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All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

Dimension Reduction of Hyperspectral Data on Beowulf Clusters

Traditional remote sensing instruments are multispectral, where observations are collected at a few different spectral bands. Recently, many hyperspectral instruments, that can collect observations at hundreds of bands, have been operation. Furthermore, there have been ongoing research efforts on ultraspectral instruments that can produce observations at thousands of spectral bands. While these remote sensing technology developments hold a great promise for new findings in the area of Earth and space science, they present many challenges. These include the need for faster processing of such increased data volumes, and methods for data reduction. Dimension Reduction is a spectral transformation, which is used widely in remote sensing, is the Principal Components Analysis (PCA). In light of the growing number of spectral channels of modern instruments, the paper reports on the development of a parallel PCA and its implementation on two Beowulf cluster configurations, on with fast Ethernet switch and the other is with a Myrinet interconnection.

El-Ghazawi, Tarek↗
DOE OSTI2022

Regularizing Invertible Neural Networks for Airfoil Design Through Dimension Reduction

This work examines how dimension reduction can improve the performance of invertible neural networks (INN) for airfoil design. Design workflows are typically expensive, relying on many evaluations of high fidelity computational fluid dynamics (CFD) models. Furthermore, the inverse design problem is typically ill-posed. That is, multiple valid solutions exist that satisfy the design criteria. Regularization can reduce this inverse design space and simplify the problem. We study the use of subspace-based input dimension reduction to act as a regularizer for the INN model and improve the recovery of new airfoil shapes with desired performance characteristics. We find that the dimension reduction identifies two dominant modes, relating to airfoil thickness and camber, that optimally determine the airfoil's aerodynamics. We demonstrate the capability of the proposed INN model to generate 100 airfoils that satisfy the specific aerodynamic and structural characteristics.

airfoil design↗
DOE OSTI2023

DRIPS: A framework for dimension reduction and interpolation in parameter space

Reduced-order models are often used to describe the behavior of complex systems, whose simulation with a full model is too expensive, or to extract salient features from the full model’s output. We introduce a new model-reduction framework DRIPS (dimension reduction and interpolation in parameter space) that combines the offline local model reduction with the online parameter interpolation of reduced-order bases (ROBs). The offline step of this framework relies on dynamic mode decomposition (DMD) to build a low-rank linear surrogate model, equipped with a local ROB, for quantities of interest derived from the training data generated by repeatedly solving the (nonlinear) high-fidelity model for multiple parameter points. The online step consists of the construction of a parametric reduced-order model for each target/test point in the parameter space, with the interpolation of ROBs done on a Grassman manifold and the interpolation of reduced-order operators done on a matrix manifold. The DMD component enables DRIPS to model (typically low-dimensional) quantities of interest directly, without having to access the (typically high-dimensional and possibly nonlinear) operators in a high-fidelity model that governs the dynamics of the underlying high-dimensional state variables, as required in projection-based reduced-order modeling. A series of numerical experiments suggests that DRIPS yields a model reduction, which is computationally more efficient than the commonly used projection-based proper orthogonal decomposition; it does so without requiring a prior knowledge of the governing equation for quantities of interest. Furthermore, for the nonlinear systems considered, DRIPS is more accurate than Gaussian-process interpolation (Kriging).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

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.

Weylandt, Michael↗
DOE OSTI2024

Data-Driven Supervised Dimension Reduction for Scientific Discovery (LDRD QTI Report)

This report summarizes the findings of a four months FY24 Advanced Science & Technology (AS&T) LDRD Quick Targeted Investigation (QTI) project focused on the exploration of supervised dimension reduction approaches based on autoencoders. Autoencoders have been extensively employed in literature for unsupervised learning tasks, however, their use for supervised regression tasks, which are common within scientific applications, has been limited. Motivated by linear dimension reduction strategies like Active Subspaces and Adaptive Basis, we explored the possibility of employing autoencoders to discover a non-linear manifold able to represent the original function in fewer dimensions. In this report, we discuss a neural network architecture and we perform a numerical campaign on several problems ranging from simple two-dimensional functions to a model problem for magnetohydrodynamics in five dimensions. In our preliminary results, we show that the proposed approach is found to be superior to linear dimension reduction strategies in representing the target function even with a single latent variable.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Efficient Dimension Reduction of Complex Three-dimensional CO2 Saturation using Deep Learning Models

In the domain of deep learning (DL), dimension reduction is crucial for enhancing training efficiency and mitigating overfitting, particularly when managing complex data such as three-dimensional (3D) saturation data. The 3D saturation data in the context of geological carbon storage (GCS) presents unique challenges due to its inherent sparsity and the abrupt transitions at plume boundaries, known as shock fronts. To address the challenges, we proposed a novel DL framework that integrates dimension reduction with advanced 3D reconstruction techniques. Our model leveraged latent variables derived from 2D average saturation data, offering a robust and efficient solution tailored to the intricate dynamics of 3D saturation fields. The proposed framework can extract the critical features of the high-dimensional data while reducing the variable numbers, which is more tractable for DL models and enhances the model robustness and accuracy. Therefore, it provides a novel approach for modeling and analyses in complex geological scenarios, which finds great potential applications in environmental monitoring and energy storage.

Wang, Hongsheng↗
DOE OSTI2022

Nonlinear dimension reduction for surrogate modeling using gradient information

We introduce a method for the nonlinear dimension reduction of a high-dimensional function $u:{\mathbb{R}}^d\rightarrow{\mathbb{R}}$, $d\gg 1$. Our objective is to identify a nonlinear feature map $g:{\mathbb{R}}^d\rightarrow{\mathbb{R}}^m$, with a prescribed intermediate dimension $m\ll d$, so that $u$ can be well approximated by $f\circ g$ for some profile function $f:{\mathbb{R}}^m\rightarrow{\mathbb{R}}$. We propose to build the feature map by aligning the Jacobian $\nabla g$ with the gradient $\nabla u$, and we theoretically analyze the properties of the resulting $g$. Once $g$ is built, we construct $f$ by solving a gradient-enhanced least squares problem. Our practical algorithm uses a sample $\{{\textbf{x}}^{(i)},u({\textbf{x}}^{(i)}),\nabla u({\textbf{x}}^{(i)})\}_{i=1}^N$ and builds both $g$ and $f$ on adaptive downward-closed polynomial spaces, using cross validation to avoid overfitting. We numerically evaluate the performance of our algorithm across different benchmarks, and explore the impact of the intermediate dimension $m$. We show that building a nonlinear feature map $g$ can permit more accurate approximation of $u$ than a linear $g$, for the same input data set.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Time Series Dimension Reduction for Surrogate Models of Port Scanning Cyber Emulations

Surrogate model development is a key resource in the scientific modeling community for providing computational expedience when simulating complex systems without loss of great fidelity. The initial step to development of a surrogate model is identification of the primary governing components of the system. Principal component analysis (PCA) is a widely used data science technique that provides inspection of such driving factors, when the objective for modeling is to capture the greatest sources of variance inherent to a dataset. Although an efficient linear dimension reduction tool, PCA makes the fundamental assumption that the data is continuous and normally distributed. Thus, it provides ideal performance when these conditions are met. In the case for which cyber emulations provide realizations of a port scanning scenario, the data to be modeled follows a discrete time series function comprised of monotonically increasing piece-wise constant steps. The sources of variance are related to the timing and magnitude of these steps. Therefore, we consider using XPCA, an extension to PCA for continuous and discrete random variates. This report provides the documentation of the trade-offs between the PCA and XPCA linear dimension reduction algorithms, for the intended purpose to identify key components of greatest variance in our time series data. These components will ultimately provide the basis for future surrogate models of port scanning cyber emulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Grassmannian Diffusion Maps--Based Dimension Reduction and Classification for High-Dimensional Data

This work introduces the Grassmannian diffusion maps (GDMaps), a novel nonlinear dimensionality reduction technique that defines the affinity between points through their representation as low-dimensional subspaces corresponding to points on the Grassmann manifold. Here, the method is designed for applications, such as image recognition and data-based classification of constrained high-dimensional data where each data point itself is a high-dimensional object (i.e., a large matrix) that can be compactly represented in a lower-dimensional subspace. The GDMaps is composed of two stages. The first is a pointwise linear dimensionality reduction wherein each high-dimensional object is mapped onto the Grassmann manifold representing the low-dimensional subspace on which it resides. The second stage is a multipoint nonlinear kernel-based dimension reduction using diffusion maps to identify the subspace structure of the points on the Grassmann manifold. To this end, an appropriate Grassmannian kernel is used to construct the transition matrix of a random walk on a graph connecting points on the Grassmann manifold. Spectral analysis of the transition matrix yields low-dimensional Grassmannian diffusion coordinates embedding the data into a low-dimensional reproducing kernel Hilbert space. Further, a novel data classification/recognition technique is developed based on the construction of an overcomplete dictionary of reduced dimension whose atoms are given by the Grassmannian diffusion coordinates. Three examples are considered. First, a "toy" example shows that the GDMaps can identify an appropriate parametrization of structured points on the unit sphere. The second example demonstrates the ability of the GDMaps to revealing the intrinsic subspace structure of high-dimensional random field data. In the last ex- ample, a face recognition problem is solved considering face images subject to varying illumination conditions, changes in face expressions, and occurrence of occlusions. The technique presented high recognition rates (i.e., 95% in the best case) using a fraction of the data required by conventional methods.

42 ENGINEERING↗
DOE OSTI2024

A deep learning-based workflow for fast prediction of 3D state variables in geological carbon storage: A dimension reduction approach

Deep learning (DL) models are extensively used as surrogate models for high-fidelity simulations of multiphase fluid flow in porous media at large scales, enabling fast forecasts of the spatial–temporal evolution of three-dimensional (3D) state variables in geological carbon storage (GCS). However, training these models in high-dimensional space remains computationally demanding and prone to overfitting because of limited training data. This paper presents a novel workflow to address these challenges by integrating dimension reduction (DR) methods. Here, the proposed workflow employed pre-trained DR models to extract the latent variables of geological models and state variables and utilized the multi-layer perceptron (MLP) for constructing mapping functions between the input and output variables in latent spaces. Subsequently, the pre-trained reconstruction models converted the MLP-predicted latent state variables to their original high-dimensional form. Furthermore, we proposed a novel strategy for the DR and reconstruction of 3D saturation fields to account for the unique data characteristics of sparsity, nonuniformity, and discontinuity. The proposed strategy applied PCA and inverse PCA for 2D average saturation fields and developed a DL-based 3D reconstruction model, leveraging three 2D average saturation fields as input to produce a 3D saturation field as output. The pre-training of DR and reconstruction models and training of MLP models were conducted on 84 Gulf of Mexico (GoM) simulations and evaluated on 12 testing simulations. Each simulation contained 720 monthly time steps, with the first 360 months as the injection period and the rest as the post-injection period. The proposed workflow, incorporating DR and DL models, accurately predicts the normalized 3D pressure fields, achieving mean square error (MSE) of 2.92 × 10 -7 compared to the ground truth obtained from a full-physics simulator. Furthermore, the proposed strategy outperformed PCA and convolutional autoencoder (CAE) models on 3D saturation fields, resulting in minor workflow prediction errors with an MSE of 2.93 × 10 -5 . The results suggest the proposed workflow provides sufficient predictive fidelity across temporal and spatial scales, and enables a speedup of 160 times compared to the full-physics simulator, facilitating improved decision-making and risk assessment for large-scale GCS management in real-time scenarios.

3D reconstruction model↗
DOE OSTI2024

ML-based Dimension Reduction Strategies

Deep learning (DL)--based surrogate models have achieved success in various applications in carbon capture and storage (CCS). However, the model training on high-dimensional spaces is computationally expensive and impractical for large-scale and complex geological models, because the models usually contain hundreds of thousands to millions of grid cells, each with a set of parameters. Furthermore, the high cost of generating training data with sufficient variation is another limitation of model training on high-dimensional spaces, which may result in overfitting and reduce the model efficiency and prediction performance. We proposed the workflow incorporating dimension reduction methods and deep learning models, which aim to extract the latent variables of input parameters and output state variables, and then build the mapping function at the latent spaces. The proposed workflow can significantly reduce the computational complexity in solving both forward and inverse problems compared to models trained on high-dimensional spaces. Dimensionality reduction models showed great potential in workflows for fast reservoir simulation, history matching, prior model generation, visualization, and more, ultimately enhancing DL model performance in related SMART Work Packages.

Hosseini, Seyyed↗
DOE OSTI2021

Bridging cognitive gaps between user and model in interactive dimension reduction

Interactive machine learning (ML) systems are difficult to design because of the "Two Black Boxes" problem that exists at the interface between human and machine. Many algorithms that are used in interactive ML systems are black boxes that are presented to users, while the human cognition represents a second black box that can be difficult for the algorithm to interpret. These two black boxes create cognitive gaps between the user and the interactive ML model when a user interacts with the system. In this paper, we identify several cognitive gaps that exist in a previously-developed interactive visual analytics (VA) system, Andromeda. These cognitive gaps that we are addressing in Andromeda are representative of common problems in other VA systems. Our goal with this work is to open both black boxes and bridge these cognitive gaps by making improvements to the original Andromeda system, including designing new visual features to help people better understand how Andromeda processes and interacts with data and improving the underlying algorithm so that the Andromeda system can better understand the intent of the user during the data exploration process. We evaluate our designs through both qualitative and quantitative analysis (i.e., user study and simulation analysis), and the results confirm that the improved Andromeda system outperforms the original version significantly in a series of high-dimensional data understanding tasks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Dimension Reduction and Redundancy Removal through Successive Schmidt Decompositions

Quantum computers are believed to have the ability to process huge data sizes, which can be seen in machine learning applications. In these applications, the data, in general, are classical. Therefore, to process them on a quantum computer, there is a need for efficient methods that can be used to map classical data on quantum states in a concise manner. On the other hand, to verify the results of quantum computers and study quantum algorithms, we need to be able to approximate quantum operations into forms that are easier to simulate on classical computers with some errors. Motivated by these needs, in this paper, we study the approximation of matrices and vectors by using their tensor products obtained through successive Schmidt decompositions. We show that data with distributions such as uniform, Poisson, exponential, or similar to these distributions can be approximated by using only a few terms, which can be easily mapped onto quantum circuits. The examples include random data with different distributions, the Gram matrices of iris flower, handwritten digits, 20newsgroup, and labeled faces in the wild. Similarly, some quantum operations, such as quantum Fourier transform and variational quantum circuits with a small depth, may also be approximated with a few terms that are easier to simulate on classical computers. Furthermore, we show how the method can be used to simplify quantum Hamiltonians: In particular, we show the application to randomly generated transverse field Ising model Hamiltonians. The reduced Hamiltonians can be mapped into quantum circuits easily and, therefore, can be simulated more efficiently.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1978

Linear dimension reduction and Bayes classification

An explicit expression for a compression matrix T of smallest possible left dimension K consistent with preserving the n variate normal Bayes assignment of X to a given one of a finite number of populations and the K variate Bayes assignment of TX to that population was developed. The Bayes population assignment of X and TX were shown to be equivalent for a compression matrix T explicitly calculated as a function of the means and covariances of the given populations.

Decell, H. P., Jr.↗
NASA NTRS2014

Neural Network Machine Learning and Dimension Reduction for Data Visualization

Neural network machine learning in computer science is a continuously developing field of study. Although neural network models have been developed which can accurately predict a numeric value or nominal classification, a general purpose method for constructing neural network architecture has yet to be developed. Computer scientists are often forced to rely on a trial-and-error process of developing and improving accurate neural network models. In many cases, models are constructed from a large number of input parameters. Understanding which input parameters have the greatest impact on the prediction of the model is often difficult to surmise, especially when the number of input variables is very high. This challenge is often labeled the "curse of dimensionality" in scientific fields. However, techniques exist for reducing the dimensionality of problems to just two dimensions. Once a problem's dimensions have been mapped to two dimensions, it can be easily plotted and understood by humans. The ability to visualize a multi-dimensional dataset can provide a means of identifying which input variables have the highest effect on determining a nominal or numeric output. Identifying these variables can provide a better means of training neural network models; models can be more easily and quickly trained using only input variables which appear to affect the outcome variable. The purpose of this project is to explore varying means of training neural networks and to utilize dimensional reduction for visualizing and understanding complex datasets.

Liles, Charles A.↗