Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “generalized singular value 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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Randomized algorithms for generalized singular value decomposition with application to sensitivity analysis

The generalized singular value decomposition (GSVD) is a valuable tool that has many applications in computational science. However, computing the GSVD for large-scale problems is challenging. Motivated by applications in hyper-differential sensitivity analysis (HDSA), in this work we propose new randomized algorithms for computing the GSVD which use randomized subspace iteration and weighted QR factorization. Detailed error analysis is given which provides insight into the accuracy of the algorithms and the choice of the algorithmic parameters. We demonstrate the performance of our algorithms on test matrices and a large-scale model problem where HDSA is used to study subsurface flow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Classification of gaseous UF 6 assay by femtosecond LIBS in the 424.4 nm spectral region using numerical HOGSVD-DTW features

This technical note presents experimental results using numerical features of fs-LIBS data to classify the assay value of a gaseous UF 6 material. Here, the data-driven feature vectors are computed by Higher Order Generalized Singular Value Decomposition (HOGSVD) and Dynamic Time Warp (DTW). The method achieves 96.97% accuracy in spectral classification testing with fs-LIBS samples obtained from a UF 6 material with five known assay values ranging from 0.287% to 61.740%, with 100% accuracy for the four largest assay values ranging from 4.615% to 61.740%.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

A flexible class of priors for orthonormal matrices with basis function-specific structure

Statistical modeling of high-dimensional matrix-valued data motivates the use of a low-rank representation that simultaneously summarizes key characteristics of the data and enables dimension reduction. Low-rank representations commonly factor the original data into the product of orthonormal basis functions and weights, where each basis function represents an independent feature of the data. However, the basis functions in these factorizations are typically computed using algorithmic methods that cannot quantify uncertainty or account for basis function correlation structure a priori. While there exist Bayesian methods that allow for a common correlation structure across basis functions, empirical examples motivate the need for basis function-specific dependence structure. We propose a prior distribution for orthonormal matrices that can explicitly model basis function-specific structure. The prior is used within a general probabilistic model for singular value decomposition to conduct posterior inference on the basis functions while accounting for measurement error and fixed effects. We discuss how the prior specification can be used for various scenarios and demonstrate favorable model properties through synthetic data examples. Finally, we apply our method to two-meter air temperature data from the Pacific Northwest, enhancing our understanding of the Earth system’s internal variability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Quantum state preparation and nonunitary evolution with diagonal operators

Realizing nonunitary transformations on unitary-gate-based quantum devices is critically important for simulating a variety of physical problems, including open quantum systems and subnormalized quantum states. Here, we present a dilation-based algorithm to simulate nonunitary operations using probabilistic quantum computing with only one ancilla qubit. We utilize the singular-value decomposition (SVD) to decompose any general quantum operator into a product of two unitary operators and a diagonal nonunitary operator, which we show can be implemented by a diagonal unitary operator in a one-qubit dilated space. While dilation techniques increase the number of qubits in the calculation, and thus the gate complexity, our algorithm limits the operations required in the dilated space to a diagonal unitary operator, which has known circuit decompositions. We use this algorithm to prepare random subnormalized two-level states on a quantum device with high fidelity. Furthermore, we present the accurate nonunitary dynamics of two-level open quantum systems in a dephasing channel and an amplitude-damping channel computed on a quantum device. The algorithm presented will be most useful for implementing general nonunitary operations when the SVD can be readily computed, which is the case for most operators in the noisy intermediate-scale quantum computing era.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Space–time reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems

A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing much accuracy, which results in a considerably more speed-up than the spatial reduction only. Recently, a novel space–time reduced order model for dynamical problems has been developed [17], where the space–time reduced order model shows an order of a hundred speed-up with a relative error of 10 –4 for small academic problems. However, in order for the method to be applicable to a large-scale problem, an efficient space–time reduced basis construction algorithm needs to be developed. Here we present the incremental space–time reduced basis construction algorithm. The incremental algorithm is fully parallel and scalable. Additionally, the block structure in the space–time reduced basis is exploited, which enables the avoidance of constructing the reduced space–time basis. These novel techniques are applied to a large-scale particle transport simulation with million and billion degrees of freedom. The numerical example shows that the algorithm is scalable and practical. Also, it achieves a tremendous speed-up, maintaining a good accuracy. Finally, error bounds for space-only and space–time reduced order models are derived.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Evaluation of data driven low-rank matrix factorization for accelerated solutions of the Vlasov equation

Low-rank methods have shown success in accelerating simulations of a collisionless plasma described by the Vlasov equation, but still rely on computationally costly linear algebra every time step. We propose a data-driven factorization method using artificial neural networks, specifically with convolutional layer architecture, that trains on existing simulation data. At inference time, the model outputs a low-rank decomposition of the distribution field of the charged particles, and we demonstrate that this step is faster than the standard linear algebra technique. Numerical experiments show that the method achieves comparable reconstruction accuracy for interpolation tasks, generalizing to unseen test data in a manner beyond just memorizing training data; patterns in factorization also inherently followed the same numerical trend as those within algebraic methods (e.g., truncated singular-value decomposition). However, when training on the first 70% of a time-series data and testing on the remaining 30%, the method fails to meaningfully extrapolate. Despite this limiting result, the technique may have benefits for simulations in a statistical steady-state or otherwise showing temporal stability. These results suggest that while the model offers a computationally efficient alternative for datasets with temporal stability, its current formulation is best suited for interpolation rather than for predicting future states in time-evolving systems. This study thus lays the groundwork for further refinement of neural network-based approaches to low-rank matrix factorization in high-dimensional plasma simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Exploring Hilbert space on a budget: Novel benchmark set and performance metric for testing electronic structure methods in the regime of strong correlation

This work explores the ability of classical electronic structure methods to efficiently represent (compress) the information content of full configuration interaction (FCI) wave functions. We introduce a benchmark set of four hydrogen model systems of different dimensionalities and distinctive electronic structures: a 1D chain, a 1D ring, a 2D triangular lattice, and a 3D close-packed pyramid. To assess the ability of a computational method to produce accurate and compact wave functions, we introduce the accuracy volume, a metric that measures the number of variational parameters necessary to achieve a target energy error. Using this metric and the hydrogen models, we examine the performance of three classical deterministic methods: (i) selected configuration interaction (sCI) realized both via an a posteriori (ap-sCI) and variational selection of the most important determinants, (ii) an a posteriori singular value decomposition (SVD) of the FCI tensor (SVD-FCI), and (iii) the matrix product state representation obtained via the density matrix renormalization group (DMRG). We find that the DMRG generally gives the most efficient wave function representation for all systems, particularly in the 1D chain with a localized basis. For the 2D and 3D systems, all methods (except DMRG) perform best with a delocalized basis, and the efficiency of sCI and SVD-FCI is closer to that of DMRG. For larger analogs of the models, the DMRG consistently requires the fewest parameters but still scales exponentially in 2D and 3D systems, and the performance of SVD-FCI is essentially equivalent to that of ap-sCI.

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

Permutation-adapted complete and independent basis for atomic cluster expansion descriptors

Atomic cluster expansion (ACE) methods provide a systematic way to describe particle local environments of arbitrary body order. For practical applications it is often required that the basis of cluster functions be symmetrized with respect to rotations and permutations. Existing methodologies yield sets of symmetrized functions that are over-complete. These methodologies thus require an additional numerical procedure, such as singular value decomposition (SVD), to eliminate redundant functions. In this work, it is shown that analytical linear relationships for subsets of cluster functions may be derived using recursion and permutation properties of generalized Wigner symbols. From these relationships, subsets (blocks) of cluster functions can be selected such that, within each block, functions are guaranteed to be linearly independent. It is conjectured that this block-wise independent set of permutation-adapted rotation and permutation invariant (PA-RPI) functions forms a complete, independent basis for ACE. Along with the first analytical proofs of block-wise linear dependence of ACE cluster functions and other theoretical arguments, numerical results are offered to demonstrate this. The utility of the method is demonstrated in the development of an ACE interatomic potential for tantalum. Using the new basis functions in combination with Bayesian compressive sensing sparse regression, some high degree descriptors are observed to persist and help achieve high-accuracy models.

Angular momentum↗
DOE OSTI2023

General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory

With a focus on universal quantum computing for quantum simulation, and through the example of lattice gauge theories, we introduce rather general quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple (bosonic and fermionic) quantum numbers with non-trivial functional coefficients. In particular, we analyze diagonalization of Hamiltonian terms using a singular-value decomposition technique, and discuss how the achieved diagonal unitaries in the digitized time-evolution operator can be implemented. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions, for which a complete quantum-resource analysis within different computational models is presented. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories. The example chosen further demonstrates the importance of adopting efficient theoretical formulations: it is shown that an explicitly gauge-invariant formulation using loop, string, and hadron degrees of freedom simplifies the algorithms and lowers the cost compared with the standard formulations based on angular-momentum as well as the Schwinger-boson degrees of freedom. The loop-string-hadron formulation further retains the non-Abelian gauge symmetry despite the inexactness of the digitized simulation, without the need for costly controlled operations. Such theoretical and algorithmic considerations are likely to be essential in quantumly simulating other complex theories of relevance to nature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Tensor decompositions for count data that leverage stochastic and deterministic optimization

There is growing interest to extend low-rank matrix decompositions to multi-way arrays, or tensors. One fundamental low-rank tensor decomposition is the canonical polyadic decomposition (CPD). The challenge of fitting a low-rank, nonnegative CPD model to Poisson-distributed count data is of particular interest. Several popular algorithms use local search methods to approximate the maximum likelihood estimator (MLE) of the Poisson CPD model. Here, this work presents two new algorithms that extend state-of-the-art local methods for Poisson CPD. Hybrid GCP-CPAPR combines Generalized Canonical Decomposition (GCP) with stochastic optimization and CP Alternating Poisson Regression (CPAPR), a deterministic algorithm, to increase the probability of converging to the MLE over either method used alone. Restarted CPAPR with SVDrop uses a heuristic based on the singular values of the CPD model unfoldings to identify convergence toward optimizers that are not the MLE and restarts within the feasible domain of the optimization problem, thus reducing overall computational cost when using a multi-start strategy. We provide empirical evidence that indicates our approaches outperform existing methods with respect to converging to the Poisson CPD MLE.

CPAPR↗
DOE OSTI2021

Modeling interval trendlines: Symbolic singular spectrum analysis for interval time series

Abstract In this article we propose an extension of singular spectrum analysis for interval‐valued time series. The proposed methods can be used to decompose and forecast the dynamics governing a set‐valued stochastic process. The resulting components on which the interval time series is decomposed can be understood as interval trendlines, cycles, or noise. Forecasting can be conducted through a linear recurrent method, and we devised generalizations of the decomposition method for the multivariate setting. The performance of the proposed methods is showcased in a simulation study. We apply the proposed methods so to track the dynamics governing the Argentina Stock Market (MERVAL) in real time, in a case study over a period of turbulence that led to discussions of the government of Argentina with the International Monetary Fund.

de Carvalho, Miguel↗
DOE OSTI2024

Distance preserving machine learning for uncertainty aware accelerator capacitance predictions

Abstract Accurate uncertainty estimations are essential for producing reliable machine learning models, especially in safety-critical applications such as accelerator systems. Gaussian process models are generally regarded as the gold standard for this task; however, they can struggle with large, high-dimensional datasets. Combining deep neural networks with Gaussian process approximation techniques has shown promising results, but dimensionality reduction through standard deep neural network layers is not guaranteed to maintain the distance information necessary for Gaussian process models. We build on previous work by comparing the use of the singular value decomposition against a spectral-normalized dense layer as a feature extractor for a deep neural Gaussian process approximation model and apply it to a capacitance prediction problem for the High Voltage Converter Modulators in the Oak Ridge Spallation Neutron Source. Our model shows improved distance preservation and predicts in-distribution capacitance values with less than 1% error.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

PythonFOAM: In-situ data analyses with OpenFOAM and Python

Here, we outline the development of a general-purpose Python-based data analysis tool for OpenFOAM. Our implementation relies on the construction of OpenFOAM applications that have bindings to data analysis libraries in Python. Double precision data in OpenFOAM is cast to a NumPy array using the NumPy C-API and Python modules may then be used for arbitrary data analysis and manipulation on flow-field information. We highlight how the proposed wrapper may be used for an in-situ online singular value decomposition (SVD) implemented in Python and accessed from the OpenFOAM solver PimpleFOAM. Here, 'in-situ' refers to a programming paradigm that allows for a concurrent computation of the data analysis on the same computational resources utilized for the partial differential equation solver. In addition, to demonstrate parallel deployments, we deploy a distributed SVD, which collects snapshot data across the ranks of a distributed simulation to compute the global left singular vectors. Crucially, both OpenFOAM and Python share the same message passing interface (MPI) communicator for this deployment which allows Python objects and functions to exchange NumPy arrays across ranks. Subsequently, we provide scaling assessments of this distributed SVD on multiple nodes of Intel Broadwell and KNL architectures for canonical test cases such as the large eddy simulations of a backward facing step and a channel flow at friction Reynolds number of 395. Finally, we demonstrate the deployment of a deep neural network for compressing the flow-field information using an autoencoder to demonstrate an ability to use state-of-the-art machine learning tools in the Python ecosystem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A learned closure method applied to phase mixing in a turbulent gradient-driven gyrokinetic system in simple geometry

We present a new method for formulating closures that learn from kinetic simulation data. We apply this method to phase mixing in a simple gyrokinetic turbulent system – temperature-gradient-driven turbulence in an unsheared slab. The closure, called the learned multi-mode (LMM) closure, is constructed by, first, extracting an optimal basis from a nonlinear kinetic simulation using singular value decomposition. Subsequent nonlinear fluid simulations are projected onto this basis and the results are used to formulate the closure. We compare the closure with other closures schemes over a broad range of the relevant two-dimensional parameter space (collisionality and gradient drive). We find that the turbulent kinetic system produces phase-mixing rates much lower than the linear expectations, which the LMM closure is capable of capturing. We also compare radial heat fluxes. A Hammett–Perkins closure, generalized to include collisional effects, is quite successful throughout the parameter space, producing ${\sim }14\,\%$ root-mean-square (r.m.s.) error. The LMM closure is also very effective: when trained at three (two) points (in a 35 point parameter grid), the LMM closure produces $8\,\%$ ( $12\,\%$ ) r.m.s. errors. The LMM procedure can be readily generalized to other closure problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Data-Driven Compression of Electron-Phonon Interactions

First-principles calculations of electron interactions in materials have seen rapid progress in recent years, with electron-phonon ( e − ph ) interactions being a prime example. However, these techniques use large matrices encoding the interactions on dense momentum grids, which reduces computational efficiency and obscures interpretability. For e − ph interactions, existing interpolation techniques leverage locality in real space, but the high dimensionality of the data remains a bottleneck to balance cost and accuracy. Here we show an efficient way to compress e − ph interactions based on singular value decomposition (SVD), a widely used matrix and image compression technique. Leveraging (un)constrained SVD methods, we accurately predict material properties related to e − ph interactions—including charge mobility, spin relaxation times, band renormalization, and superconducting critical temperature—while using only a small fraction (1%–2%) of the interaction data. These findings unveil the hidden low-dimensional nature of e − ph interactions. Furthermore, they accelerate state-of-the-art first-principles e − ph calculations by about 2 orders of magnitude without sacrificing accuracy. Our Pareto-optimal parametrization of e − ph interactions can be readily generalized to electron-electron and electron-defect interactions, as well as to other couplings, advancing quantitative studies of condensed matter. Published by the American Physical Society 2024

Physics↗
DOE OSTI2020

Pulsed Thermal Tomography Nondestructive Examination of Additively Manufactured Reactor Materials (Second Annual Progress Report)

Additive manufacturing (AM) is an emerging method for cost-efficient fabrication of nuclear reactor parts. AM of metallic structures for nuclear energy applications is currently based on laser powder bed fusion (LPBF) process, which can introduce internal material flaws, such as pores and anisotropy. Integrity of AM structures needs to be evaluated nondestructively because material flaws could lead to premature failures due to exposure to high temperature, radiation and corrosive environment in a nuclear reactor. Thermal tomography (TT) provides a capability for non-destructive evaluation of sub-surface defects in arbitrary size structures. Thermal tomography is a computational method for heat diffusion-based imaging of solids, which provides 3D visualization of data from flash thermography measurements. We investigate thermal tomography imaging and nondestructive evaluation of stainless steel and nickel super alloy metallic structures produced with laser powder bed fusion (LPBF) additive manufacturing (AM) process. Metallic structures produced with LPBF contain defects, and there are limited capabilities to evaluate these structures non-destructively. Thermal tomography reconstruction of 3D apparent spatial effusivity provides information about AM structure geometry and internal material flaws. We study performance of thermal tomography in imaging of metallic structures through COMSOL computer simulations of transient heat transfer, and through reconstruction of data obtained from experimental measurements. Reconstruction of internal defects is investigated using a stainless steel 316L specimen with flat bottom hole (FBH) indentations, and Inconel 718 plate produced with laser powder bed fusion (LPBF) method, which contains imprinted hemispherical shape low density regions containing non-sintered metallic powder. The FBH’s have the same sizes as the imprinted defects in the LPBF specimens, but offer better imaging contrast. Thermal tomography reconstructions provide visualizations of internal defects, and allow for estimation of their sizes and locations. Detection sensitivity of TT is limited by noises. We investigate separation of signal from noise in thermography images using several machine learning (ML) methods, including new spatio-temporal blind source separation (STBSS) and spatio-temporal sparse dictionary learning (STSDL) methods. Performance of the ML methods is benchmarked using thermography data obtained from imaging stainless steel 316L and Inconel 718 specimens produced LPBF method with imprinted calibrated porosity defects. The ML methods are ranked by F-score and execution runtime. Finally, we investigate TT of AM stainless steel 316L specimen with imprinted internal porosity defects using relatively low-cost, small form factor infrared (IR) camera based on uncooled micro bolometer detector. Sparse coding related K-means singular value decomposition (SVD) machine learning, image processing algorithms are developed to improve quality of TT images through removal of Additive white Gaussian noise without blurring the images. Following initial qualification of an AM component for deployment in a nuclear reactor, a compact TT can also be used for in-service nondestructive evaluation (NDE). With capability to perform in-service NDE of the AM component lifecycle, TT data can be used for development of a component digital twin.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Nonlinear Matrix Approximation with Radial Basis Function Components

We introduce and investigate matrix approximation by decomposition into a sum of radial basis function (RBF) components. An RBF component is a generalization of the outer product between a pair of vectors, where an RBF function replaces the scalar multiplication between individual vector elements. Even though the RBF functions are positive definite, the summation across components is not restricted to convex combinations and allows us to compute the decomposition for any real matrix that is not necessarily symmetric or positive definite. We formulate the problem of seeking such a decomposition as an optimization problem with a nonlinear and non-convex loss function. Several modern versions of the gradient descent method, including their scalable stochastic counterparts, are used to solve this problem. We provide extensive empirical evidence of the effectiveness of the RBF decomposition and that of the gradient-based fitting algorithm. While being conceptually motivated by singular value decomposition (SVD), our proposed nonlinear counterpart outperforms SVD by drastically reducing the memory required to approximate a data matrix with the same L2 error for a wide range of matrix types. For example, it leads to 2 to 6 times memory save for Gaussian noise, graph adjacency matrices, and kernel matrices. Moreover, this proximity-based decomposition can offer additional interpretability in applications that involve, e.g., capturing the inner low-dimensional structure of the data, retaining graph connectivity structure, and preserving the acutance of images.

Rebrova, Elizaveta↗
DOE OSTI2022

Neutron diffusion calculation in heterogeneous geometry based on local/global iteration using proper orthogonal decomposition

This study newly proposes a heterogeneous core calculation method based on local/global iteration using proper orthogonal decomposition (POD). By using the singular value decomposition (SVD) and the low-rank approximation, appropriate POD bases for expanding the neutron flux can be obtained from snapshot data of the neutron flux obtained by fine mesh calculations. By projection using the POD bases, the dimension of the target equation (e.g., discretized neutron diffusion equation) can be dramatically reduced. In the proposed method, POD is effectively applied to each single assembly calculation (local calculation). Furthermore, using the local/global iteration, the effective neutron multiplication factor and the neutron flux distribution in the whole core geometry can be obtained by combining the numerical results of the local calculation for each fuel assembly and the global calculation for the whole core. As a feasibility study, the proposed method is applied to a one-dimensional heterogeneous core analysis, and the accuracy is investigated by changing the total number of POD bases. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗