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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
NASA NTRS2023

The Impact of Dimensionality Reduction of Ion Counts Distributions on Preserving Moments, With Applications to Data Compression

The field of space physics has a long history of utilizing dimensionality reduction methods to distill data, including but not limited to spherical harmonics, the Fourier Transform, and the wavelet transform. Here, we present a technique for performing dimensionality reduction on ion counts distributions from the Multiscale Mission/Fast Plasma Investigation (MMS/FPI) instrument using a data-adaptive method powered by neural networks. This has applications to both feeding low-dimensional parameterizations of the counts distributions into other machine learning algorithms, and the problem of data compression to reduce transmission volume for space missions. The algorithm presented here is lossy, and in this work, we present the technique of validating the reconstruction performance with calculated plasma moments under the argument that preserving the moments also preserves fluid-level physics, and in turn a degree of scientific validity. The method presented here is an improvement over other lossy compressions in loss-tolerant scenarios like the Multiscale Mission/Fast Plasma Investigation Fast Survey or in non-research space weather applications.

D. da Silva↗
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 OSTI2019

Learning nonlinear level sets for dimensionality reduction in function approximation

We developed a Nonlinear Level-set Learning (NLL) method for dimensionality reduction in high-dimensional function approximation with small data. This work is motivated by a variety of design tasks in real-world engineering applications, where practitioners would replace their computationally intensive physical models (e.g., high-resolution fluid simulators) with fast-to-evaluate predictive machine learning models, so as to accelerate the engineering design processes. There are two major challenges in constructing such predictive models: (a) high-dimensional inputs (e.g., many independent design parameters) and (b) small training data, generated by running extremely time-consuming simulations. Thus, reducing the input dimension is critical to alleviate the over-fitting issue caused by data insufficiency. Existing methods, including sliced inverse regression and active subspace approaches, reduce the input dimension by learning a linear coordinate transformation; our main contribution is to extend the transformation approach to a nonlinear regime. Specifically, we exploit reversible networks (RevNets) to learn nonlinear level sets of a high-dimensional function and parameterize its level sets in low-dimensional spaces. A new loss function was designed to utilize samples of the target functions' gradient to encourage the transformed function to be sensitive to only a few transformed coordinates. The NLL approach is demonstrated by applying it to three 2D functions and two 20D functions for showing the improved approximation accuracy with the use of nonlinear transformation, as well as to an 8D composite material design problem for optimizing the buckling-resistance performance of composite shells of rocket inter-stages.

Zhang, Guannan↗
NASA NTRS2007

Lightning Charge Retrievals: Dimensional Reduction, LDAR Constraints, and a First Comparison with LIS Satellite Data

A "dimensional reduction" (DR) method is introduced for analyzing lightning field changes (DELTAEs) whereby the number of unknowns in a discrete two-charge model is reduced from the standard eight (x, y, z, Q, x', y', z', Q') to just four (x, y, z, Q). The four unknowns (x, y, z, Q) are found by performing a numerical minimization of a chi-square function. At each step of the minimization, an Overdetermined Fixed Matrix (OFM) method is used to immediately retrieve the best "residual source" (x', y', z', Q'), given the values of (x, y, z, Q). In this way, all 8 parameters (x, y, z, Q, x', y', z', Q') are found, yet a numerical search of only 4 parameters (x, y, z, Q) is required. The DR method has been used to analyze lightning-caused DeltaEs derived from multiple ground-based electric field measurements at the NASA Kennedy Space Center (KSC) and USAF Eastern Range (ER). The accuracy of the DR method has been assessed by comparing retrievals with data provided by the Lightning Detection And Ranging (LDAR) system at the KSC-ER, and from least squares error estimation theory, and the method is shown to be a useful "stand-alone" charge retrieval tool. Since more than one charge distribution describes a finite set of DELTAEs (i.e., solutions are non-unique), and since there can exist appreciable differences in the physical characteristics of these solutions, not all DR solutions are physically acceptable. Hence, an alternative and more accurate method of analysis is introduced that uses LDAR data to constrain the geometry of the charge solutions, thereby removing physically unacceptable retrievals. The charge solutions derived from this method are shown to compare well with independent satellite- and ground-based observations of lightning in several Florida storms.

Koshak, W. J.↗
NASA NTRS2007

Lightning Charge Retrievals: Dimensional Reduction, LDAR Constraints, and a First Comparison w/ LIS Satellite Data

A "dimensional reduction" (DR) method is introduced for analyzing lightning field changes whereby the number of unknowns in a discrete two-charge model is reduced from the standard eight to just four. The four unknowns are found by performing a numerical minimization of a chi-squared goodness-of-fit function. At each step of the minimization, an Overdetermined Fixed Matrix (OFM) method is used to immediately retrieve the best "residual source". In this way, all 8 parameters are found, yet a numerical search of only 4 parameters is required. The inversion method is applied to the understanding of lightning charge retrievals. The accuracy of the DR method has been assessed by comparing retrievals with data provided by the Lightning Detection And Ranging (LDAR) instrument. Because lightning effectively deposits charge within thundercloud charge centers and because LDAR traces the geometrical development of the lightning channel with high precision, the LDAR data provides an ideal constraint for finding the best model charge solutions. In particular, LDAR data can be used to help determine both the horizontal and vertical positions of the model charges, thereby eliminating dipole ambiguities. The results of the LDAR-constrained charge retrieval method have been compared to the locations of optical pulses/flash locations detected by the Lightning Imaging Sensor (LIS).

Koshak, William↗
NASA NTRS2007

Lightning Charge Retrievals: Dimensional Reduction, LDAR Constraints, and a First Comparison with LIS Satellite Data

A "dimensional reduction" ("DR") method is introduced for analyzing lightning field changes ((Delta)Es) whereby the number of unknowns in a discrete two-charge model is reduced from the standard eight (x, y, z, Q, x', y', z', Q') to just four (x, y, z, Q). The four unknowns (x, y, z, Q) are found by performing a numerical minimization of a chi-square function. At each step of the minimization, an overdetermined fixed matrix (OFM) method is used to immediately retrieve the best "residual source" (x', y', z', Q'), given the values of (x, y, z, Q). In this way, all eight parameters Ix. y, z, Q, x', y', z', Q') are found, yet a numerical search of only four parameters (x, y, z, Q) is required. The DR method has been used to analyze lightning-caused (Delta)Es derived from multiple ground-based electric field measurements at the NASA Kennedy Space Center (KSC) and U.S. Air Force Eastern Range (ER). The accuracy of the DR method has been assessed by comparing retrievals with data provided by the lightning detection and ranging (LDAR) system at the KSC-ER. and from least squares error estimation theory, and the method is shown to be a useful "stand alone" charge retrieval tool. Since more than one charge distribution describes a finite set of (Delta)Es (i.e., solutions are nonunique), and since there can be appreciable differences in the physical characteristics of these solutions, not all DR solutions are physically acceptable. Hence. an alternative and more accurate method of analysis is introduced that uses LDAR data to constrain the geometry of the charge solutions. thereby removing physically unacceptable retrievals. The charge solutions derived from this method are shown to compare well with independent satellite- and ground-based observations of lightning m several Florida storms.

Koshak, W. J.↗
DOE OSTI2019

Dimension and Dimensional Reduction in Quantum Gravity

If gravity is asymptotically safe, operators will exhibit anomalous scaling at the ultraviolet fixed point in a way that makes the theory effectively two-dimensional. A number of independent lines of evidence, based on different approaches to quantization, indicate a similar short-distance dimensional reduction. I will review the evidence for this behavior, emphasizing the physical question of what one means by “dimension” in a quantum spacetime, and will discuss possible mechanisms that could explain the universality of this phenomenon.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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 OSTI2019

Neural correlates of sparse coding and dimensionality reduction

Supported by recent computational studies, there is increasing evidence that a wide range of neuronal responses can be understood as an emergent property of nonnegative sparse coding (NSC), an efficient population coding scheme based on dimensionality reduction and sparsity constraints. We review evidence that NSC might be employed by sensory areas to efficiently encode external stimulus spaces, by some associative areas to conjunctively represent multiple behaviorally relevant variables, and possibly by the basal ganglia to coordinate movement. In addition, NSC might provide a useful theoretical framework under which to understand the often complex and nonintuitive response properties of neurons in other brain areas. Although NSC might not apply to all brain areas (for example, motor or executive function areas) the success of NSC-based models, especially in sensory areas, warrants further investigation for neural correlates in other regions.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS2004

Dimensional Reduction: A Method for Retrieving Lightning Charge

A method is introduced for retrieving the locations and magnitudes of charges deposited by a lightning flash using multiple ground-based electric field change measurements. The method, called Dimensional Reduction, reduces the number of unknowns in a discrete 2-charge model from the standard of eight (x, y, z, Q, x' , y' , z' , Q') to just four (x, y, z, Q). This reduction is accomplished by analyzing "residual measurements" that are formed by subtracting from each ground-based electric field change the contribution due to the source (x, y, z, Q). Using an improved analytic solution to the four-parameter point charge model (or "Q-model") the residual measurements are inverted to find the associated "residual source." For flash charge depositions that look approximately like two arbitrary charges, the residual source will be modeled accurately when (x, y, z, Q) is accurate. Hence, one need only minimize a chi-squared goodness-of-fit that is a function of the four variables (x, y, z, Q), rather than one that is a function of the eight variables (x, y, z, Q, x , y , z , Q ). The accuracy of the method is assessed by inverting computer-simulated electric field changes produced from known charge sources. The method is also applied to analyze real lightning electric field change data derived from the NASA Kennedy Space Center (KSC) and United States Air Force (USAF) Eastern Range (ER) ground-based field mill network It is shown that the charge retrievals compare favorably with associated ancillary ground- and satellite- based lightning measurements.

Koshak, William↗
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↗
NASA NTRS1976

Classification improvement by optimal dimensionality reduction when training sets are of small size

A computer simulation was performed to test the conjecture that, when the sizes of the training sets are small, classification in a subspace of the original data space may give rise to a smaller probability of error than the classification in the data space itself; this is because the gain in the accuracy of estimation of the likelihood functions used in classification in the lower dimensional space (subspace) offsets the loss of information associated with dimensionality reduction (feature extraction). A number of pseudo-random training and data vectors were generated from two four-dimensional Gaussian classes. A special algorithm was used to create an optimal one-dimensional feature space on which to project the data. When the sizes of the training sets are small, classification of the data in the optimal one-dimensional space is found to yield lower error rates than the one in the original four-dimensional space.

Starks, S. A.↗
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 OSTI2018

NSVZ Relation and the Dimensional Reduction in N = 1 SQED

It is known that factorization of the β-function loop integrals into integrals of double total derivatives is an important ingredient needed for deriving the NSVZ relation by direct perturbative calculations in N=1 SQED regularized by thehigher derivatives. It allows to relate the β-function and the anomalous dimension of the matter superfields defined in terms of the bare coupling constant. In this work we find the analog of this result in the case of using dimensional reduction regularization in the lowest orders. However, we demonstrate that in this case the NSVZ relation is not satisfied for the RG functions defined in terms of the bare coupling constant. Nevertheless, it is possible to impose boundary conditions to the renormalization constants determining the NSVZ scheme in the three-loop order for the RG functions defined in terms of the renormalized coupling constant.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1993

Optimal band selection for dimensionality reduction of hyperspectral imagery

Hyperspectral images have many bands requiring significant computational power for machine interpretation. During image pre-processing, regions of interest that warrant full examination need to be identified quickly. One technique for speeding up the processing is to use only a small subset of bands to determine the 'interesting' regions. The problem addressed here is how to determine the fewest bands required to achieve a specified performance goal for pixel classification. The band selection problem has been addressed previously Chen et al., Ghassemian et al., Henderson et al., and Kim et al.. Some popular techniques for reducing the dimensionality of a feature space, such as principal components analysis, reduce dimensionality by computing new features that are linear combinations of the original features. However, such approaches require measuring and processing all the available bands before the dimensionality is reduced. Our approach, adapted from previous multidimensional signal analysis research, is simpler and achieves dimensionality reduction by selecting bands. Feature selection algorithms are used to determine which combination of bands has the lowest probability of pixel misclassification. Two elements required by this approach are a choice of objective function and a choice of search strategy.

Stearns, Stephen D.↗
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↗