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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
DOE OSTI2024

Collocation methods for nonlinear differential equations on low-rank manifolds

We introduce new methods for integrating nonlinear differential equations on low-rank manifolds. These methods rely on interpolatory projections onto the tangent space, enabling low-rank time integration of vector fields that can be evaluated entry-wise. A key advantage of our approach is that it does not require the vector field to exhibit low-rank structure, thereby overcoming significant limitations of traditional dynamical low-rank methods based on orthogonal projection. To construct the interpolatory projectors, we develop a sparse tensor sampling algorithm based on the discrete empirical interpolation method (DEIM) that parameterizes tensor train manifolds and their tangent spaces with cross interpolation. Using these projectors, we propose two time integration schemes on low-rank tensor train manifolds. The first scheme integrates the solution at selected interpolation indices and constructs the solution with cross interpolation. The second scheme generalizes the well-known orthogonal projector-splitting integrator to interpolatory projectors. We demonstrate the proposed methods with applications to several tensor differential equations arising from the discretization of partial differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Sampling two-dimensional isometric tensor network states

Sampling a quantum system’s underlying probability distributions is an important computational task, e.g., for quantum advantage experiments and quantum Monte Carlo algorithms. Tensor networks are an invaluable tool for efficiently representing states of large quantum systems with limited entanglement. Algorithms for sampling one-dimensional (1D) tensor networks are well-established and utilized in several 1D tensor network methods. In this paper we introduce two novel sampling algorithms for two-dimensional (2D) isometric tensor network states (isoTNS) that generalize existing 1D tensor network sampling algorithms. Our first proposed algorithm performs independent sampling and yields a single configuration together with its associated probability. The second algorithm employs a greedy search strategy to identify high-probability configurations and their corresponding probabilities. Numerical results demonstrate the effectiveness of these algorithms across quantum states with varying entanglement and system size.

Dumitrescu, Eugene [ORNL] (ORCID:0000000158519567)↗
DOE OSTI2020

Denoising atomic resolution 4D scanning transmission electron microscopy data with tensor singular value decomposition

Tensor singular value decomposition (SVD) is a method to find a low-dimensional representation of data with meaningful structure in three or more dimensions. Here, tensor SVD has been applied to denoise atomic-resolution 4D scanning transmission electron microscopy (4D STEM) data. On data simulated from a SrTiO 3 [100] perfect crystal and a Si [110] edge dislocation, tensor SVD achieved an average peak signal-to-noise ratio (PSNR) of ~40 dB, which matches or exceeds the performance of other denoising methods, with processing times at least 100 times shorter. On experimental data from SrTiO 3 [100] and LiZnSb [11 2 ¯ 0]/GaSb [110] samples, tensor SVD denoises multiple GB 4D STEM data sets in ten minutes on a typical personal computer. Denoising with tensor SVD improves both convergent beam electron diffraction patterns and virtual-aperture annular dark field images.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Stochastic Gradients for Large-Scale Tensor Decomposition

Tensor decomposition is a well-known tool for multiway data analysis. This work proposes using stochastic gradients for efficient generalized canonical polyadic (GCP) tensor decomposition of large-scale tensors. GCP tensor decomposition is a recently proposed version of tensor decomposition that allows for a variety of loss functions such as Bernoulli loss for binary data or Huber loss for robust estimation. Here, the stochastic gradient is formed from randomly sampled elements of the tensor and is efficient because it can be computed using the sparse matricized-tensor times Khatri--Rao product tensor kernel. For dense tensors, we simply use uniform sampling. For sparse tensors, we propose two types of stratified sampling that give precedence to sampling nonzeros. Numerical results demonstrate the advantages of the proposed approach and its scalability to large-scale problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Multiplexing Focusing Analyzer for Efficient Stress-Strain Measurements

Statement of the problem or situation that is being addressed. Although thermal and cold neutron scattering is widely used and is critical for success in many areas of materials science and engineering, relatively low neutron fluxes severely limit applications of not only laboratory neutrons generators, but also large national neutron facilities. State-of-the-art thermal and cold neutron sources are large expensive national facilities, which serve diverse community of scientific and industrial users. The constant need to improve the instruments performance, stems from the fact that neutron methods are gaining in popularity, and becoming more and more powerful, while new neutron sources are not being constructed to keep pace with the developments and needs of the scientific community. Small research reactors at universities and National Labs, and laboratory-based neutron generators, are necessary not only for education and training, but also when samples cannot be transported to other facilities. However, the standard neutron techniques, which were developed for high-flux facilities, require much higher efficiencies to be used effectively with the low fluxes of small sources. Thus, the efficient use of neutron sources, such as with our proposed analyzer, is important for the progress and broader use of these neutron techniques. General statement of how this problem is being addressed. We propose to design and demonstrate novel diffractive optical device, which will enable very efficient residual stress neutron diffractometers. The proposed device will be a multi-foil analyzer, where each foil is constructed of focusing bent single crystals of Si. Such device will enable polychromatic residual stress neutron diffraction. At large national facilities, such as at Oak Ridge National Laboratory, these analyzers would enable very fast measurements for determining residual stress tensors, raster large samples or screen multiple samples. Commercial Applications and Other Benefits The outcome of this project would be the demonstration of commercial devices, novel neutron optical components, which could be utilized to improve the performance of existing instruments or build novel neutron scattering instruments at DOE neutron facilities and commercial laboratory neutron sources. These new devices will widen the scope of research conducted using neutrons and enable measurements not feasible at present. Summary for Members of Congress Thermal and cold neutron beams are a powerful materials science probe, which provide unique information about the structure of matter. The proposed innovations expand the reach of neutron-based investigations to new materials and industries by enabling new instrumentation capabilities, thereby greatly enhancing and expanding the role of small, laboratory-based neutron instrumentation, and improving education and training of neutron users.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
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 OSTI2020

Model-Free State Estimation Using Low-Rank Canonical Polyadic Decomposition

As electric grids experience high penetration levels of renewable generation, fundamental changes are required to address real-time situational awareness. Here, we utilize unique traits of tensors to devise a model-free situational awareness and energy forecasting framework for distribution networks. This work formulates the state of the network at multiple time instants as a three-way tensor; hence, recovering full state information of the network is tantamount to estimating all the values of the tensor. Given measurements received from µphasor measurement units and/or smart meters, the recovery of unobserved quantities is carried out using the low-rank canonical polyadic decomposition of the state tensor—that is, the state estimation task is posed as a tensor imputation problem utilizing observed patterns in measured (sampled) quantities. Two structured sampling schemes are considered, namely, asynchronous slab and fiber sampling. For both schemes, we present sufficient conditions on the number of sampled slabs and fibers that guarantee identifiability of the factors of the state tensor. Numerical results demonstrate the ability of the proposed framework to achieve high estimation accuracy in multiple sampling scenarios.

42 ENGINEERING↗
DOE OSTI2024

The Average Spectrum Norm and Near-Optimal Tensor Completion

We propose the average spectrum norm to study the minimum number of measurements required to approximate a multidimensional array (i.e., sample complexity) via low-rank tensor recovery. Our focus is on the tensor completion problem, where the aim is to estimate a multiway array using a subset of tensor entries corrupted by noise. Our average spectrum norm-based analysis provides near-optimal sample complexities, exhibiting dependence on the ambient dimensions and rank that do not suffer from exponential scaling as the order increases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Using silicon-vacancy centers in diamond to probe the full strain tensor

An ensemble of silicon vacancy (SiV−) centers in diamond is probed using two-pulse correlation spectroscopy and multidimensional coherent spectroscopy. Two main distinct families of SiV− centers are identified, and these families are paired with two orientation groups by comparing spectra from different linear polarizations of the incident laser. By tracking the peak centers in the measured spectra, the full diamond strain tensor is calculated local to the laser spot. Measurements are made at multiple points on the sample surface, and variations in the strain tensor are observed.

Bates, Kelsey M. (ORCID:0000000324961124)↗
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 OSTI2024

Angle-Resolved Polarized Raman Study of Layered Cr 2 Se 3

The polarization-resolved Raman spectra of two-dimensional Cr 2 Se 3 synthesized via chemical vapor deposition (CVD) and chemical vapor transport (CVT) techniques were investigated in detail. The samples were characterized using X-ray diffraction (XRD), transmission electron microscopy (TEM), and energy-dispersive X-ray spectroscopy (EDS). A distinct polarization dependence was observed in the Raman intensity of all the Cr-Cr, Cr-Se, and Se-Se modes in both samples. The observed angle-dependent Raman intensities of each peak could be related to the crystal structure-specific Raman tensor. XRD results of the bulk Cr 2 Se 3 sample synthesized via CVT confirm its trigonal crystal structure, and the Raman peaks can be fitted using the Raman tensors for the A g and E g modes for both the parallel and crossed polarizations. However, for the Cr 2 Se 3 samples directly grown on Si/SiO 2 substrates by CVD, it was necessary to assume the triclinic crystal structure in order to explain the polarized Raman dependence of all the peaks in both parallel and crossed polarization directions. Furthermore, this is the first experimental result suggesting the existence of triclinic Cr 2 Se 3 crystal structure, which has been theoretically predicted in the Materials Project database.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Absence of Barren Plateaus and Scaling of Gradients in the Energy Optimization of Isometric Tensor Network States

Abstract Vanishing gradients can pose substantial obstacles for high-dimensional optimization problems. Here we consider energy minimization problems for quantum many-body systems with extensive Hamiltonians and finite-range interactions, which can be studied on classical computers or in the form of variational quantum eigensolvers on quantum computers. Barren plateaus correspond to scenarios where the average amplitude of the energy gradient decreases exponentially with increasing system size. This occurs, for example, for quantum neural networks and for brickwall quantum circuits when the depth increases polynomially in the system size. Here we prove that the variational optimization problems for matrix product states, tree tensor networks, and the multiscale entanglement renormalization ansatz are free of barren plateaus. The derived scaling properties for the gradient variance provide an analytical guarantee for the trainability of randomly initialized tensor network states (TNS) and motivate certain initialization schemes. In a suitable representation, unitary tensors that parametrize the TNS are sampled according to the uniform Haar measure. We employ a Riemannian formulation of the gradient based optimizations which simplifies the analytical evaluation.

Barthel, Thomas↗
DOE OSTI2024

Robust training of machine learning interatomic potentials with dimensionality reduction and stratified sampling

Abstract Machine learning interatomic potentials (MLIPs) enable accurate simulations of materials at scales beyond that accessible by ab initio methods and play an increasingly important role in the study and design of materials. However, MLIPs are only as accurate and robust as the data on which they are trained. Here, we present DImensionality-Reduced Encoded Clusters with sTratified (DIRECT) sampling as an approach to select a robust training set of structures from a large and complex configuration space. By applying DIRECT sampling on the Materials Project relaxation trajectories dataset with over one million structures and 89 elements, we develop an improved materials 3-body graph network (M3GNet) universal potential that extrapolates more reliably to unseen structures. We further show that molecular dynamics (MD) simulations with the M3GNet universal potential can be used instead of expensive ab initio MD to rapidly create a large configuration space for target systems. We combined this scheme with DIRECT sampling to develop a reliable moment tensor potential for titanium hydrides without the need for iterative augmentation of training structures. This work paves the way for robust high-throughput development of MLIPs across any compositional complexity.

Qi, Ji (ORCID:0000000158089931)↗
DOE OSTI2021

Effective point-charge analysis of crystal fields: Application to rare-earth pyrochlores and tripod kagome magnets 𝑅 ⁢3⁢ Mg⁢ 2 ⁢Sb⁢ 3⁢ O⁢ 14

An indispensable step to understand collective magnetic phenomena in rare-earth compounds is the determination of spatially anisotropic single-ion properties resulting from spin-orbit coupling and crystal field (CF). The CF Hamiltonian has a discrete energy spectrum—accessible to spectroscopic probes such as neutron scattering—controlled by a number of independent parameters reflecting the point symmetry of the magnetic sites. Determining these parameters in low-symmetry systems is often challenging. Here, we describe a general method to analyze CF excitation spectra using adjustable effective point-charges. We benchmark our method to existing neutron-scattering measurements on pyrochlore rare-earth oxides and obtain a universal point-charge model that describes a large family of related materials. We adapt this model to the newly discovered tripod kagome magnets (𝑅 3 ⁢Mg 2 ⁢Sb 3 ⁢O 14 , 𝑅 = Tb, Ho, Er, Yb) for which we report broadband inelastic neutron-scattering spectra. Analysis of these data using adjustable point-charges yields the CF wave functions for each compound. From this, we calculate thermomagnetic properties that accurately reflect our measurements on powder samples and predict the effective gyromagnetic tensor for pseudospin degrees of freedom—a crucial step to understand the exotic collective properties of these kagome magnets at low temperature. We present further applications of our method to other tripod kagome materials and triangular rare-earth compounds 𝑅⁢MgGaO 4 (𝑅 =Yb, Tm). Overall, this study establishes a widely applicable methodology to predict CF and single-ion properties of rare-earth compounds based on interpretable and adjustable models of effective point charges.

Crystal-field theory↗