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Results for “sparse tensor decomposition”

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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47 records · Page 3
All sourcesNASA NTRSDOE OSTI
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 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 OSTI2017

Model's sparse representation based on reduced mixed GMsFE basis methods

In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. A typical application for the elliptic PDEs is the flow in heterogeneous random porous media. Mixed generalized multiscale finite element method (GMsFEM) is one of the accurate and efficient approaches to solve the flow problem in a coarse grid and obtain the velocity with local mass conservation. When the inputs of the PDEs are parameterized by the random variables, the GMsFE basis functions usually depend on the random parameters. This leads to a large number degree of freedoms for the mixed GMsFEM and substantially impacts on the computation efficiency. In order to overcome the difficulty, we develop reduced mixed GMsFE basis methods such that the multiscale basis functions are independent of the random parameters and span a low-dimensional space. To this end, a greedy algorithm is used to find a set of optimal samples from a training set scattered in the parameter space. Reduced mixed GMsFE basis functions are constructed based on the optimal samples using two optimal sampling strategies: basis-oriented cross-validation and proper orthogonal decomposition. Although the dimension of the space spanned by the reduced mixed GMsFE basis functions is much smaller than the dimension of the original full order model, the online computation still depends on the number of coarse degree of freedoms. To significantly improve the online computation, we integrate the reduced mixed GMsFE basis methods with sparse tensor approximation and obtain a sparse representation for the model's outputs. The sparse representation is very efficient for evaluating the model's outputs for many instances of parameters. To illustrate the efficacy of the proposed methods, we present a few numerical examples for elliptic PDEs with multiscale and random inputs. In particular, a two-phase flow model in random porous media is simulated by the proposed sparse representation method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Scalable Quantum Monte Carlo Method for Polariton Chemistry via Mixed Block Sparsity and Tensor Hypercontraction Method

We present a reduced-scaling auxiliary-field quantum Monte Carlo (AFQMC) framework designed for large molecular systems and ensembles, with or without coupling to optical cavities. Our approach leverages the natural block sparsity of the Cholesky decomposition (CD) of electron repulsion integrals in molecular ensembles and employs tensor hypercontraction (THC) to efficiently compress low-rank Cholesky blocks. By representing the Cholesky vectors in a mixed format, keeping high-rank blocks in block-sparse form and compressing low-rank blocks with THC, we reduce the scaling of exchange-energy evaluation from quartic to robust cubic in the number of molecular orbitals N, while lowering memory from cubic toward quadratic. Benchmark analyses on one-, two-, and three-dimensional molecular ensembles (up to ∼1,200 orbitals) show that (a) the number of nonzeros in Cholesky tensors grows linearly with system size across dimensions; (b) the average numerical rank increases sublinearly and does not saturate at these sizes; and (c) rank heterogeneity─some blocks nearly full rank and many low rank, naturally motivates the proposed mixed block sparsity and THC scheme for efficient calculation of exchange energy. In conclusion, we demonstrate that the mixed scheme yields cubic wall-time scaling with favorable prefactors and preserves AFQMC accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Reducing Computation and Communication in Scientific Computing: Connecting Theory to Practice.

This report summarizes the work produced as part of a Truman Fellowship appointment and its associated LDRD project. The overall goal of the project was to develop better algorithms and implementations for key computational kernels within the field of scientific computing by designing them to be communication efficient, moving as little data as possible. The primary problem of interest was dense matrix multiplication; other computations that were addressed include sparse matrix-matrix multiplication, QR factorization, solving symmetric linear systems, and the symmetric eigendecomposition. The project also involved the study of computations at the intersection of scientific computing and data analysis, including nonnegative matrix factorization for discovering latent factors, Tucker tensor decomposition for data compression, and sampling methods for similarity search.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Sparsity of Radiating Characteristic Modes on Infinite Periodic Structures

Characteristic modes on infinite periodic structures are studied using spectral dyadic Green’s functions. This formulation demonstrates that, in contrast to the modal analysis of finite structures, the number of radiating characteristic modes is limited by unit cell size and incident wave vector (i.e., scan angle or phase shift per unit cell). Here, the reflection tensor is decomposed into modal contributions from radiating modes, indicating that characteristic modes are a predictably sparse basis in which to study reflection phenomena.

42 ENGINEERING↗
DOE OSTI2021

pyDRESCALk

Modern data scientists are tasked to analyze ever-growing data sets with increasingly complex relationships. Tensor decompositions have come to play a central role in identifying underlying latent structures in higher-order data. The problem of fitting tensor models to different distributions is complicated by the combinations of size, dimensionality, and sparsity present in real world data. The situation demands efficient algorithms designed for shared-memory and distributed systems. This work will present new research that tackles these challenges on several different fronts, leveraging optimizations in numerical algorithms and sparse tensor representations in heterogeneous high performance computing environments.

Bhattarai, Manish↗
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↗
DOE OSTI2019

Sparse low rank approximation of potential energy surfaces with applications in estimation of anharmonic zero point energies and frequencies

We introduce a method that exploits sparse representation of potential energy surfaces (PES) on a polynomial basis set selected by compressed sensing . The method is useful for studies involving large numbers of PES evaluations, such as the search for local minima, transition states, or integration. We apply this method for estimating zero point energies and frequencies of molecules using a three step approach. In the first step, we interpret the PES as a sparse tensor on polynomial basis and determine its entries by a compressed sensing based algorithm using only a few PES evaluations. Then, we establish a rank reduction strategy to compress this tensor in a suitable low-rank canonical tensor format using standard tensor compression tools. This allows representing a high dimensional PES as a small sum of products of one dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate the product of sparse canonical low-rank representation of PES and Green’s function in the second-order diagrammatic vibrational many-body Green’s function theory (XVH2) for estimation of zero-point energies and frequencies. Numerical tests on molecules considered in this work indicate a more efficient scaling of computational cost with molecular size as compared to other methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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 OSTI2020

On the Virasoro six-point identity block and chaos

We study six-point correlation functions in two dimensional conformal field theory, where the six operators are grouped in pairs with equal conformal dimension. Assuming large central charge $c$ and a sparse spectrum, the leading contribution to this correlation function is the six-point Virasoro identity block - corresponding to each distinct pair of operators fusing into the identity and its descendants. We call this the star channel. One particular term in the star channel identity block is the stress tensor $SL(2,\mathbb{R})$ (global) block, for which we derive an explicit expression. In the holographic context, this object corresponds to a direct measure of nonlinear effects in pure gravity. We calculate additional terms in the star channel identity block that contribute at the same order at large $c$ as the global block using the novel theory of reparametrizations, which extends the shadow operator formalism in a natural way. We investigate these blocks' relevance to quantum chaos in the form of six-point scrambling in an out-of time ordered correlator. Interestingly, the global block does not contribute to the scrambling mode of this correlator, implying that, to leading order, six-point scrambling is insensitive to the three-point graviton coupling in the bulk dual. Finally, we compare our findings with a different OPE channel, called the comb channel, and find the same result for the chaos exponent in this decomposition.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗