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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Calculated electron paramagnetic resonance g-tensor and hyperfine parameters for zinc vacancy and N related defects in ZnO

Various defects in ZnO, focused on substitutional N O and N 2 in various sites, O-site, interstitial and Zn-site are studied using first-principles calculations with the goal of understanding the electron paramagnetic resonance (EPR) center reported for N 2 in ZnO and substitutional N on the O-site. The g tensors are calculated using the gauge including projector augmented wave (GIPAW) method and compared with experiments. The g-tensor of the free $N^{+}_{2}$ and $N^{–}_{2}$ radicals and their various contributions within the GIPAW theory are analyzed first to provide a baseline reference for the accuracy of the method and for understanding the N 2 behavior in ZnO. Previous controversies on the site location of N 2 in ZnO for this EPR center and on the shallow or deep nature and donor or acceptor nature of this center are resolved. Here, we find that the N 2 on the Zn site is mostly zinc-vacancy like in its spin density and g-tensor, while for the O-site, a model with the N 2 axis lying in-the basal plane and the singly occupied π g -orbital along the c axis provides good agreement with experiment. For the interstitial location, if the N 2 is not strongly interacting with the surroundings, no levels in the gap are found and hence also no possible EPR center. The calculated g-tensors for N O and V Zn are also found to be in good agreement with experiment. The effects of different functionals affecting the localization of the spin density are shown to affect the g-tensor values.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Precision Reconstruction of Rational Conformal Field Theory from Exact Fixed-Point Tensor Network

The novel concept of entanglement renormalization and its corresponding tensor network renormalization technique have been highly successful in developing a controlled real-space renormalization group (RG) scheme. Numerically approximate fixed-point (FP) tensors are widely used to extract the conformal data of the underlying conformal field theory (CFT) describing critical phenomena. In this paper, we present an explicit analytical construction of the FP tensor for 2D rational CFT. We define it as a correlation function between the “boundary-changing operators” (BCO) on triangles. Our construction fully captures all the real-space RG conditions. We also provide concrete examples, such as Ising, Yang-Lee, and tricritical Ising models, to compute the scaling dimensions explicitly based on the corresponding FP tensor. The BCO descendants turn out to be an optimal basis such that truncation in bond dimensions naturally produces comparable accuracies with the leading existing FP algorithms. Interestingly, our construction of FP tensors is closely related to a strange correlator, where the holographic picture naturally emerges. Our results also open a new door toward understanding CFT in higher dimensions. Published by the American Physical Society 2025

Cheng, Gong (ORCID:0009000891587404)↗
DOE OSTI2026

Loop series expansions for tensor networks

Belief propagation (BP) can be a useful tool to approximately contract a tensor network, provided that the contributions from any closed loops in the network are sufficiently weak. In this article, we describe how a loop series expansion can be applied to systematically improve the accuracy of a BP approximation to a tensor network contraction, in principle converging arbitrarily close to the exact result. More generally, our result provides a framework for expanding a tensor network as a sum of component networks in a hierarchy of increasing complexity. We benchmark this proposal for the contraction of infinite projected entangled pair states, either representing the ground state of an Affleck-Kennedy-Lieb-Tasaki (AKLT) model or with randomly defined tensors, where it is shown to improve in accuracy over standard BP by several orders of magnitude while incurring only a minor increase in computational cost. These results indicate that the proposed series expansions could be a useful tool to accurately evaluate tensor networks in cases that otherwise exceed the limits of established contraction routines.

Evenbly, Glen [AWS Center for Quantum Computing, P↗
DOE OSTI2024

Accelerated Constrained Sparse Tensor Factorization on Massively Parallel Architectures

This study presents the first constrained sparse tensor factorization (cSTF) framework that optimizes and fully offloads computation to massively parallel GPU architectures, and the first performance characterization of cSTF on GPU architectures. In contrast to prior work on tensor factorization, where the matricized tensor times Khatri-Rao product (MTTKRP) is the primary performance bottleneck, our systematic analysis of the cSTF algorithm on GPUs reveals that adding constraints creates an additional bottleneck in the update operation for many real-world sparse tensors. While executing the update operation on the GPU brings significant speedup over its CPU counterpart, it remains a significant bottleneck. To further accelerate the update operation, we propose cuADMM, a new update algorithm that leverages algorithmic and code optimization strategies to minimize both computation and data movement on GPUs. As a result, our framework delivers significantly improved performance compared to prior state-of-the-art. On 10 real-world sparse tensors, our framework achieves geometric mean speedup of 5.1 × (max 41.59 ×) and 7.01 × (max 58.05 ×) on the NIVIDA A100 and H100 GPUs, respectively, over the state-of-the-art SPLATT library running on a 26-core Intel Ice Lake Xeon CPU.

Soh, Yongseok↗
DOE OSTI2024

Moment Tensor Inversion Toolkit

The MTINV toolkit (2002-present) is a collection of computer codes and applications written to invert for the moment tensor of a seismic source given the three components of ground motion recorded at regional seismic stations (e.g., Ichinose et al., 2003). The computer codes and workflow are organized to generate moment tensor solutions for a range of source depths and origin times because of the trade-off between these two quantities. The metric used is the variance reduction and variance reduction modulated by the percent double-couple to determine the best-fit moment-tensor solution. We can solve for a deviatoric moment tensor with a constraint added for no isotropic component although this constraint can be lifted for estimating the full moment tensor like mining collapses or explosion sources.

Ichinose, GeneA↗
DOE OSTI2021

Fast tensor disentangling algorithm

Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an approximate, fast, and simple algorithm to optimize disentangling unitary tensors. Our algorithm is asymptotically faster than previous iterative algorithms and often results in a residual entanglement entropy that is within 10 to 40% of the minimum. For certain input tensors, our algorithm returns an optimal solution. When disentangling order-4 tensors with equal bond dimensions, our algorithm achieves an entanglement spectrum where nearly half of the singular values are zero. We further validate our algorithm by showing that it can efficiently disentangle random 1D states of qubits.

Slagle, Kevin↗
DOE OSTI2023

Bayesian inference for the seismic moment tensor using regional waveforms and a data-derived distribution of velocity models

The largest source of uncertainty in any source inversion is the velocity model used to construct the transfer function employed in the forward model that relates observed ground motion to the seismic moment tensor. However, standard inverse procedures often does not quantify uncertainty in the seismic moment tensor due to error in the Green’s functions from uncertain event location and Earth structure. We attempt to incorporate this uncertainty into an estimation of the seismic moment tensor using a distribution of velocity models calculated in a prior effort based on different and complementary data sets. The posterior distribution of velocity models is then used to construct Green’s functions for use in Bayesian inference of an unknown seismic moment tensor using regional waveform data. The combined likelihood is estimated using data-specific error models and the posterior of the seismic moment tensor is estimated and can be interpreted in terms of most-probable source-type.

58 GEOSCIENCES↗
DOE OSTI2024

Journey to Time-Variable Moment Tensors through Inversion of Acoustic and Seismoacoustic Data

We explore the capability of acoustic and seismoacoustic datasets to directly resolve a complex, time-variable source consisting of a buried mechanism, represented as a moment tensor, and a spall mechanism, represented as a vertical force at the surface. Traditionally, each component of a resolved moment tensor assumes one underlying source time function, which likely fails to capture the full evolution of a dynamic source, such as an explosion followed by slip on near-source joints or development of spallation. Specifically, we expand previous work to resolve a time-variable moment tensor using single-modality and joint-modality inversion frameworks through analysis of infrasound and seismoacoustic data recorded as part of the Source Physics Experiment Phase II: Dry Alluvium Geology (DAG). We investigate the impact of including signals from seismic-to-air coupling that are local to each infrasound sensor in comparison to mainly atmosphere-propagating acoustic signals, which occur from coupling of the wavefield from the subsurface to the atmosphere directly above the source. Additionally, we assess the ability of our inversion algorithm to fit observed infrasound data using a variety of time-variable source mechanisms. First, we consider the buried moment tensor source alone, which assumes that the determined Green’s functions incorporate effects from spallation or that the impact from spallation is minimal. Second, we examine the estimated buried moment tensor and vertical surface spallation as terms that must both be resolved in the inversion. Third, we assess the ability for an estimated vertical surface spallation source to fit the acoustic data on its own. Finally, we compare results from the joint inversion of both seismic geophone and infrasound acoustic data for the buried-only source compared to buried and spallation sources. Our results are a preliminary investigation into the applications of the inversion technique to recorded datasets and show the technique has limited capabilities using acoustic data alone. Instead, this method shows promise for seismic and seismoacoustic datasets to resolve the time-variable mechanisms of a buried source.

47 OTHER INSTRUMENTATION↗
NASA NTRS1985

Nonlinear optimal control with tensors - Some computational issues

Some computational issues associated with the calcualtion of optimal feedback controls for nonlinear systems in a tensor setting are described. The specific issues addressed pertain to the combinatorial nature of the loading of the elements into tensors used to represent the system, cost, and feedback, and the subsequent calculations involving these elements. Particular attention is given to: the symmetric tensor algebra which is a natural setting for representing polynomials; the conversions between symmetric and nonsymmetric tensors; the general nature of the calculations required; and the solution equation for nonlinear optimal feedback control. It is concluded that nonlinear tensor feedback can improve performance both in terms of system responses and in terms of system stability region.

Osullivan, J. A.↗
NASA NTRS1992

The Hamiltonian structure of Dirac's equation in tensor form and its Fermi quantization

Currently, there is some interest in studying the tensor forms of the Dirac equation to elucidate the possibility of the constrained tensor fields admitting Fermi quantization. We demonstrate that the bispinor and tensor Hamiltonian systems have equivalent Fermi quantizations. Although the tensor Hamiltonian system is noncanonical, representing the tensor Poisson brackets as commutators for the Heisenberg operators directly leads to Fermi quantization without the use of bispinors.

Reifler, Frank↗
NASA NTRS1993

Tensoral: A system for post-processing turbulence simulation data

Many computer simulations in engineering and science -- and especially in computational fluid dynamics (CFD) -- produce huge quantities of numerical data. These data are often so large as to make even relatively simple post-processing of this data unwieldy. The data, once computed and quality-assured, is most likely analyzed by only a few people. As a result, much useful numerical data is under-utilized. Since future state-of-the-art simulations will produce even larger datasets, will use more complex flow geometries, and will be performed on more complex supercomputers, data management issues will become increasingly cumbersome. My goal is to provide software which will automate the present and future task of managing and post-processing large turbulence datasets. My research has focused on the development of these software tools -- specifically, through the development of a very high-level language called 'Tensoral'. The ultimate goal of Tensoral is to convert high-level mathematical expressions (tensor algebra, calculus, and statistics) into efficient low-level programs which numerically calculate these expressions given simulation datasets. This approach to the database and post-processing problem has several advantages. Using Tensoral the numerical and data management details of a simulation are shielded from the concerns of the end user. This shielding is carried out without sacrificing post-processor efficiency and robustness. Another advantage of Tensoral is that its very high-level nature lends itself to portability across a wide variety of computing (and supercomputing) platforms. This is especially important considering the rapidity of changes in supercomputing hardware.

Dresselhaus, Eliot↗
NASA NTRS1993

Visualizing second order tensor fields with hyperstreamlines

Hyperstreamlines are a generalization to second order tensor fields of the conventional streamlines used in vector field visualization. As opposed to point icons commonly used in visualizing tensor fields, hyperstreamlines form a continuous representation of the complete tensor information along a three-dimensional path. This technique is useful in visulaizing both symmetric and unsymmetric three-dimensional tensor data. Several examples of tensor field visualization in solid materials and fluid flows are provided.

Delmarcelle, Thierry↗
DOE OSTI2026

QuadSync: Quadrifocal tensor synchronization via Tucker decomposition

In structure from motion, quadrifocal tensors capture more information than their pairwise counterparts (essential matrices), yet they have often been thought of as impractical and only of theoretical interest. In this work, we challenge such beliefs by providing a new framework to recover n cameras from the corresponding collection of quadrifocal tensors. We form the block quadrifocal tensor and show that it admits a Tucker decomposition whose factor matrices are the stacked camera matrices, and which thus has a multilinear rank of (4,4,4,4) independent of n. We develop the first synchronization algorithm for quadrifocal tensors, using Tucker decomposition, alternating direction method of multipliers, and iteratively reweighted least squares. We further establish relationships between the block quadrifocal, trifocal, and bifocal tensors, and introduce an algorithm that jointly synchronizes these three entities. Numerical experiments demonstrate the effectiveness of our methods on modern datasets, indicating the potential and importance of using higher-order information in synchronization.

Miao, Daniel [University of Minnesota]↗
DOE OSTI2023

High-dimensional data analytics in civil engineering: A review on matrix and tensor decomposition

Recent developments in sensing and monitoring techniques have led to the generation of high-dimensional data in the field of civil engineering. High-dimensional data analytics methods have thus been developed to interpret such complex data. Among the different high-dimensional data analytics techniques, matrix and tensor decomposition methods have acquired a notable interest in the civil engineering community over the past decade. Due to their unique ability to deal with highly redundant and correlated data, these methods are establishing themselves as promising and efficient tools to analyze high-dimensional data in the civil engineering arena. In this paper, high-dimensional data is referred to as a data set in which the number of features is comparable or larger than the number of observations. This review paper aims to summarize the applications of matrix and tensor decomposition methods in civil engineering over the last decade. The survey begins with a general overview of matrix and tensor decomposition followed by highlighting their significance in the field. Afterward, various applications of these high-dimensional data analytics methods in civil engineering are presented, while the advantages offered by these methods are discussed. Lastly, challenges and potential research avenues for employing matrix and tensor decomposition and future emerging trends for their novel use are highlighted.

42 ENGINEERING↗
DOE OSTI2023

Real-time evolution of Anderson impurity models via tensor network influence functionals

In this work, we present and analyze two tensor network-based influence functional approaches for simulating the real-time dynamics of quantum impurity models such as the Anderson model. Via comparison with recent numerically exact simulations, we show that such methods accurately capture the long-time nonequilibrium quench dynamics. The two parameters that must be controlled in these tensor network influence functional approaches are a time discretization (Trotter) error and a bond dimension (tensor network truncation) error. We show that the actual numerical uncertainties are controlled by an intricate interplay of these two approximations, which we demonstrate in different regimes. Our work opens the door to using these tensor network influence functional methods as general impurity solvers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Breaking the curse of dimensionality: Solving configurational integrals for crystalline solids by tensor networks

Accurately evaluating configurational integrals for dense solids remains a central and difficult challenge in the statistical mechanics of condensed systems. Here, we present a tensor network approach that reformulates the high-dimensional configurational integral for identical-particle crystals into a sequence of computationally efficient summations. We represent the integrand as a high-dimensional tensor and apply tensor-train (TT) decomposition together with a custom TT-cross interpolation. This approach circumvents the need to explicitly construct the full tensor. We introduce tailored rank-1 and rank-2 schemes optimized for sharply peaked Boltzmann probability densities, typical for identical-particle crystals. When applied to the calculation of internal energy and pressure-temperature curves for crystalline Cu and Ar at high (GPa) pressures, as well as the alpha-to-beta phase transition diagram of Sn, our method accurately reproduces molecular dynamics simulation results using tight-binding, machine learning, hierarchical interacting particle–neural network, and modified embedded atom method potentials,all within seconds of computation time.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Assessment of Accelerated Stress Testing Data for Silicon Photovoltaics Using Tensor Decomposition Methods

In this work, we examine the use of high-order tensor decompositions to analyze degradation pathways emerging from accelerated stress testing of silicon photovoltaic (PV) modules. Matrix-based decompositions are powerful tools for studying two-dimensional data arrays and form the foundation of a host of classical data analysis techniques. Tensors are high-order extrapolations of matrices that are able to account for more parameter dimensions, and a variety of tensor decomposition methods have been developed that similarly seek to extend insights from matrix decompositions to higher dimensions. Applying and interpreting tensor decomposition methods to sequences of PV module image data, we seek to uncover and isolate different degradation modes occurring from accelerated stress testing procedures. Further, we consider the contributions of different modes to PV module performance degradations.

data analysis↗
DOE OSTI2022

Multiarea Distribution System State Estimation via Distributed Tensor Completion

Here, this paper proposes a model-free distribution system state estimation method 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 three-way tensor is constructed to collect these measured quantities. The measurements are analyzed locally to recover the full state information of the network. A distributed 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. The convergence properties of the distributed algorithm and the sufficient conditions on the number of samples for each smaller network that guarantee the identifiability of the factors of the state tensor are presented. To demonstrate the efficacy of the proposed algorithm and to check the identifiability conditions, numerical simulations are carried out using the IEEE 123-bus system and a large-scale real utility feeder.

24 POWER TRANSMISSION AND DISTRIBUTION↗