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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Random projection using random quantum circuits

The random sampling task performed by Google's Sycamore processor gave us a glimpse of the “quantum supremacy era.” This has definitely shed some light on the power of random quantum circuits in this abstract task of sampling outputs from the (pseudo)random circuits. In this paper, we explore a practical near-term use of local random quantum circuits in dimensional reduction of large low-rank data sets. We make use of the well-studied dimensionality reduction technique called the random projection method. This method has been extensively used in various applications such as image processing, logistic regression, entropy computation of low-rank matrices, etc. We prove that the matrix representations of local random quantum circuits with sufficiently shorter depths [ ∼ O ( n ) ] serve as good candidates for random projection. We demonstrate numerically that their projection abilities are not far off from the computationally expensive classical principal components analysis on MNIST and CIFAR-100 image datasets. We also benchmark the performance of quantum random projection against the commonly used classical random projection in the tasks of dimensionality reduction of image data sets and computing von Neumann entropies of large low-rank density matrices. And finally, using variational quantum singular value decomposition, we demonstrate a near-term implementation of extracting the singular vectors with dominant singular values after quantum random projecting a large low-rank matrix to lower dimensions. All such numerical experiments unequivocally demonstrate the ability of local random circuits to randomize a large Hilbert space at sufficiently shorter depths with robust retention of properties of large data sets in reduced dimensions. Published by the American Physical Society 2024

Kumaran, Keerthi (ORCID:0009000949125721)↗
DOE OSTI2020

Randomized Projection for Rank-Revealing Matrix Factorizations and Low-Rank Approximations

Rank-revealing matrix decompositions provide an essential tool in spectral analysis of matrices, including the Singular Value Decomposition (SVD) and related low-rank approximation techniques. QR with Column Pivoting (QRCP) is usually suitable for these purposes, but it can be much slower than the unpivoted QR algorithm. For large matrices, the difference in performance is due to increased communication between the processor and slow memory, which QRCP needs in order to choose pivots during decomposition. Our main algorithm, Randomized QR with Column Pivoting (RQRCP), uses randomized projection to make pivot decisions from a much smaller sample matrix, which we can construct to reside in a faster level of memory than the original matrix. This technique may be understood as trading vastly reduced communication for a controlled increase in uncertainty during the decision process. Furthermore, for rank-revealing purposes, the selection mechanism in RQRCP produces results that are the same quality as the standard algorithm, but with performance near that of unpivoted QR (often an order of magnitude faster for large matrices). Additionally, we also propose two formulas that facilitate further performance improvements. The first efficiently updates sample matrices to avoid computing new randomized projections. The second avoids large trailing updates during the decomposition in truncated low-rank approximations. Our truncated version of RQRCP also provides a key initial step in our truncated SVD approximation, TUXV. These advances open up a new performance domain for large matrix factorizations that will support efficient problem-solving techniques for challenging applications in science, engineering, and data analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

RandONets: Shallow networks with random projections for learning linear and nonlinear operators

Deep neural networks have been extensively used for the solution of both the forward and the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space of parameters and hyperparameters. This fact, along with the requirement of substantial computational resources, pose a barrier to achieving high numerical accuracy, but also interpretability. Here, to address the above challenges, we present Random Projection-based Operator Networks (RandONets): shallow networks with random projections and tailor-made numerical analysis methods that learn accurately and fast linear and nonlinear operators. Building on previous works, we prove that RandOnets are universal approximators of linear and nonlinear operators. Due to their simplicity, RandONets provide a one-step transformation of the input space, facilitating interpretability. For the evaluation of their performance, we focus on operators of PDEs. We show, that RandONets outperform by several orders of magnitude, both in terms of numerical approximation accuracy and computational cost, the “vanilla” DeepONets. Hence, we believe that our method will trigger further developments in the field of scientific machine learning, for the development of new ‘’light”schemes that will provide high accuracy while reducing dramatically the computational cost. A MATLAB toolbox for RandONets, including demos, is available on GitHub at https://github.com/GianlucaFabiani/RandONets.

Interpretable machine learning↗
DOE OSTI2023

An Analysis of the Johnson-Lindenstrauss Lemma with the Bivariate Gamma Distribution

Probabilistic proofs of the Johnson-Lindenstrauss lemma imply that random projection can reduce the dimension of a data set and approximately preserve pairwise distances. If a distance being approximately preserved is called a success, and the complement of this event is called a failure, then such a random projection likely results in no failures. Assuming a Gaussian random projection, the lemma is proved by showing that the no-failure probability is positive using a combination of Bonferroni's inequality and Markov's inequality. This paper modifies this proof in two ways to obtain a greater lower bound on the no-failure probability. First, Bonferroni's inequality is applied to pairs of failures instead of individual failures. Second, since a pair of projection errors has a bivariate gamma distribution, this probability of a pair of successes is bounded using an inequality from [Jensen, 1969]. If n is the number of points to be embedded and μ is the probability of success, then this leads to an increase in the lower bound on the no-failure probability of $\frac{1}{2}$ ($\genfrac{}{}{0pt}{}{n}{2}$) (1- μ ) 2 is ($\genfrac{}{}{0pt}{}{n}{2}$) is even and $\frac{1}{2}$ (($\genfrac{}{}{0pt}{}{n}{2}$)-1) (1- μ ) 2 if ($\genfrac{}{}{0pt}{}{n}{2}$) is odd. For example, if n =10 5 points are to be embedded in k =10 4 dimensions with a tolerance of ϵ=0.1, then the improvement in the lower bound is on the order of 10 -14 . We also show that further improvement is possible if the inequality in [Jensen, 1969] extends to three successes, though we do not have a proof of this result.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2023

Spatio-Temporal Surrogates for Interaction of a Jet with High Explosives: Part II - Clustering Extremely High-Dimensional Grid-Based Data

Building an accurate surrogate model for the spatio-temporal outputs of a computer simulation is a challenging task. A simple approach to improve the accuracy of the surrogate is to cluster the outputs based on similarity and build a separate surrogate model for each cluster. This clustering is relatively straightforward when the output at each time step is of moderate size. However, when the spatial domain is represented by a large number of grid points, numbering in the millions, the clustering of the data becomes more challenging. In this report, we consider output data from simulations of a jet interacting with high explosives. These data are available on spatial domains of different sizes, at grid points that vary in their spatial coordinates, and in a format that distributes the output across multiple files at each time step of the simulation. We first describe how we bring these data into a consistent format prior to clustering. Borrowing the idea of random projections from data mining, we reduce the dimension of our data by a factor of thousand, making it possible to use the iterative k-means method for clustering. We show how we can use the randomness of both the random projections, and the choice of initial centroids in k-means clustering, to determine the number of clusters in our data set. Our approach makes clustering of extremely high dimensional data tractable, generating meaningful cluster assignments for our problem, despite the approximation introduced in the random projections.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

CCD observations of Abell clusters. IV - Surface photometry of 175 brightest cluster galaxies

The present data from a consistent body of CCD aperture and surface photometry for the brightest galaxies in 175 clusters from the Abell catalog confirm the dispersion in the aperture luminosities for first-ranked cluster galaxies of about 0.32 mag, as well as the documented trends of luminosity with Bautz-Morgan class and cluster richness. Half of these objects are multiple-nucleus systems; multiplicity is not strongly correlated with cluster morphology or richness, and the fraction of multiples is 2-10 times higher than would be produced by random projection in the cores of Hubble-law clusters. The average distance of the secondary nuclei from the luminosity center of the galaxy is significantly less than the value expected from random projections.

Hoessel, J. G.↗
DOE OSTI2021

Online Voltage Event Detection Using Synchrophasor Data with Structured Sparsity-Inducing Norms

This paper develops an accurate and computationally efficient data-driven framework to detect voltage events from PMU data streams. It develops an innovative Proximal Bilateral Random Projection (PBRP) algorithm to quickly decompose the PMU data matrix into a low-rank matrix, a row-sparse event-pattern matrix and a noise matrix. Here, the row-sparse pattern matrix significantly distinguishes events from normal behavior. These matrices are then fed into a clustering algorithm to separate voltage events from normal operating conditions. Large-scale numerical study results on real-world PMU data show that the proposed algorithm is computationally more efficient and achieves higher F scores than state-of-the-art benchmarks.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Subhaloes are anisotropically distributed and aligned with the smooth matter distribution of their host haloes

ABSTRACT We investigate the distributions of subhaloes about their hosts in two suites of zoom-in N-body simulations of halo growth – one suite focused on Milky Way-Mass haloes ($\sim 10^{12} \, \mathrm{M}_{\odot }$) and another focused on cluster-mass haloes ($\sim 10^{15} \, \mathrm{M}_{\odot }$) in the Symphony simulation suite. We find, in agreement with previous work on this subject, that subhaloes are distributed anisotropically about their host haloes. In particular, the positions of subhaloes lie preferentially near the major axes of their host haloes, possibly implying that satellite galaxies will exhibit a similar alignment. Furthermore, we show that in two-dimensional projection subhaloes are more likely to be observed near the halo centre (where the central galaxy presumably resides) when the host halo is projected nearly along its major axis. This projection effect is significant. Within projected radii of a few per cent of the virial radius of the host halo, the fraction of mass in subhaloes is $\sim 175~{{\ \rm per\ cent}}$ larger for Milky Way-mass haloes and as much as $\sim 195~{{\ \rm per\ cent}}$ larger for cluster haloes when projected along the major axis as compared to the average from a random projection. This result has consequences for many applications including the interpretation of gravitational lenses. Finally, we find that the orbital angular momentum vector of subhaloes is aligned with the angular momentum vector of their host halo, indicating that a significant component of a halo’s angular momentum may be carried in its subhaloes. This has consequences for galaxy formation models which use host halo angular momentum as a proxy for galaxy momentum.

Mezini, Lorena (ORCID:0000000300053973)↗
DOE OSTI2020

Petz reconstruction in random tensor networks

We illustrate the ideas of bulk reconstruction in the context of random tensor network toy models of holography. Specifically, we demonstrate how the Petz reconstruction map works to obtain bulk operators from the boundary data by exploiting the replica trick. We also take the opportunity to comment on the differences between coarse-graining and random projections.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Comments on the entanglement spectrum of de Sitter space

We argue that the Schwarzschild-de Sitter black hole entropy formula does not imply that the entanglement spectrum of the vacuum density matrix of de Sitter space is flat. Specifically, we show that the expectation value of a random projection operator of dimension d >> 1, on a Hilbert space of dimension D >> d and in a density matrix ρ = e –K with strictly positive spectrum, is $\frac{d}{D} \large{(}1 + o \large{(}\frac{1}{\sqrt{d}}\large{)}$, independent of the spectrum of the density matrix. In addition, for a suitable class of spectra the asymptotic estimates Tr (ρK) ~ ln D – o(1) and Tr [ρ(K – $\langle$K$\rangle$) 2 ] = a $\langle$K$\rangle$ are compatible for any order one constant a. We discuss a simple family of matrix models and projections that can replicate such modular Hamiltonians and the SdS entropy formula.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Integrated photonic encoder for low power and high-speed image processing

Abstract Modern lens designs are capable of resolving greater than 10 gigapixels, while advances in camera frame-rate and hyperspectral imaging have made data acquisition rates of Terapixel/second a real possibility. The main bottlenecks preventing such high data-rate systems are power consumption and data storage. In this work, we show that analog photonic encoders could address this challenge, enabling high-speed image compression using orders-of-magnitude lower power than digital electronics. Our approach relies on a silicon-photonics front-end to compress raw image data, foregoing energy-intensive image conditioning and reducing data storage requirements. The compression scheme uses a passive disordered photonic structure to perform kernel-type random projections of the raw image data with minimal power consumption and low latency. A back-end neural network can then reconstruct the original images with structural similarity exceeding 90%. This scheme has the potential to process data streams exceeding Terapixel/second using less than 100 fJ/pixel, providing a path to ultra-high-resolution data and image acquisition systems.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Zero-Power Analog Optical Processing

The motivation behind this research is the growing challenge of handling the massive amounts of data generated by modern imaging systems. Conventional digital image processing techniques are struggling to keep pace with the demands of high-resolution and high-speed imaging systems for remote sensing due to their high-power consumption and data storage requirements. We present a novel approach based on analog photonics to address this challenge. The proposed system utilizes a silicon-photonics-based image encoder positioned after image formation and initial optical-to-electrical conversion. The photonic encoder compresses image data using a passive disordered photonic structure to perform kernel-type random projections of the raw data. The compressed data is then processed by a back-end neural network, which reconstructs the original image with high fidelity (structural similarity exceeding 90%). Our proposed approach has the potential to compress images with ~ 1000X lower power consumption compared to digital approaches with data rates exceeding 1 terapixel/second.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Gearbox bearing crack growth prognostics and uncertainty quantification with physics-informed machine learning

This paper introduces the extreme theory of functional connections (X-TFC), a physics-informed machine learning algorithm, and tailors it to estimate the remaining useful life (RUL) of wind turbine gearbox bearings experiencing fatigue crack growth. Unlike purely data-driven methods, X-TFC embeds a physics model, based on Head's theory in this work, into its training objective. The core of X-TFC is a random-projection single-layer neural network trained via an extreme learning machine, which requires only limited damage progression data and solves for output weights with a least-squares optimization algorithm. A composite loss function balances the network's fit to observed degradation data against the residuals of the governing crack growth differential equation, ensuring the learned damage trajectory remains physically plausible. When applied to a vibration-based health-index (HI) dataset measured during the growth of a crack on the inner ring of a high-speed bearing in a wind turbine gearbox (Bechhoefer and Dubé, 2020), X-TFC achieves near-zero prediction bias. Even when trained on only the first 10 %–20 % of the damage progression data, with sufficient physics weighting its predictions remain monotonic and smooth, delivering high prognosability and trendability. To quantify the epistemic uncertainty, we employ a Monte Carlo ensemble of independently initialized X-TFC models trained on noise-perturbed data, which yields confidence intervals around each RUL estimate and captures both model-parameter and epistemic uncertainty. In addition to a vibration-based HI, we demonstrate that the proposed framework can be directly applied to a supervisory control and data acquisition (SCADA) data-based HI (Eftekhari Milani et al., 2026) measured during similar wind turbine gearbox bearing crack faults, preserving its accuracy and interpretability. This extension shows the versatility of our approach, which is applicable to bearings of multiple gearbox manufacturers, models, and ratings using only SCADA data. By integrating domain knowledge with machine learning, X-TFC offers a rapid, reliable tool for crack prognostics. Its adaptability to other bearing failure modes, such as pitch bearing ring cracks, positions X-TFC as a powerful enabler of data-driven, physics-informed asset management in the wind energy sector and beyond.

17 WIND ENERGY↗
NASA NTRS1988

Discordant redshifts in compact groups of galaxies

The field galaxy contamination of galaxy quintets in Hickson's catalog of compact groups is estimated by computing the probability of the random projection of field galaxies on or near quartets in the catalog. This is done by Monte Carlo simulations based on galaxy counts in fields surrounding the quartets. Thirty-five percent of all quintets are predicted to contain a single discordant redshift due to a projected field galaxy. This agrees with the observed number of four discordant quintets in 10. These results are consistent with the cosmological interpretation of galaxy redshifts.

Hickson, Paul↗
NASA NTRS2019

Structural Dynamic Testing Results for Air-Independent Proton Exchange Membrane (PEM) Fuel Cell Technologies for Space Applications

In 2016, the NASA Advanced Exploration Systems (AES) project office funded research at the NASA Glenn Research Center to evaluate the maturity of the Proton Exchange Membrane (PEM) fuel cell technology and its viability for supporting launch vehicle and space applications. This technology evaluation included vibration, reactant purity, and vacuum exposure sensitivity testing. The evaluation process did not include microgravity testing. This paper discusses the vibration sensitivity testing of two air-independent fuel cell stacks provided by different vendors to assess the ability of currently available fuel cell stack hardware to survive the projected random vibrational environment that would be encountered in an upper stage launch vehicle. Baseline performance testing was utilized to quantify stack performance and overboard leak rate at standard atmospheric conditions in order to provide a reference for post-test comparison. Both fuel cell stacks were tested at a random vibration qualification level of 10.4 grms for five minutes in each axis. Low-level sinusoidal sweeps were conducted before and after each random vibration level run to see if any significant change in resonances were detected. Following vibration facility testing, the baseline performance testing was repeated. Test results demonstrated no measurable change in fuel cell electrochemical or mechanical performance, indicating that the two evaluated PEM fuel cell stacks may be suitable for space applications pending microgravity testing.

Gilligan, Ryan P.↗