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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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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
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 OSTI2025

The tensor-train stochastic finite volume method for uncertainty quantification

The stochastic finite volume method offers an efficient one-pass approach for assessing uncertainty in hyperbolic conservation laws. Still, it struggles with the curse of dimensionality when dealing with multiple stochastic variables. Here, we introduce the stochastic finite volume method within the tensor-train framework to counteract this limitation. This integration, however, comes with its own set of difficulties, mainly due to the propensity for shock formation in hyperbolic systems. To overcome these issues, we have developed a tensor-train-adapted stochastic finite volume method that employs a global WENO reconstruction, making it suitable for such complex systems. This approach represents the first step in designing tensor-train techniques for hyperbolic systems and conservation laws involving shocks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Enhanced tensor polarization in solid-state targets

In this work, we report measurements of enhanced tensor polarization on solid-state targets. The results here represent an increase in tensor polarization over that previously achieved in high energy and nuclear scattering experiments that focused on the measurement of tensor polarized observables. Enhancement techniques are used which require RF produced close to the Larmor frequency of the target spins and use selective semi-saturation resulting from two sources of irradiation, microwave for the DNP process and the additional RF used to manipulate the population of the energy levels in the target material. The spin dynamics of the solid target are used to align the spins enhancing the ensemble average to improve the figure of merit of the scattering experiment. Target rotation at an optimized rate can lead to additional enhancement by applying selective semi-saturation in polycrystalline materials that possess a Pake doublet in their NMR signal.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Systematic Generation of Moment Invariant Bases for 2D and 3D Tensor Fields

Moment invariants have been successfully applied to pattern detection tasks in 2D and 3D scalar, vector, and matrix valued data. However so far no flexible basis of invariants exists, i.e., no set that is optimal in the sense that it is complete and independent for every input pattern. Here, we prove that a basis of moment invariants can be generated that consists of tensor contractions of not more than two different moment tensors each under the conjecture of the set of all possible tensor contractions to be complete. This result allows us to derive the first generator algorithm that produces flexible bases of moment invariants with respect to orthogonal transformations by selecting a single non-zero moment to pair with all others in these two-factor products. Since at least one non-zero moment can be found in every non-zero pattern, this approach always generates a complete set of descriptors.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Determination of the mutual orientation between proton CSA tensors mediated through band-selective 1 H– 1 H recoupling under fast MAS

We report the mutual orientation of nuclear spin interaction tensors provides critical information on the conformation and arrangement of molecules in chemicals, materials, and biological systems at an atomic level. Proton is a ubiquitous and important element in a variety of substances, and its NMR is highly sensitive due to their virtually 100% natural abundance and large gyromagnetic ratio. Nevertheless, the measurement of mutual orientation between the 1 H CSA tensors has remained largely untouched in the past due to strong 1 H– 1 H homonuclear interactions in a dense network of protons. In this study, we have developed a proton-detected 3D 1 H CSA/ 1 H CSA/ 1 H CS correlation method that utilizes three techniques to manage homonuclear interactions, namely fast magic-angle spinning, windowless C-symmetry-based CSA recoupling (windowless-ROCSA), and a band-selective 1 H– 1 H polarization transfer. The asymmetric 1 H CSA/ 1 H CSA correlated powder patterns produced by the C-symmetry-based methods are highly sensitive to the sign and asymmetry parameter of the 1 H CSA, and the Euler angle β as compared to the symmetric pattern obtained by the existing γ-encoded R-symmetry-based CSA/CSA correlation methods and allows a larger spectral area for data fitting. These features are beneficial for determining the mutual orientation between the nuclear spin interaction tensors with improved accuracy.

1H CSA↗
DOE OSTI2021

Constructing tensor network influence functionals for general quantum dynamics

Here, we describe an iterative formalism to compute influence functionals that describe the general quantum dynamics of a subsystem beyond the assumption of linear coupling to a quadratic bath. We use a space-time tensor network representation of the influence functional and investigate its approximability in terms of its bond dimension and time-like entanglement in the tensor network description. We study two numerical models, the spin-boson model and a model of interacting hard-core bosons in a 1D harmonic trap. We find that the influence functional and the intermediates involved in its construction can be efficiently approximated by low bond dimension tensor networks in certain dynamical regimes, which allows the quantum dynamics to be accurately computed for longer times than with direct time evolution methods. However, as one iteratively integrates out the bath, the correlations in the influence functional can first increase before decreasing, indicating that the final compressibility of the influence functional is achieved via non-trivial cancellation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Diagonal isometric form for tensor network states in two dimensions

Isometric tensor network states (isoTNS) generalize the isometric form of the one-dimensional matrix product states to tensor networks in two and higher dimensions. Here, we introduce an alternative isometric form for isoTNS by incorporating auxiliary tensors to represent the orthogonality hypersurface. We implement the time evolving block decimation algorithm on this new isometric form and benchmark the method by computing ground states and the real time evolution of the transverse field Ising model in two dimensions on large square lattices of up to 1250 sites. Our results demonstrate that isoTNS can efficiently capture the entanglement structure of two-dimensional area law states. The short-time dynamics is also accurately reproduced even at the critical point. Our isoTNS formulation further allows for a natural extension to different lattice geometries, such as the honeycomb or kagome lattice.

2-dimensional systems↗
DOE OSTI2020

Mean-field entanglement transitions in random tree tensor networks

Entanglement phase transitions in quantum chaotic systems subject to projective measurements and in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a mean-field theory of such transitions by studying the entanglement properties of random tree tensor networks. As a function of bond dimension, we find a phase transition separating area-law from logarithmic scaling of the entanglement entropy. Using a mapping onto a replica statistical mechanics model defined on a Cayley tree and the cavity method, we analyze the scaling properties of such transitions. Our approach provides a tractable, mean-field-like example of an entanglement transition. Furthermore, we verify our predictions numerically by computing directly the entanglement of random tree tensor network states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Tensor network formulation of two-dimensional gravity

We show how to formulate a lattice gauge theory whose naive continuum limit corresponds to two-dimensional (Euclidean) quantum gravity including a positive cosmological constant. More precisely the resultant continuum theory corresponds to gravity in a first-order formalism in which the local frame and spin connection are treated as independent fields. Recasting this lattice theory as a tensor network allows us to study the theory at strong coupling without encountering a sign problem. In two dimensions this tensor network is exactly soluble and we show that the system has a series of critical points that occur for pure imaginary coupling and are associated with first order phase transitions. We then augment the action with a Yang-Mills term which allows us to control the lattice spacing and show how to apply the tensor renormalization group to compute the free energy and look for critical behavior. Finally we perform an analytic continuation in the gravity coupling in this extended model and show that its critical behavior in a certain scaling limit depends only on the topology of the underlying lattice. We also show how the lattice gauge theory can be naturally generalized to generate the Polyakov or Liouville action for two dimensional quantum gravity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Multi-Area Model-Free State Estimation via Distributed Tensor Decomposition

This paper proposes a model-free method for distribution system state estimation based on tensor completion using canonical polyadic decomposition. In particular, we consider a setting where the network is divided into multiple areas. The measured physical quantities at buses located in the same area are processed by an area controller. A third-order tensor is constructed to collect these measured quantities. The measurements are analyzed locally to recover the full state information of the network. A closed-form iterative algorithm based on the alternating direction method of multipliers is developed to obtain the low-rank factors of the whole network state tensor where information exchange happens only between neighboring areas. To demonstrate the efficacy of the developed algorithm, numerical simulations are carried out using an IEEE test system.

alternating direction method of multipliers↗
DOE OSTI2021

MONTI: A Multi-Omics Non-negative Tensor Decomposition Framework for Gene-Level Integrative Analysis

Multi-omics data is frequently measured to enrich the comprehension of biological mechanisms underlying certain phenotypes. However, due to the complex relations and high dimension of multi-omics data, it is difficult to associate omics features to certain biological traits of interest. For example, the clinically valuable breast cancer subtypes are well-defined at the molecular level, but are poorly classified using gene expression data. Here, we propose a multi-omics analysis method called MONTI (Multi-Omics Non-negative Tensor decomposition for Integrative analysis), which goal is to select multi-omics features that are able to represent trait specific characteristics. Here, we demonstrate the strength of multi-omics integrated analysis in terms of cancer subtyping. The multi-omics data are first integrated in a biologically meaningful manner to form a three dimensional tensor, which is then decomposed using a non-negative tensor decomposition method. From the result, MONTI selects highly informative subtype specific multi-omics features. MONTI was applied to three case studies of 597 breast cancer, 314 colon cancer, and 305 stomach cancer cohorts. For all the case studies, we found that the subtype classification accuracy significantly improved when utilizing all available multi-omics data. MONTI was able to detect subtype specific gene sets that showed to be strongly regulated by certain omics, from which correlation between omics types could be inferred. Furthermore, various clinical attributes of nine cancer types were analyzed using MONTI, which showed that some clinical attributes could be well explained using multi-omics data. We demonstrated that integrating multi-omics data in a gene centric manner improves detecting cancer subtype specific features and other clinical features, which may be used to further understand the molecular characteristics of interest. The software and data used in this study are available at: https://github.com/inukj/MONTI.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS2018

Change of Inertia Tensor Due to a Severed Radial Boom for Spinning Spacecraft

Many spinning spacecraft have long, flexible, radial booms to carry science instrumentation. These radial booms often have low mass but contribute significantly to the spacecraft moment of inertia due to their length. There are historical cases where radial booms have been severed or have failed to deploy. This paper presents models for the center of mass (CM) and inertia tensor that account for variable boom geometry and investigates how the CM and inertia tensor change when a radial boom is severed.The CM and inertia tensor models presented here will be included in the Attitude Ground System (AGS) for the Magnetospheric Multiscale (MMS) mission. This work prepares the AGS to provide uninterrupted support in the event of a radial boom anomaly. These models will improve the AGS computations for spin-axis precession prediction, Kalman filter propagation for the definitive attitude, and mass property generation needed for the onboard control system. As an additional application, a method is developed for approximating the location on the boom where the break occurred based on the new models and readily observable attitude parameters.

Inertia↗
DOE OSTI2025

Randomized Algorithms for Low-Rank Matrix and Tensor Decompositions

This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimensionality reduction, such as the singular value decomposition (SVD) or interpolative (ID) and CUR decompositions. Recent advances in randomized dimensionality reduction are discussed, including new methods of fast matrix sketching and sampling techniques, which are incorporated into classical matrix algorithms for fast low-rank matrix approximations. The extension of randomized matrix algorithms to tensors is then explored for several low-rank tensor decompositions in the CP and Tucker formats, including the higher-order SVD, ID, and CUR decomposition.

Pearce, Katherine J. [The University of Texas at A↗
DOE OSTI2024

Holographic tensor networks with bulk gauge symmetries

Abstract Tensor networks are useful toy models for understanding the structure of entanglement in holographic states and reconstruction of bulk operators within the entanglement wedge. They are, however, constrained to only prepare so-called “fixed-area states” with flat entanglement spectra, limiting their utility in understanding general features of holographic entanglement. Here, we overcome this limitation by constructing a variant of random tensor networks that enjoys bulk gauge symmetries. Our model includes a gauge theory on a general graph, whose gauge-invariant states are fed into a random tensor network. We show that the model satisfies the quantum-corrected Ryu-Takayanagi formula with a nontrivial area operator living in the center of a gauge-invariant algebra. We also demonstrate nontrivial,n-dependent contributions to the Rényi entropy and Rényi mutual information from this area operator, a feature shared by general holographic states.

Physics↗
DOE OSTI2026

Coarse-grained fixed-point tensor networks and holographic reflected entropy in 3D gravity

We use the framework of fixed-point BCFT tensor networks to present a microscopic CFT derivation of the correspondence between reflected entropy (RE) and entanglement wedge cross section (EW) in AdS 3 /CFT 2 , for both bipartite and multipartite settings. These fixed-point tensor networks, obtained by triangulating Euclidean CFT path integrals, allow us to explicitly construct the canonical purification via cutting-and-gluing CFT path integrals. Employing modular flow in the large-c limit, we demonstrate that these intrinsic CFT manipulations reproduce bulk geometric prescriptions, without assuming the AdS/CFT dictionary. The emergence of bulk geometry is traced to coarse-graining over heavy states in the large-c limit. Universal coarse-grained BCFT data for compact 2D CFTs, through the relation to Liouville theory with ZZ boundary conditions, yields hyperbolic geometry on the Cauchy slice. The corresponding averaged replica partition functions reproduce all candidate EWs, arising from different averaging patterns, with the dominant one providing the correct RE and EW. In this way, many heuristic tensor-network intuitions in toy models are made precise and established directly from intrinsic CFT data.

AdS-CFT correspondence↗
DOE OSTI2024

Non-compact gauge groups, tensor fields and Yang-Mills-Einstein amplitudes

Abstract Scattering amplitudes in Yang-Mills-Einstein theories have been investigated mostly for compact gauge groups. While non-compact gauge groups are not physically viable in Yang-Mills theory, non-compact gaugings feature prominently in the supergravity literature, where any choice of perturbative vacuum spontaneously breaks the gauge group to a compact subgroup. In this paper, we formulate double-copy constructions for several five-dimensional$$ \mathcal{N} $$ N = 2 supergravities with non-compact gauge groups. On one side of the double copy, we employ amplitudes from a super-Yang-Mills theory with a massive hypermultiplet. On the other, we use amplitudes from particular non-supersymmetric Yang-Mills-scalar theories with massive fermions, chosen to obey constraints coming from color/kinematics duality. Supergravities with massive self-dual tensors in five dimensions are also considered, showing that tensors are straightforwardly realized as double copies of gauge-theory fermions with suitable choices of signs in the corresponding solutions of the Dirac equation. We present several examples of these constructions, noting in particular the appearance of Heisenberg groups in the supergravity gauge symmetry and, in some cases, the possibility of exotic tensor-vector matter couplings.

Physics↗
DOE OSTI2025

Spinor representations for fields with any spin: Lorentz tensor basis for operators and covariant multipole decomposition

This paper discusses a framework to parametrize and decompose operator matrix elements for particles with higher spin (j > 1/2) using chiral representations of the Lorentz group, i.e. the (j, 0) and (0, j) representations and their parity-invariant direct sum. Unlike traditional approaches that require imposing constraints to eliminate spurious degrees of freedom, these chiral representations contain exactly the 2j + 1 components needed to describe a spin-j particle. The central objects in the construction are the t-tensors, which are generalizations of the Pauli four-vector σ μ for higher spin. For the generalized spinors of these representations, we demonstrate how the algebra of the t-tensors allows to formulate a generalization of the Dirac matrix basis for any spin. For on-shell bilinears, we show that a set consisting exclusively of covariant multipoles of order 0 ≤ m ≤ 2j forms a complete basis. We provide explicit expressions for all bilinears of the generalized Dirac matrix basis, which are valid for any spin value. As a byproduct of our derivations we present an efficient algorithm to compute the t-tensor matrix elements. The formalism presented here paves the way to use a more unified approach to analyze the non-perturbative QCD structure of hadrons and nuclei across different spin values, with clear physical interpretation of the resulting distributions as covariant multipoles.

Angular momentum of light↗
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↗