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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 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↗
DOE OSTI2019

Software for Sparse Tensor Decomposition on Emerging Computing Architectures

In this paper, we develop software for decomposing sparse tensors that is portable to and performant on a variety of multicore, manycore, and GPU computing architectures. The result is a single code whose performance matches optimized architecture-specific implementations. The key to a portable approach is to determine multiple levels of parallelism that can be mapped in different ways to different architectures, and we explain how to do this for the matricized tensor times Khatri--Rao product (MTTKRP), which is the key kernel in canonical polyadic tensor decomposition. Our implementation leverages the Kokkos framework, which enables a single code to achieve high performance across multiple architectures that differ in how they approach fine-grained parallelism. We also introduce a new construct for portable thread-local arrays, which we call compile-time polymorphic arrays. Not only are the specifics of our approaches and implementation interesting for tuning tensor computations, but they also provide a roadmap for developing other portable high-performance codes. As a last step in optimizing performance, we modify the MTTKRP algorithm itself to do a permuted traversal of tensor nonzeros to reduce atomic-write contention. Lastly, we test the performance of our implementation on 16- and 68-core Intel CPUs and the K80 and P100 NVIDIA GPUs, showing that we are competitive with state-of-the-art architecture-specific codes while having the advantage of being able to run on a variety of architectures.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2013

Tensor decomposition in post-Hartree–Fock methods. II. CCD implementation

In a previous publication, we have discussed the usage of tensor decomposition in the canonical polyadic (CP) tensor format for electronic structure methods. There, we focused on two-electron integrals and second order Møller-Plesset perturbation theory (MP2). In this work, we discuss the CP format for Coupled Cluster (CC) theory and present a pilot implementation for the Coupled Cluster Doubles method. We discuss the iterative solution of the CC amplitude equations using tensors in CP representation and present a tensor contraction scheme that minimizes the effort necessary for the rank reductions during the iterations. Furthermore, several details concerning the reduction of complexity of the algorithm, convergence of the CC iterations, truncation errors, and the choice of threshold for chemical accuracy are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Computing Sparse Tensor Decompositions via Chapel and C++/MPI Interoperability without Intermediate I/O

We extend an existing approach for efficient use of shared mapped memory across Chapel and C++ for graph data stored as 1-D arrays to sparse tensor data stored using a combination of 2-D and 1-D arrays. We describe the specific extensions that provide use of shared mapped memory tensor data for a particular C++ tensor decomposition tool called GentenMPI. We then demonstrate our approach on several real-world datasets, providing timing results that illustrate minimal overhead incurred using this approach. Finally, we extend our work to improve memory usage and provide convenient random access to sparse shared mapped memory tensor elements in Chapel, while still being capable of leveraging high performance implementations of tensor algorithms in C++.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Parallel Tensor Decompositions for Massive Heterogeneous, Incomplete Data (Final Report: LDRD Project 199986).

We extended the fundamental capabilities of tensor decomposition to a broader range of problems - handling new data types and larger problems. This has implications for data analysis across a range of applications in sensor monitoring, cybersecurity, treaty verification, signal processing, etc. Identifies latent structure within data, enabling anomaly detection, process monitoring, scientific discovery.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Tensor Decomposition Analysis for UAV Anomaly Detection

Vibrational anomalies can provide valuable insights into the health status of an unmanned aerial vehicle, potentially indicating system degradation including propeller, motor, or sensor damage, as well as environmental anomalies such as strong wind gusts and turbulence. However, many causes for vibrational anomalies are not related to vehicle health, such as sharp shifts in velocity or direction of flight. Thus, depending strictly on vibration signals to detect anomalies can result in false positives for failures. Hence, it is important to include additional telemetries in detecting and diagnosing in-flight anomalies. This paper considers an approach to anomaly detection based on tensor decompositions that incorporates information from vibration signals, as well as additional flight data such as velocity, current draw, voltage drop, and attitude. Using experimental flight data collected by the University of Notre Dame, we construct third-order tensors then apply the CANDECOMP/PARAFAC decomposition to identify trends within each flight and classify flights as nominal or anomalous.

unmanned aviation↗
DOE OSTI2019

Efficient Ab Initio Auxiliary-Field Quantum Monte Carlo Calculations in Gaussian Bases via Low-Rank Tensor Decomposition

We describe an algorithm to reduce the cost of auxiliary-field quantum Monte Carlo (AFQMC) calculations for the electronic structure problem. The technique uses a nested low-rank factorization of the electron repulsion integral (ERI). While the cost of conventional AFQMC calculations in Gaussian bases scales as O(N 4 ), where N is the size of the basis, we show that ground-state energies can be computed through tensor decomposition with reduced memory requirements and subquartic scaling. Here, the algorithm is applied to hydrogen chains and square grids, water clusters, and hexagonal BN. In all cases, we observe significant memory savings and, for larger systems, reduced, subquartic simulation time.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Numerical optimization for symmetric tensor decomposition

We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on real-valued decompositions, both unconstrained and nonnegative. We discuss when solutions exist and how to formulate the mathematical program. Numerical results show the properties of the proposed formulations (including one that ignores symmetry) on a set of test problems and illustrate that these straightforward formulations can be effective even though the problem is nonconvex.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

Here, a new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrational zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss–Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm -1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Estimating Higher-Order Moments Using Symmetric Tensor Decomposition

In this paper, we consider the problem of decomposing higher-order moment tensors, i.e., the sum of symmetric outer products of data vectors. Such a decomposition can be used to estimate the means in a Gaussian mixture model and for other applications in machine learning. The dth-order empirical moment tensor of a set of p observations of n variables is a symmetric d-way tensor. Our goal is to nd a low-rank tensor approximation comprising r $\ll$ p symmetric outer products. The challenge is that forming the empirical moment tensor costs O(pn d ) operations and O(n d ) storage, which may be prohibitively expensive; additionally, the algorithm to compute the low-rank approximation costs O(n d ) per iteration. Our contribution is avoiding formation of the moment tensor, computing the low-rank tensor approximation of the moment tensor implicitly using O(pnr) operations per iteration and no extra memory. This advance opens the door to more applications of higher-order moments since they can now be efficiently computed. We present numerical evidence of the computational savings and show an example of estimating the means for higher-order moments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Bayesian Tensor Decompositions for Scalable Supervised Learning of Scientific Data (Final Report)

In this document we highlight the detailed accomplishments and progress that we have made in this period. This progress seeks to address the three main objectives to provide new algorithms for quantifying uncertainty in low-multilinear-rank models and to leverage them for data analysis. These include: (1) develop probabilistic models for low-multilinear-rank functions; (2) develop a suite of Bayesian learning approaches to learn the probabilistic models from data; (3) apply the techniques on challenging problems arising in DOE-relevant applications.

97 MATHEMATICS AND COMPUTING↗
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 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 OSTI2024

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

The photovoltaic (PV) industry is simultaneously targeting long warranties and new materials/designs for high-energy-yield modules, requiring an advanced methodology to forecast long-term durability of products with un-proven materials combinations. Extended, sequential, and combined stress testing methods are gaining popularity for assessing durability of PV modules/materials beyond the early-stage mortalities. Importantly, multiple degradation mechanisms can proceed simultaneously, and their separate contributions to the overall power loss should ideally be quantified. This work examines the use of data-driven tools towards developing a strategy for faster learning cycles in accelerated stress testing.

accelerated stress testing↗
DOE OSTI2022

Zero-Truncated Poisson Tensor Decomposition for Sparse Count Data

We propose a novel statistical inference paradigm for zero-inflated multiway count data that dispenses with the need to distinguish between true and false zero counts. Our approach ignores all zero entries and applies zero-truncated Poisson regression on the positive counts. Inference is accomplished via tensor completion that imposes low-rank structure on the Poisson parameter space. Our main result shows that an $\textit{N}$-way rank-R parametric tensor 𝓜 ϵ (0, ∞) $I$Χ∙∙∙Χ$I$ generating Poisson observations can be accurately estimated from approximately $IR^2 \text{log}^2_2(I)$ non-zero counts for a nonnegative canonical polyadic decomposition. Several numerical experiments are presented demonstrating that our zero-truncated paradigm is comparable to the ideal scenario where the locations of false zero counts are known $\textit{a priori}$.

97 MATHEMATICS AND COMPUTING↗