Search NASA⌕ Search

SEARCH · Search NASA

Results for “Tensor valued data”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Elliptically-Contoured Tensor-variate Distributions with Application to Image Learning

Statistical analysis of tensor-valued data has largely used the tensor-variate normal (TVN) distribution that may be inadequate for data arising from distributions with heavier or lighter tails. We study a general family of elliptically contoured (EC) TV distributions and derive its characterizations, moments, marginal, and conditional distributions. We describe procedures for maximum likelihood estimation from data that are (1) uncorrelated draws from an EC distribution, (2) from a scale mixture of the TVN distribution, and (3) from an underlying but unknown EC distribution, for which we extend Tyler’s robust estimator. A detailed simulation study highlights the benefits of choosing an EC distribution over the TVN for heavier-tailed data. We develop TV classification rules using discriminant analysis and EC errors and show that they better predict cats and dogs from images in the Animal Faces-HQ dataset than the TVN-based rules. A novel tensor-on-tensor regression and TV analysis of variance (TANOVA) framework under EC errors is also demonstrated to better characterize gender, age, and ethnic origin than the usual TVN-based TANOVA in the celebrated labeled faces of the wild dataset.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Kronecker-structured covariance models for multiway data

Many applications produce multiway data of exceedingly high dimension. Modeling such multi-way data is important in multichannel signal and video processing where sensors produce multi-indexed data, e.g. over spatial, frequency, and temporal dimensions. We will address the challenges of covariance representation of multiway data and review some of the progress in statistical modeling of multiway covariance over the past two decades, focusing on tensor-valued covariance models and their inference. We will illustrate through a space weather application: predicting the evolution of solar active regions over time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Parallel Randomized Tucker Decomposition Algorithms

The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. Here, we propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two algorithms that scale to large data and many processors, significantly reduce both computation and communication cost compared to previous deterministic and randomized approaches, and obtain nearly the same approximation errors. The key idea in our algorithms is to perform randomized sketches with Kronecker-structured random matrices, which reduces computation compared to unstructured matrices and can be implemented using a fundamental tensor computational kernel. We provide probabilistic error analysis of our algorithms and implement a new parallel algorithm for the structured randomized sketch. Our experimental results demonstrate that our combination of randomization and parallelization achieves accurate Tucker decompositions much faster than alternative approaches. We observe up to a 16X speedup over the fastest deterministic parallel implementation on 3D simulation data.

Tucker decompositions↗
NASA NTRSDate not supplied

Active Thermography Based on Tensor Rank Decomposition

Principal Component Thermography applies Singular Value Decomposition (SVD) to post-process data that are derived from active thermographic inspections. SVD provides useful compression of the data and allows for better understanding of substructure and indications of potential damage. In the standard approach, SVD is applied to a certain reshaping of a three-dimensional data stack into a two-dimensional array. This work applies the CANDECOMP-PARAFAC (CP) tensor rank decomposition directly to the three-dimensional data to avoid the initial reshaping step in order to begin to develop an inspection method that can more accurately detect defects in non-homogeneous and anisotropic materials. Tests against simulated data that compare the CP decomposition method with traditional Principal Component Thermography based on SVD are described. Finally, the method of Proper Generalized Decomposition (PGD) is used to derive the CP decomposition, and its performance against other algorithms is also discussed.

Thermography↗
NASA NTRS1995

Stress Tuning of Laser Crystals

The topic of stress tunable laser crystals is addressed in this study with the purpose of determining the piezo-optic coefficients of a new laser material. This data was collected using a quadruple pass birefringence technique because of its high degree of sensitivity relative to the other methods examined including fringe shift analysis using a Mach-Zender interferometer. A green He-Ne laser was passed through a light chopper and Glan-Thompson prism before entering a crystal of Erbium doped Yttrium Aluminum Garnet (Er:YAG) (used in order to validate the experimental technique). The Er:YAG crystal is mounted in a press mechanism and the laser is quadruple passed through test specimen before being returned through the prism and the orthogonally polarized portion of the beam measured with a optical sensor. At a later stage, the Er:YAG crystal was replaced with a new crystal in order to determine the piezo-optic coefficients of this uncharacterized material. The applied load was monitored with the use of a 50 lb. load cell placed in line with the press. Light transmission readings were taken using a lock-in amplifier while load cell measurements were taken with a voltmeter from a 5 volt, 0.5 amp power supply. Despite the fact that an effective crystal press damping system was developed, size limitations precluded the use of the complete system. For this reason, data points were taken only once per full turn so as to minimize the effect of non uniform load application on the collected data. Good correlation was found in the transmission data between the experimentally determined Er:YAG and the previously known peizo-optic constants of non-doped crystal with which it was compared. The variation which was found between the two could be accounted for by the aforementioned presence of Erbium in the experimental sample (for which exact empirical data was not known). The same test procedure was then carried out on a Yttrium Gallium Aluminum garnet (YGAG) for the purpose of establishing values of its unknown piezo-optic constant tensor using experimentally collected transmission data. Significant variation between the piezo-optic constants of YAG and YGAG crystals was found however, the excellent data correlation of separate experimental runs carried out on the YGAG sample demonstrates the validity of these results. The data collected during the stressing of the YGAG was of high quality, however the amount of data collected was somewhat limited by a fracture of YGAG specimen which undoubted altered the crystalline lattice structure and hence precluded any further testing.

Carty, Atherton A.↗
DOE OSTI2025

The Poisson tensor completion non-parametric differential entropy estimator

We introduce the Poisson tensor completion (PTC) estimator, a non-parametric differential entropy estimator. The PTC estimator leverages inter-sample relationships to compute a low-rank Poisson tensor decomposition of the frequency histogram. Our crucial observation is that the histogram bins are an instance of a space partitioning of counts and thus can be identified with a spatial Poisson process. The Poisson tensor decomposition leads to a completion of the intensity measure over all bins—including those containing few to no samples—and leads to our proposed PTC differential entropy estimator. A Poisson tensor decomposition models the underlying distribution of the count data and guarantees non-negative estimated values and so can be safely used directly in entropy estimation. Our estimator is the first tensor-based estimator that exploits the underlying spatial Poisson process related to the histogram explicitly when estimating the probability density with low-rank tensor decompositions for the purpose of tensor completion. Furthermore, we demonstrate that our PTC estimator is a substantial improvement over standard histogram-based estimators for sub-Gaussian probability distributions because of the concentration of norm phenomenon.

42 ENGINEERING↗
DOE OSTI2023

Proxy-based Bayesian inversion of strain tensor data measured during well tests

Recent instrument developments have made it possible to measure the strain tensor caused by injecting or pumping fluid from aquifers or reservoirs, but the full value of these data is limited because the long runtimes of poroelastic forward models makes it impractical to use many inversion schemes. This limits the interpretation of strain data for managing the recovery of resources or storage of wastes in the subsurface. This paper describes a method of inverting deformation data using a poroelastic numerical simulator so the results can be used to manage reservoirs or aquifers. We developed a workflow designed to reduce the number of simulations sufficiently to make it feasible to use DREAMzs, an advanced Bayesian inversion method that translates the uncertainties from different sources into unbiased posterior parameter distributions and uncertainty envelopes around the field data. Using a KNN proxy model for the poroelastic simulator is key to reducing the overall computations, and the workflow includes a strategy for ensuring the proxy model results converge on the results from the simulator. The workflow is tested using an idealized example that verifies the ability to correctly identify parameters and characterize noise used to perturb the data. Field data from an injection test at an oil reservoir near Tulsa, Oklahoma, are also used to evaluate the efficacy of the workflow with a real dataset. The workflow identified 265 history matching solutions out of 1240 total simulation runs (21% acceptance ratio), where the results were used to characterize posterior parameter distribution and evaluate the prediction uncertainty. Furthermore, this workflow is significant because it enables strain tensor, or other geomechanical measurements to be interpreted to guide decision-making during energy and environmental processes in the subsurface.

42 ENGINEERING↗
DOE OSTI2022

Constraining scale dependent growth with redshift surveys

Ongoing and future redshift surveys have the capability to measure the growth rate of large scale structure at the percent level over a broad range of redshifts, tightly constraining cosmological parameters. Beyond general relativity, however, the growth rate in the linear density perturbation regime can be not only redshift dependent but scale dependent, revealing important clues to modified gravity. We demonstrate that a fully model independent approach of binning the gravitational strength G eff (k,z) matches scalar-tensor results for the growth rate fσ 8 (k,z) to 0.02%–0.27% rms accuracy. For data of the quality of the Dark Energy Spectroscopic Instrument (DESI) we find the bin values can be constrained to 1.4%–28%. We also explore the general scalar-tensor form, constraining the amplitude and past and future scalaron mass/shape parameters. Perhaps most interesting is the strong complementarity of low redshift peculiar velocity data with DESI-like redshift space distortion measurements, enabling improvements up to a factor 6–7 on 2D joint confidence contour areas. Finally, we quantify some issues with gravity parametrizations that do not include all the key physics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Microseismic Monitoring at the Farnsworth CO 2 -EOR Field

The Farnsworth Unit in northern Texas is a field site for studying geologic carbon storage during enhanced oil recovery (EOR) using CO 2 . Microseismic monitoring is essential for risk assessment by detecting fluid leakage and fractures. We analyzed borehole microseismic data acquired during CO 2 injection and migration, including data denoising, event detection, event location, magnitude estimation, moment tensor inversion, and stress field inversion. We detected and located two shallow clusters, which occurred during increasing injection pressure. The two shallow clusters were also featured by large b values and tensile cracking moment tensors that are obtained based on a newly developed moment tensor inversion method using single-borehole data. The inverted stress fields at the two clusters showed large deviations from the regional stress field. The results provide evidence for microseismic responses to CO 2 /fluid injection and migration.

02 PETROLEUM↗
DOE OSTI2025

Minimizing CGYRO HPC Communication Costs in Ensembles with XGYRO by Sharing the Collisional Constant Tensor Structure

First-principles fusion plasma simulations are both compute and memory intensive, and CGYRO is no exception. The use of many HPC nodes to fit the problem in the available memory thus results in significant communication overhead, which is hard to avoid for any single simulation. That said, most fusion studies are composed of ensembles of simulations, so we developed a new tool, named XGYRO, that executes a whole ensemble of CGYRO simulations as a single HPC job. By treating the ensemble as a unit, XGYRO can alter the global buffer distribution logic and apply optimizations that are not feasible on any single simulation, but only on the ensemble as a whole. The main saving comes from the sharing of the collisional constant tensor structure, since its values are typically identical between parameter-sweep simulations. This data structure dominates the memory consumption of CGYRO simulations, so distributing it among the whole ensemble results in drastic memory savings for each simulation, which in turn results in overall lower communication overhead.

CGYRO↗
NASA NTRS1978

Characterization of oriented cracks with differential strain analysis

Linear strain of a rock sample as a function of hydrostatic pressure can be measured with a precision of 2 millionths. Such high-precision data for three orthogonal directions allow calculation of the distribution function for the porosity due to cracks' closing completely at a given pressure. Such data for at least six independent directions yield the zero-pressure strain tensor due to cracks' closing completely at a given pressure. The principal values and axes of this tensor distribution function provide information about the orientation of cracks as a function of closure pressure. The mathematical basis for the technique is developed, and the technique is illustrated with differential strain data for two samples, the Westerly (Rhode Island) granite and the Twin Sisters (Washington) dunite. Strain-tensor calculations reveal that each of these samples has a different type of anisotropic crack distribution.

Siegfried, R.↗
DOE OSTI2026

The Poisson tensor completion parametric estimator

We introduce the Poisson tensor completion (PTC) estimator that exploits inter-sample relationships to compute a low-rank Poisson tensor decomposition of the frequency histogram for samples of a multivariate distribution. Our crucial observation is that the histogram bins are an instance of a space partitioning of counts and thus can be identified with a spatial non-homogeneous Poisson process. The Poisson tensor decomposition leads to a completion of the mean measure over all bins—including those containing few to no samples—and leads to our proposed estimator. A Poisson tensor decomposition models the underlying distribution of the count data and guarantees non-negative estimated values obviating the need for additional constraints to ensure non-negativity. Furthermore, we demonstrate that our PTC estimator is a substantial improvement over standard histogram-based estimators for sub-Gaussian probability distributions because of the concentration of norm phenomenon.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Tencoder: tensor-product encoder-decoder architecture for predicting solutions of PDEs with variable boundary data

It is widely hoped that artificial intelligence will boost data-driven surrogate models in science and engineering. However, fundamental spatial aspects of AI surrogate models remain under-studied. We investigate the ability of neural-network surrogate models to predict solutions to PDEs under variable boundary values. We do not wish to retrain the model when the boundary values change but to make them inputs to the model and infer the solution of the PDE under those boundary conditions. Such a capability is essential to making AI-based surrogate models practically useful. While simple feedforward networks are used for one-dimensional (1D) Poisson equation, an encoder-decoder architecture with a tensor-product layer is developed for the two-dimensional Poisson equation posed on a rectangular domain. We show that it is indeed possible to infer solutions to PDEs from variable boundary data using neural networks in this relatively simple setting, and point to future directions.

Kashi, Aditya↗
DOE OSTI2023

Using the Shallow Strain Tensor to Characterize Deep Geologic Reservoirs

Abstract Storing and recovering water, carbon, and heat from geologic reservoirs is central to managing resources in a changing climate. We tested the hypothesis that the strain tensor caused by injecting or producing fluids can be measured at shallow depths and interpreted to advance understanding of underlying deep aquifers or reservoirs. Geodetic‐grade strainmeters were deployed at 30 m depth overlying the Bartlesville Formation, a 500‐m‐deep sandstone near Tulsa, OK. The strainmeters are 220 m east of injection well 9A completed in a permeable lens at the base of the Bartlesville Formation. Water was injected into well 9A at approximately 1.0 L/s during four tests that ranged in duration from a few hours to a few weeks. The horizontal strain increased (tension) and the circumferential strain was a few times larger than the radial strain. The vertical strain decreased (compression) during injection. Strain rates were approximately 100 nε/day during the first few hours, but the rates decreased and were approximately 10 nε/day during most of the tests. Four independent methods of poroelastic simulation and inversion predict reservoir properties and geometries that are similar to each other and consistent with independent information about the reservoir. All strain interpretations predict that a boundary to the permeable lens occurs beneath the vicinity of the strainmeters, which is consistent with core data from the site. The boundary of the permeable lens is located by matching the vertical, radial and circumferential strains, which demonstrates the value of measuring the strain tensor.

Murdoch, Lawrence C.↗
NASA NTRS1972

Theoretical frameworks for testing relativistic gravity. IV - A compendium of metric theories of gravity and their post-Newtonian limits.

Metric theories of gravity are compiled and classified according to the types of gravitational fields they contain, and the modes of interaction among those fields. The gravitation theories considered are classified as (1) general relativity, (2) scalar-tensor theories, (3) conformally flat theories, and (4) stratified theories with conformally flat space slices. The post-Newtonian limit of each theory is constructed and its Parametrized Post-Newtonian (PPN) values are obtained by comparing it with Will's version of the formalism. Results obtained here, when combined with experimental data and with recent work by Nordtvedt and Will and by Ni, show that, of all theories thus far examined by our group, the only currently viable ones are general relativity, the Bergmann-Wagoner scalar-tensor theory and its special cases (Nordtvedt; Brans-Dicke-Jordan), and a recent, new vector-tensor theory by Nordtvedt, Hellings, and Will.

Ni, W.-T.↗
DOE OSTI2025

Informed unsupervised machine learning analysis of dislocation microstructure from high-resolution differential aperture X-ray structural microscopy data

This study leverages high-resolution differential-aperture X-ray structural microscopy (DAXM) to probe the local dislocation structure in deformed 304L-stainless steel at small strain, by measuring the lattice rotation and deviatoric elastic strain with a sub-micron resolution. For a single grain in a polycrystalline specimen, the measured lattice rotation field over the measured volume exhibited a multimodal distribution while the deviatoric elastic strain showed a single-mode distribution. An unsupervised Cauchy mixture machine learning model was developed to resolve the multimodal distribution of the lattice rotation. By mapping the lattice rotation data associated with each Cauchy peak in the model back onto the measured volume, we identify contiguous regions of the crystal rotated near the average values corresponding to the peaks of the overall rotation distribution. These regions represent the grain subdivision in the microstructure. Finally, the dislocation density tensor was also computed and its norm was laid over the rotation field to detect the subgrain boundaries. This step provided a validation of the Cauchy mixture model for the analysis of the lattice rotation distribution. The current study highlights the integration of advanced X-ray microscopy techniques with data-driven analysis methods to uncover detailed microstructure scales in deformed crystals.

Machine learning; Lattice rotation; High-energy X-↗
DOE OSTI2023

Zero-truncated Poisson regression for sparse multiway count data corrupted by false zeros

Abstract We propose a novel statistical inference methodology for multiway count data that is corrupted by false zeros that are indistinguishable from true zero counts. Our approach consists of zero-truncating the Poisson distribution to neglect all zero values. This simple truncated approach dispenses with the need to distinguish between true and false zero counts and reduces the amount of data to be processed. Inference is accomplished via tensor completion that imposes low-rank tensor structure on the Poisson parameter space. Our main result shows that an $N$-way rank-$R$ parametric tensor $\boldsymbol{\mathscr{M}}\in (0,\infty )^{I\times \cdots \times I}$ generating Poisson observations can be accurately estimated by zero-truncated Poisson regression from approximately $IR^2\log _2^2(I)$ non-zero counts under the nonnegative canonical polyadic decomposition. Our result also quantifies the error made by zero-truncating the Poisson distribution when the parameter is uniformly bounded from below. Therefore, under a low-rank multiparameter model, we propose an implementable approach guaranteed to achieve accurate regression in under-determined scenarios with substantial corruption by false zeros. Several numerical experiments are presented to explore the theoretical results.

97 MATHEMATICS AND COMPUTING↗