensional reduction on halide double perovskites have revealed an intriguing change in band structure when the three-dimensional (3D) perovskite is reduced to a two-dimensional (2D) perovskite with inorganic sheets of monolayer thickness (n = 1). The indirect bandgap of 3D Cs 2 AgBiBr 6 becomes direct in the n = 1 perovskite whereas the direct bandgap of 3D Cs 2 AgTlBr 6 becomes indirect at the n = 1 limit. Here, we apply a linear combination of atomic orbitals approach to uncover the orbital basis for this bandgap symmetry transition with dimensional reduction. We adapt our previously established method for predicting band structures of 3D double perovskites for application to their 2D congeners, emphasizing new considerations required for the 2D lattice. In particular, we consider the inequivalence of the terminal and bridging halides and the consequences of applying translational symmetry only along two dimensions. The valence and conduction bands of the layered perovskites can be derived from symmetry adapted linear combinations of halide p orbitals propagated across the 2D lattice. The dispersion of each band is then determined by the bonding and antibonding interactions of the metal and halide orbitals, thus affording predictions of the essential features of the band structure. We demonstrate this analysis for 2D Ag–Bi and Ag–Tl perovskites with sheets of mono- and bilayer thickness, establishing a detailed understanding of their band structures, which enables us to identify the key factors that drive the bandgap symmetry transitions observed at the n = 1 limit. Importantly, these insights also allow us to make the general prediction that direct → indirect or indirect → direct bandgap transitions in the monolayer limit are most likely in double perovskite compositions that involve participation of metal d orbitals at the band edges or that have no metal-orbital contributions to the valence band, laying the groundwork for the targeted realization of this phenomenon.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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 OSTI2022

Trajectory prediction dimensionality reduction for low-cost connected automated vehicle systems

Here, to facilitate low-cost connected automated vehicle (CAV) system development, this study proposes two interpretable dimensionality reduction techniques in vehicle trajectory prediction, i.e., the piecewise Taylor series approximation (PTA) and the piecewise Fourier series approximation (PFA), to lower computation complexity, reduce device investment, and decrease computation energy consumption. Two benchmarks are developed, the long short-term memory (LSTM)-based model without dimensionality reduction and the LSTM-based model with encoder-decoder (a widely used dimensionality reduction technique). Results show that the four predictions have similar accuracy, and the training time (proportional to computation energy consumption) of models with dimensionality reduction techniques is greatly reduced. The reduction is even more significant when PTA/PFA is used. Sensitivity analysis advises PFA/PTA parameter selections to reduce computation complexity without significant loss of prediction accuracy. Further, the robustness of the LSTM PTA/PFA is proven by the investigation of data noises.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Data-Efficient Dimensionality Reduction and Surrogate Modeling of High-Dimensional Stress Fields

Tensor datatypes representing field variables like stress, displacement, velocity, etc., have increasingly become a common occurrence in data-driven modeling and analysis of simulations. Numerous methods [such as convolutional neural networks (CNNs)] exist to address the meta-modeling of field data from simulations. As the complexity of the simulation increases, so does the cost of acquisition, leading to limited data scenarios. Modeling of tensor datatypes under limited data scenarios remains a hindrance for engineering applications. Here, in this article, we introduce a direct image-to-image modeling framework of convolutional autoencoders enhanced by information bottleneck loss function to tackle the tensor data types with limited data. The information bottleneck method penalizes the nuisance information in the latent space while maximizing relevant information making it robust for limited data scenarios. The entire neural network framework is further combined with robust hyperparameter optimization. We perform numerical studies to compare the predictive performance of the proposed method with a dimensionality reduction-based surrogate modeling framework on a representative linear elastic ellipsoidal void problem with uniaxial loading. The data structure focuses on the low-data regime (fewer than 100 data points) and includes the parameterized geometry of the ellipsoidal void as the input and the predicted stress field as the output. The results of the numerical studies show that the information bottleneck approach yields improved overall accuracy and more precise prediction of the extremes of the stress field. Additionally, an in-depth analysis is carried out to elucidate the information compression behavior of the proposed framework.

artificial intelligence↗
DOE OSTI2021

Dimensionality reduction

This chapter presents an introduction to some of the key dimensionality reduction methods currently used in data science. The intended audience is pure mathematicians. The chapter puts special emphasis on connecting the fundamental ideas in dimensionality reduction to a diverse set of mathematical domains, including geometry, dynamical systems, representation theory, and category theory.

dimension reduction, geometry, dynamical systems, ↗
DOE OSTI2023

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.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Energy conserving quadrature based dimensionality reduction for nonlinear hydrodynamics problems

Projection based dimensionality reduction is used to approximate the full discretiza tion of a PDE problem in order to reduce the cost of its numerical simulation while staying faithful to the full dynamics. For nonlinear problems, hyperreduction methods are additionally needed to remove the dependence of the nonlinear terms on the full problem’s size. In this project, we develop an energy conserving hyperreduction method and apply it to Eulerian-Lagrangian hydrodynamics problems, demonstrating that the reduced model successfully accelerates the numerical simulations while conserving the problem’s total energy with high accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Feasibility of DEIM for retrieving the initial field via dimensionality reduction

When parameter estimation is solved in a high-dimensional space, the dimensionality reduction strategy becomes the primary consideration for alleviating the tremendous computational cost. Here, the discrete empirical interpolation method (DEIM) is explored to retrieve the initial condition (IC) by combining the polynomial chaos (PC) based ensemble Kalman filter (i.e. PC-EnKF), where a non-intrusive PC expansion is considered as a surrogate model in place of the forward model in the prediction step of the ensemble Kalman filter, resulting in fewer forward model integrations but with a comparable accuracy as Monte Carlo-based approaches. The DEIM acts as a hyper-reduction tool to provide the low-dimensional input for the high-dimensional initial field, which can be reconstructed using the information on the sparse interpolation grid points that is adaptively obtained through PC-EnKF data assimilation method. Thus an innovative framework to reconstruct the IC is developed. The detailed procedure at each assimilation iteration includes: the determination of the spatial interpolation points, the estimation of the initial values on the interpolation locations using the optimal observations, and the reconstruction of IC in the full space. The current study uses the reconstruction field of initial conditions of the Navier-Stokes equations as an example to illustrate the efficacy of our method. The experimental results demonstrate the proposed algorithm achieves a satisfactory reconstruction for the initial field. The proposed method helps to extend the applicable area of DEIM in solving inverse problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Dimensionality reduction using elastic measures

With the recent surge in big data analytics for hyperdimensional data, there is a renewed interest in dimensionality reduction techniques. In order for these methods to improve performance gains and understanding of the underlying data, a proper metric needs to be identified. This step is often overlooked, and metrics are typically chosen without consideration of the underlying geometry of the data. Here, in this paper, we present a method for incorporating elastic metrics into the t-distributed stochastic neighbour embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP). We apply our method to functional data, which is uniquely characterized by rotations, parameterization and scale. If these properties are ignored, they can lead to incorrect analysis and poor classification performance. Through our method, we demonstrate improved performance on shape identification tasks for three benchmark data sets (MPEG-7, Car data set and Plane data set of Thankoor), where we achieve 0.77, 0.95 and 1.00 F1 score, respectively.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Dimensionality Reduction of SDSS Spectra with Variational Autoencoders

High-resolution galaxy spectra contain much information about galactic physics, but the high dimensionality of these spectra makes it difficult to fully utilize the information they contain. We apply variational autoencoders (VAEs), a nonlinear dimensionality reduction technique, to a sample of spectra from the Sloan Digital Sky Survey (SDSS). In contrast to principal component analysis (PCA), a widely used technique, VAEs can capture nonlinear relationships between latent parameters and the data. We find that a VAE can reconstruct the SDSS spectra well with only six latent parameters, outperforming PCA with the same number of components. Different galaxy classes are naturally separated in this latent space, without class labels having been given to the VAE. The VAE latent space is interpretable because the VAE can be used to make synthetic spectra at any point in latent space. For example, making synthetic spectra along tracks in latent space yields sequences of realistic spectra that interpolate between two different types of galaxies. Using the latent space to find outliers may yield interesting spectra: in our small sample, we immediately find unusual data artifacts and stars misclassified as galaxies. In this exploratory work, we show that VAEs create compact, interpretable latent spaces that capture nonlinear features of the data. While a VAE takes substantial time to train (≈1 day for 48,000 spectra), once trained, VAEs can enable the fast exploration of large astronomical data sets.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Non‐Linear Dimensionality Reduction With a Variational Encoder Decoder to Understand Convective Processes in Climate Models

Abstract Deep learning can accurately represent sub‐grid‐scale convective processes in climate models, learning from high resolution simulations. However, deep learning methods usually lack interpretability due to large internal dimensionality, resulting in reduced trustworthiness in these methods. Here, we use Variational Encoder Decoder structures (VED), a non‐linear dimensionality reduction technique, to learn and understand convective processes in an aquaplanet superparameterized climate model simulation, where deep convective processes are simulated explicitly. We show that similar to previous deep learning studies based on feed‐forward neural nets, the VED is capable of learning and accurately reproducing convective processes. In contrast to past work, we show this can be achieved by compressing the original information into only five latent nodes. As a result, the VED can be used to understand convective processes and delineate modes of convection through the exploration of its latent dimensions. A close investigation of the latent space enables the identification of different convective regimes: (a) stable conditions are clearly distinguished from deep convection with low outgoing longwave radiation and strong precipitation; (b) high optically thin cirrus‐like clouds are separated from low optically thick cumulus clouds; and (c) shallow convective processes are associated with large‐scale moisture content and surface diabatic heating. Our results demonstrate that VEDs can accurately represent convective processes in climate models, while enabling interpretability and better understanding of sub‐grid‐scale physical processes, paving the way to increasingly interpretable machine learning parameterizations with promising generative properties.

54 ENVIRONMENTAL SCIENCES↗
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 OSTI2022

Application of Dimensionality Reduction in Machine Learning Modeling of CO2 Storage

In this study, we developed deep learning models that are capable of predicting spatio-temporal outputs of CO2 saturation, pressure, and brine production in a 3D saline storage reservoir over 30 years of continuous CO2 injection and a 50-year post-injection timeframe. To improve computational efficiency and maintain performance accuracy, the model framework involves ensembling multi-layer autoencoder networks that provide dimensionality reduction of geologic inputs with fully connected long short-term memory (LSTM) neural networks that generate time-series prediction. This study was presented as poster at the 2022 Carbon Management Project Review Meeting held in Pittsburgh, PA (August 15 – 19, 2022).

Bello, Kolawole↗
DOE OSTI2024

Improved multifidelity Monte Carlo estimators based on normalizing flows and dimensionality reduction techniques

Here, we study the problem of multifidelity uncertainty propagation for computationally expensive models. In particular, we consider the general setting where the high-fidelity and low-fidelity models have a dissimilar parameterization both in terms of number of random inputs and their probability distributions, which can be either known in closed form or provided through samples. We derive novel multifidelity Monte Carlo estimators which rely on a shared subspace between the high-fidelity and low-fidelity models where the parameters follow the same probability distribution, i.e., a standard Gaussian. We build the shared space employing normalizing flows to map different probability distributions into a common one, together with linear and nonlinear dimensionality reduction techniques, active subspaces and autoencoders, respectively, which capture the subspaces where the models vary the most. We then compose the existing low-fidelity model with these transformations and construct modified models with an increased correlation with the high-fidelity model, which therefore yield multifidelity estimators with reduced variance. A series of numerical experiments illustrate the properties and advantages of our approaches.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2023

Classical and quantum compression for edge computing: the ubiquitous data dimensionality reduction

Edge computing aims to address the challenges associated with communicating and transferring large amounts of data generated remotely to a data center in a timely and efficient manner. A central pillar of edge computing is local (i.e., at- or near-source) data processing capability so that data transfer to a data center for processing can be minimized. Data compression at the edge is therefore a natural component of edge workflows. Here we present a survey of data compression algorithms with a focus on edge computing. Not all compression algorithms can accommodate the data type heterogeneity, tight processing and communication time constraints, or energy efficiency requirement characteristics of edge computing. We discuss specific examples of compression algorithms that are being explored in the context of edge computing. We end our review with a brief survey of emerging quantum compression techniques that are of importance in quantum information processing, including the proposed concept of quantum edge computing.

97 MATHEMATICS AND COMPUTING↗