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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 OSTI2010

B{yields}V, A, T tensor form factors in the covariant light-front approach: Implications on radiative B decays

We reanalyze the B{yields}M tensor form factors in a covariant light-front quark model, where M represents a vector meson V, an axial-vector meson A, or a tensor meson T. The treatment of masses and mixing angles in the K{sub 1A,1B} systems is improved, where K{sub 1A} and K{sub 1B} are the {sup 3}P{sub 1} and {sup 1}P{sub 1} states of the axial-vector meson K{sub 1}, respectively. Rates of B{yields}M{gamma} decays are then calculated using the QCD factorization approach. The updated B{yields}K*{gamma}, B{yields}K{sub 1}(1270){gamma}, K{sub 1}(1400){gamma}, and K{sub 2{gamma}} rates agree with the data. The K{sub 1}(1270)-K{sub 1}(1400) mixing angle is found to be about 51 deg. The sign of the mixing angle is fixed by the observed relative strength of B{yields}K{sub 1}(1270){gamma} and K{sub 1}(1400){gamma}. The formalism is then applied to B{sub s{yields}}M tensor form factors. We find that the calculated B{sub s{yields}{phi}{gamma}} rate is consistent with experiment, though in the lower end of the data. The branching fractions of B{sub s{yields}}f{sub 1}(1420){gamma} and f{sub 2}{sup '}(1525){gamma} are predicted to be of order 10{sup -5} and it will be interesting to search for these modes. Rates on B{sub s{yields}}f{sub 1}(1285){gamma}, h{sub 1}(1380){gamma}, h{sub 1}(1170){gamma}, f{sub 2}(1270){gamma} decays are also predicted.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Nonnegative canonical tensor decomposition with linear constraints: nnCANDELINC

Abstract There is an emerging interest for tensor factorization applications in big‐data analytics and machine learning. To speed up the factorization of extra‐large datasets, organized in multidimensional arrays (also known as tensors), easy to compute compression‐based tensor representations, such as, Tucker and tensor train formats, are used to approximate the initial large‐tensor. Further, tensor factorization is used to extract latent features that can facilitate discoveries of new mechanisms and signatures hidden in the data, where the explainability of the latent features is of principal importance. Nonnegative tensor factorization extracts latent features that are naturally sparse and parts of the data, which makes them easily interpretable. However, to take into account available domain knowledge and subject matter expertise, often additional constraints need to be imposed, which lead us to canonical decomposition with linear constraints (CANDELINC), a canonical polyadic decomposition with rank deficient factors. In CANDELINC, Tucker compression is used as a preprocessing step, which lead to a larger residual error but to more explainable latent features. Here, we propose a nonnegative CANDELINC (nnCANDELINC) accomplished via a specific nonnegative Tucker decomposition; we refer to as minimal or canonical nonnegative Tucker. We derive several results required to understand the specificity of nnCANDELINC, focusing on the difficulties of preserving the nonnegative rank of a tensor to its Tucker core and comparing the real valued to nonnegative case. Finally, we demonstrate nnCANDELINC performance on synthetic and real‐world examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Bootstrapping a stress-tensor form factor through eight loops

We bootstrap the three-point form factor of the chiral stress-tensor multiplet in planar $\mathcal{N}$ = 4 supersymmetric Yang-Mills theory at six, seven, and eight loops, using boundary data from the form factor operator product expansion. This may represent the highest perturbative order to which multi-variate quantities in a unitary four-dimensional quantum field theory have been computed. In computing this form factor, we observe and employ new restrictions on pairs and triples of adjacent letters in the symbol. We provide details about the function space required to describe the form factor through eight loops. Plotting the results on various lines provides striking numerical evidence for a finite radius of convergence of perturbation theory. By the principle of maximal transcendentality, our results are expected to give the highest weight part of the gg → Hg and H → ggg amplitudes in the heavy-top limit of QCD through eight loops. These results were also recently used to discover a new antipodal duality between this form factor and a six-point amplitude in the same theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Sandia-UT Academic Alliance Project Summary

This project seeks to leverage various hyperspectral tensor products for the purposes of target classification/detection/prediction. In addition to hyperspectral, these products may be images, time series, geometries, or other modalities. The scenarios in which the targets of interest must be identified are typically from remote sensing platforms such as satellites. As such, there are numerous real-world constraints that drive algorithmic formulation. Cost, complexity, and feasibility of the algorithm should all be considered. Targets of interest are exceedingly rare, and collecting many data samples is prohibitively expensive. Furthermore, model interpretability is paramount due to the application space. The goal of this project is to develop a constrained supervised tensor factorization framework for use on hyperspectral data products. Supervised tensor factorizations already exist in the literature, although they have not seen widespread adoption in the remote sensing domain. The novelty of this project will be the formulation and inclusion of constraints that take into account mission considerations and physics based limits to learn a factorization that is both physically interpretable and mission deployable. This will represent a new contribution to the field of remote sensing for performing supervised learning tasks with hyperspectral data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

DNTTD (Distributed Non-Negative Tensor Train Decomposition)

The era of exascale computing opens new venues for innovations and discoveries in many scientific, engineering, and commercial fields. However, with the exa flops also come the extra-large high-dimensional data generated by high performance computing. High-dimensional data is presented as multidimensional arrays, aka tensors. The presence of latent (not directly observable) structures in the tensor allows a unique representation and compression of the data by classical tensor factorization techniques. However, the classical tensor methods are not always stable or they can be exponential in their memory requirements, which makes them not suitable for high-dimensional tensors. Tensor train (TT) is a state-of-the-art tensor network introduced for factorization of high-dimensional tensors. TT transforms the initial high-dimensional tensor in a network of three-dimensional tensors that requires only a linear storage. Many real-world data, such as, density, temperature, population, probability, etc., are non-negative and for an easy interpretation, the algorithms preserving non-negativity are preferred. Here, we introduce a distributed non-negative tensor-train and demonstrate its scalability and the compression on synthetic and real world big datasets.

Bhattarai, Manish↗
DOE OSTI2010

LDRD final report : leveraging multi-way linkages on heterogeneous data.

This report is a summary of the accomplishments of the 'Leveraging Multi-way Linkages on Heterogeneous Data' which ran from FY08 through FY10. The goal was to investigate scalable and robust methods for multi-way data analysis. We developed a new optimization-based method called CPOPT for fitting a particular type of tensor factorization to data; CPOPT was compared against existing methods and found to be more accurate than any faster method and faster than any equally accurate method. We extended this method to computing tensor factorizations for problems with incomplete data; our results show that you can recover scientifically meaningfully factorizations with large amounts of missing data (50% or more). The project has involved 5 members of the technical staff, 2 postdocs, and 1 summer intern. It has resulted in a total of 13 publications, 2 software releases, and over 30 presentations. Several follow-on projects have already begun, with more potential projects in development.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

ExaTN: Scalable GPU-Accelerated High-Performance Processing of General Tensor Networks at Exascale

We present ExaTN (Exascale Tensor Networks), a scalable GPU-accelerated C++ library which can express and process tensor networks on shared- as well as distributed-memory high-performance computing platforms, including those equipped with GPU accelerators. Specifically, ExaTN provides the ability to build, transform, and numerically evaluate tensor networks with arbitrary graph structures and complexity. It also provides algorithmic primitives for the optimization of tensor factors inside a given tensor network in order to find an extremum of a chosen tensor network functional, which is one of the key numerical procedures in quantum many-body theory and quantum-inspired machine learning. Numerical primitives exposed by ExaTN provide the foundation for composing rather complex tensor network algorithms. We enumerate multiple application domains which can benefit from the capabilities of our library, including condensed matter physics, quantum chemistry, quantum circuit simulations, as well as quantum and classical machine learning, for some of which we provide preliminary demonstrations and performance benchmarks just to emphasize a broad utility of our library.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Nonnegative tensor decomposition with custom clustering for microphase separation of block copolymers

High–dimensional datasets are becoming ubiquitous in many applications and therefore unsupervised tensor methods to interrogate them are needed. Here, we report a new unsupervised machine learning (ML) approach (NTFk) based on nonnegative tensor factorization integrated with a custom k–means clustering. We demonstrate the ability of NTFk to extracting temporal and spatial features of phase separation of copolymers as they are modeled by self–consistent field theory. Microphase separation of block copolymers has been extensively studied both experimentally and theoretically. However, the interpretation of computer simulations and/or experimental data, representing temporal and spatial changes of molecular species concentration is still a challenging task. Thus, extracting the phase diagram from simulations or experimental data as well as the interpretation of data requires discernment of the model/experimental parameters (such as, temperature, concentrations, the number of molecular species and the interaction between species) impact on the microphase separation process. An attractive and unique aspect of the introduced ML method is that it ensures the nonnegativity of the extracted latent features. Nonnegativity is an essential constraint needed to obtain interpretable and sparse latent features that are parts–based representation of the data. The custom clustering in NTFk serves to estimate the number of latent features in the data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Beyond toy models: distilling tensor networks in full AdS/CFT

We present a general procedure for constructing tensor networks that accurately reproduce holographic states in conformal field theories (CFTs). Given a state in a large-N CFT with a static, semiclassical gravitational dual, we build a tensor network by an iterative series of approximations that eliminate redundant degrees of freedom and minimize the bond dimensions of the resulting network. We argue that the bond dimensions of the tensor network will match the areas of the corresponding bulk surfaces. For “tree” tensor networks (i.e., those that are constructed by discretizing spacetime with nonintersecting Ryu-Takayanagi surfaces), our arguments can be made rigorous using a version of one-shot entanglement distillation in the CFT. Using the known quantum error correcting properties of AdS/CFT, we show that bulk legs can be added to the tensor networks to create holographic quantum error correcting codes. These codes behave similarly to previous holographic tensor network toy models, but describe actual bulk excitations in continuum AdS/CFT. By assuming some natural generalizations of the “holographic entanglement of purification” conjecture, we are able to construct tensor networks for more general bulk discretizations, leading to finer-grained networks that partition the information content of a Ryu-Takayanagi surface into tensor-factorized subregions. While the granularity of such a tensor network must be set larger than the string/Planck scales, we expect that it can be chosen to lie well below the AdS scale. However, we also prove a no-go theorem which shows that the bulk-to-boundary maps cannot all be isometries in a tensor network with intersecting Ryu-Takayanagi surfaces.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Tensorized Feature Spaces for Feature Explosion

In this paper 1 1 This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-000R22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan) This research used resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC05-000R22725., we present a novel framework that uses tensor factorization to generate richer feature spaces for pixel classification in hyperspectral images. In particular, we assess the performance of different tensor rank decomposition methods as compared to the traditional kernel-based approaches for the hyperspectral image classification problem. We propose Orion, which takes as input a hyperspectral image tensor and a rank and outputs an enhanced feature space from the factor matrices of the decomposed tensor. Our method is a feature explosion technique that inherently maps low dimensional input space in $\mathbb{R}^{K}$ to high dimensional space in $\mathbb{R}^{R}$ , where $R\gg K$ , say in the order of 1000x, like a kernel. We show how the proposed method exploits the multi-linear structure of hyperspectral three dimensional tensor. We demonstrate the effectiveness of our method with experiments on three publicly available hyperspectral datasets with labeled pixels and compare their classification performance against traditional linear and non-linear supervised learning methods such as SVM with Linear, Polynomial, RBF kernels, and the Multi-Layer Perceptron model. Finally, we explore the relationship between the rank of the tensor decomposition and the classification accuracy using several hyperspectral datasets with ground truth.

Pasricha, Ravdeep Singh↗
DOE OSTI2020

Super-resolution and signal separation in contact Kelvin probe force microscopy of electrochemically active ferroelectric materials

In this work, imaging mechanisms in contact Kelvin probe force microscopy (cKPFM) are explored via information theory-based methods. Gaussian processes are used to achieve super-resolution in the cKPFM signal, effectively extrapolating across the spatial and parameter space. Tensor factorization is applied to reduce the multidimensional signal to the tensor convolution of the scalar functions that show a clear trending behavior with the imaging parameters. These methods establish a workflow for the analysis of the multidimensional datasets that can then be related to the relevant physical mechanisms. We also provide an interactive Google Colab notebook that goes through all the analyses discussed in the paper.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Tensor-decomposition techniques for ab initio nuclear structure calculations: From chiral nuclear potentials to ground-state energies

The computational resources needed to generate the ab initio solution of the nuclear many-body problem for increasing mass number and/or accuracy necessitates innovative developments to improve upon (i) the storage of many-body operators and (ii) the scaling of many-body methods used to evaluate nuclear observables. The storing and efficient handling of many-body operators with high particle ranks is currently one of the major bottlenecks limiting the applicability range of ab initio studies with respect to mass number and accuracy. Recently, the application of tensor decomposition techniques to many-body tensors has proven highly beneficial to reduce the computational cost of ab initio calculations in quantum chemistry and solid-state physics. The impact of applying state-of-the-art tensor factorization techniques to modern nuclear Hamiltonians derived from chiral effective field theory is investigated. Subsequently, the error induced by the tensor decomposition of the input Hamiltonian on ground-state energies of closed-shell nuclei calculated via second-order many-body perturbation theory is benchmarked. The first proof-of-principles application of tensor-decomposition techniques to the nuclear Hamiltonian is performed. Two different tensor formats are investigated by systematically benchmarking the approximation error on matrix elements stored in various bases of interest. The analysis is achieved while including normal-ordered three-nucleon interactions that are nowadays used as input to the most advanced ab initio calculations in medium-mass nuclei. With the aid of the factorized Hamiltonian, the second-order perturbative correction to ground-state energies is decomposed and the scaling properties of the underlying tensor network are discussed. The employed tensor formats are found to lead to an efficient data compression of two-body matrix elements of the nuclear Hamiltonian. In particular, the sophisticated tensor hypercontraction scheme yields low tensor ranks with respect to both harmonic-oscillator and Hartree-Fock single-particle bases. It is found that the tensor rank depends on the two-body total angular momentum J for which one performs the decomposition, which is itself directly related to the sparsity of the corresponding tensor. Furthermore, including normal-ordered two-body contributions originating from three-body interactions does not compromise the efficient data compression. Ultimately, the use of factorized matrix elements authorizes controlled approximations of the exact second-order ground-state energy corrections. In particular, a small enough error is obtained from low-rank factorizations in He4,O16, and Ca40. It is presently demonstrated that tensor-decomposition techniques can be efficiently applied to systematically approximate the nuclear many-body Hamiltonian in terms of lower-rank tensors. Beyond the input Hamiltonian, tensor-decomposition techniques can be envisioned to scale down the cost of state-of-the-art nonperturbative many-body methods in order to extend ab initio studies to (i) higher precisions, (ii) larger masses, and (iii) nuclei of doubly open-shell character.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

Low-rank factorization of electron integral tensors and its application in electronic structure theory

In this letter, we introduce the reverse Cuthill-McKee (RCM) algorithm, which is often used for the bandwidth reduction of sparse tensors, to transform the two-electron integral tensors to their block diagonal forms. By further applying the pivoted Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates the low-rank factorization of the high-dimensional tensor contractions that are usually encountered in post-Hartree-Fock calculations. In this letter, we discuss the second-order Møller-Plesset (MP2) method and linear coupled- cluster model with doubles (L-CCD) as two simple examples to demonstrate the efficiency of the RCM-CD technique in representing two-electron integrals in a compact form.

electronic structure theory↗
DOE OSTI2017

HPC formulations of optimization algorithms for tensor completion

Tensor completion is a powerful tool used to estimate or recover missing values in multi-way data. It has seen great success in domains such as product recommendation and healthcare. Tensor completion is most often accomplished via low-rank sparse tensor factorization, a computationally expensive non-convex optimization problem which has only recently been studied in the context of parallel computing. In this work, we study three optimization algorithms that have been successfully applied to tensor completion: alternating least squares (ALS), stochastic gradient descent (SGD), and coordinate descent (CCD++). We explore opportunities for parallelism on shared- and distributed-memory systems and address challenges such as memory- and operation-efficiency, load balance, cache locality, and communication. Among our advancements are a communication-efficient CCD++ algorithm, an ALS algorithm rich in level-3 BLAS routines, and an SGD algorithm which combines stratification with asynchronous communication. Furthermore, we show that introducing randomization during ALS and CCD++ can accelerate convergence. We evaluate our parallel formulations on a variety of real datasets on a modern supercomputer and demonstrate speedups through 16384 cores. Further, these improvements reduce time-to-solution from hours to seconds on real-world datasets. We show that after our optimizations, ALS is advantageous on parallel systems of small-to-moderate scale, while both ALS and CCD++ provide the lowest time-to-solution on large-scale distributed systems.

97 MATHEMATICS AND COMPUTING↗