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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Computing rank‐revealing factorizations of matrices stored out‐of‐core

This paper describes efficient algorithms for computing rank-revealing factorizations of matrices that are too large to fit in main memory (RAM), and must instead be stored on slow external memory devices such as disks (out-of-core or out-of-memory). Traditional algorithms for computing rank-revealing factorizations (such as the column pivoted QR factorization and the singular value decomposition) are very communication intensive as they require many vector-vector and matrix-vector operations, which become prohibitively expensive when data is not in RAM. Randomization allows to reformulate new methods so that large contiguous blocks of the matrix are processed in bulk. The paper describes two distinct methods. The first is a blocked version of column pivoted Householder QR, organized as a “left-looking” method to minimize the number of the expensive write operations. The second method results employs a UTV factorization. It is organized as an algorithm-by-blocks to overlap computations and I/O operations. As it incorporates power iterations, it is much better at revealing the numerical rank. Numerical experiments on several computers demonstrate that the new algorithms are almost as fast when processing data stored on slow memory devices as traditional algorithms are for data stored in RAM.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

First-Principles Elucidation of Initial Dehydrogenation Pathways in Mg(BH 4 ) 2

Complex borohydrides such as Mg(BH 4 ) 2 offer one of highest capacities to chemically store hydrogen for onboard applications; however, it suffers greatly from kinetic constraints that prevent realization of full capacity and reversibility. Understanding these kinetic limitations solely from experiments is extremely challenging due to the unusual complexity of various competing elemental reaction steps involved during the de/rehydrogenation reaction. This work aims to map out the energetics associated with initial dehydrogenation of Mg(BH 4 ) 2 from first-principles simulations and to identify the preferred reaction pathways. Our calculations suggest the rate-limiting step during BH 4 – –B 3 H 8 – conversion is the formation of the B 2 H 7 – intermediate. We further emphasize and clarify that the B 3 H 8 – and H – intermediates, formed during initial Mg(BH 4 ) 2 decomposition, appear as molecular species that are embedded in the Mg–BH 4 –Mg matrix as evidenced in the nuclear magnetic resonance measurements and not as bulk MgH 2 and Mg(B 3 H 8 ) 2 as previously assumed in theoretical predictions of the thermodynamics.

08 HYDROGEN↗
DOE OSTI2020

Mechanisms of Asymmetric Membrane Formation in Nonsolvent-Induced Phase Separation

We report the first simulations of nonsolvent-induced phase separation (NIPS) that predict membrane microstructures with graded asymmetric pore size distribution. In NIPS, a polymer solution film is immersed in a nonsolvent bath, enriching the film in nonsolvent, and leading to phase separation that forms a solid polymer-rich membrane matrix and polymer-poor membrane pores. We demonstrate how mass-transfer-induced spinodal decomposition, thermal fluctuations, and glass-transition dynamics implemented with mobility contrast between the polymer-rich and polymer-poor phases are essential to the formation of asymmetric membrane microstructures. Specifically, we show that the competition between the propagation of the phase-separation and glass-transition fronts determines the degree of pore-size asymmetry. In conclusion, we also explore the sensitivity of these microstructures to the initial film composition, and compare their formation in 2D and 3D.

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

Code for the manuscript "Mori-Zwanzig Modal Decomposition"

We would like to create an open source repository in LANL's github on code written in Julia, in which we implement and extend the data-driven Mori-Zwanzig method for extracting large-scale spatio-temporal structures from data, which we call MZMD. This method is an extension of Dynamic Mode Decomposition (DMD) in which Mori-Zwanzig memory kernels are included into the associated companion matrix. In the code we would like to release, we apply MZMD to a flow over a cylinder with Reynolds number 100 rather than the much larger data set used in the associated manuscript. DMD is used extensively in the fluid dynamics community mainly for extracting large scale spatio-temporal structures (patters) from flow data. This is useful for understanding the key mechanisms that generate certain complex dynamical process relevant in engineering design. In MZMD, we improve upon DMD by adding the Mori-Zwanzig memory kernels, and show this improvement is especially important in strongly nonlinear regions of the flow.

Woodward, Michael↗
DOE OSTI2024

Jacobian-based Model Diagnostics and Application to Equation Oriented Modeling of a Carbon Capture System

Equation-oriented (EO) modeling has the potential to enable the effective design and optimization of the operation of advanced energy systems. However, advanced modeling of energy systems results in a large number of variables and non-linear equations, and it can be difficult to search through these to identify the culprit(s) responsible for convergence issues. The Institute for the Design of Advanced Energy Systems Integrated Platform (IDAES-IP) contains a tool to identify poorly scaled constraints and variables by searching for rows and columns of the Jacobian matrix with small L2-norms so they can be rescaled. A further singular value decomposition can be per-formed to identify degenerate sets of equations and remaining scaling issues. This work presents an EO model of a flowsheet developed for post-combustion carbon capture using a monoethanolamine (MEA) solvent system as a case study. The IDAES diagnostics tools were successfully applied to this flowsheet to identify problems to improve model robustness and enable the optimization of process design and operating conditions of a carbon capture system.

Allan, Douglas↗
DOE OSTI2025

Modular-Invariant Random Matrix Theory and AdS 3 Wormholes

We develop a nonperturbative definition of RMT 2 : a generalization of random matrix theory that is compatible with the symmetries of two-dimensional conformal field theory. Given any random matrix ensemble, its 𝑛-point spectral correlations admit a prescribed modular-invariant lift to RMT 2 , which moreover reduce to the original random matrix correlators in a near-extremal limit. Central to the prescription is a presentation of random matrix theory in Mellin space, which lifts to two dimensions via the SL⁡(2,ℤ) spectral decomposition employed in previous work. As a demonstration we perform the explicit RMT 2 lift of two-point correlations of the GUE Airy model. We propose that in AdS 3 pure gravity, semiclassical amplitudes for off-shell 𝑛-boundary torus wormholes with topology Σ 0,𝑛 × 𝑆 1 are given by the RMT 2 lift of JT gravity wormhole amplitudes. For the three-boundary case, we identify a gravity calculation which matches the RMT 2 result.

conformal field theory↗
DOE OSTI2025

SymProp: Scaling Sparse Symmetric Tucker Decomposition via Symmetry Propagation

Sparse symmetric tensors are an important class of tensors, and their decompositions serve as powerful tools for revealing low-rank structures. This paper introduces SymProp, a novel approach for scaling sparse symmetric Tucker decomposition by propagating symmetry through intermediate computations. SymProp optimizes two key computational kernels: Sparse Symmetric Tensor Times Same Matrix chain (S3 TTMc) for Higher-Order Orthogonal Iteration (HOOI) and Sparse Symmetric Tensor Times Same Matrix chain Times Core (S3 TTMcTC) for Higher-Order QR Iteration (HOQRI). Our method employs a metaprogramming-based index iteration approach to efficiently handle the upper triangular parts of intermediate dense symmetric tensors. SymProp achieves up to 50.9× speedup over SPLATT and up to 360.8× over Compressed Sparse Symmetric (CSS) format on the S3 TTMc operation. Moreover, our S3 TTMc and S3 TTMcTC implementations support tensor orders four levels higher than state-of-the-art methods. Our HOQRI demonstrates superior scalability and up to a 33.6× speedup over optimized HOOI. By enabling more scalable Tucker decompositions for higher orders, decomposition ranks, and dimension sizes, SymProp opens new possibilities for analyzing complex hypergraph structures in fields such as network science, data mining, and machine learning.

Li, Zecheng [North Carolina State University]↗
DOE OSTI2024

Communication Lower Bounds and Optimal Algorithms for Multiple Tensor-Times-Matrix Computation

Multiple tensor-times-matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. Here, we establish communication lower bounds that determine how much data movement is required (under mild conditions) to perform the Multi-TTM computation in parallel. The crux of the proof relies on analytically solving a constrained, nonlinear optimization problem. We also present a parallel algorithm to perform this computation that organizes the processors into a logical grid with twice as many modes as the input tensor. We show that, with correct choices of grid dimensions, the communication cost of the algorithm attains the lower bounds and is therefore communication optimal. Finally, we show that our algorithm can significantly reduce communication compared to the straightforward approach of expressing the computation as a sequence of tensor-times-matrix operations when the input and output tensors vary greatly in size.

HBL-inequalities↗
DOE OSTI2022

Status on lattice calculations of the proton spin decomposition

Abstract Lattice calculations of the proton spin components is reviewed. The lattice results of the quark spin from the axial-vector current matrix element at ∼ 0.3−0.4 is smaller than those from the constituent quark models. This is largely due to the fact that the vacuum polarization contribution from the disconnected insertion is negative. Its connection with the anomalous Ward identity is clarified and verified numerically. This resolves the contentious issue in the “proton spin crisis.” The glue spin and angular momentum are found to be large and there is notable contribution from the quark orbital angular momentum. Renormalization, mixing, and normalization of the quark and glue angular momenta are discussed. With sufficient precision, they can be compared with more precise experimental measurements when the electron-ion collider facility is available.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Root-N Krylov-space correction vectors for spectral functions with the density matrix renormalization group

In this work, we propose a method to compute spectral functions of generic Hamiltonians using the density matrix renormalization group (DMRG) algorithm directly in the frequency domain, based on a modified Krylov-space decomposition to compute the correction vectors. Our approach entails the calculation of the root-N (N=2 is the standard square root) of the Hamiltonian propagator using Krylov-space decomposition and repeating this procedure N times to obtain the actual correction vector. We show that our method greatly alleviates the burden of keeping a large bond dimension at large target frequencies, a problem found with conventional correction-vector DMRG, whereas achieving better computational performance at large N. We apply our method to spin and charge spectral functions of t-J and Hubbard models in the challenging two-leg ladder geometry and provide evidence that the root-N approach reaches a much improved spectral resolution compared to the conventional correction vector.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Wormholes, branes and finite matrices in sine dilaton gravity

We compute the double trumpet in sine dilaton gravity via WdW quantization. The wormhole size is discretized. The wormhole amplitude matches the spectral correlation of a finite-cut matrix integral, where matrices have large but finite dimensions. This strongly suggests an identification of the sine dilaton gravity theory with the q-deformed JT gravity matrix integral. At the very least, it captures all universal content of that matrix model. The disk decomposes into the physical (gauge invariant) solutions of the WdW equation, which are trumpets with discrete sizes. This decomposition modifies the usual no-boundary wavefunction to a normalizable one in sine dilaton gravity.

2D Gravity↗
DOE OSTI2021

Direct evidence for the role of microbial community composition in the formation of soil organic matter composition and persistence

The largest terrestrial carbon sink on earth is soil carbon stocks. As the climate changes, the rate at which the Earth’s climate warms depends in part on the persistence of soil organic carbon. Microbial turnover forms the backbone of soil organic matter (SOM) formation and it has been recently proposed that SOM molecular complexity is a key driver of stability. Despite this, the links between microbial diversity, chemical complexity and biogeochemical nature of SOM remain missing. Here we tested the hypotheses that distinct microbial communities shape the composition of SOM, and microbial-derived SOM has distinct decomposition potential depending on its community of origin. We inoculated microbial communities of varying diversities into a model soil matrix amended with simple carbon (cellobiose) and measured the thermal stability of the resultant SOM. Using a Rock-Eval ® ramped thermal analysis, we found that microbial community composition drives the chemical fingerprint of soil carbon. While diversity was not a driver of SOM composition, bacteria-only communities lead to more thermally labile soil C pools than communities with bacteria and fungi. Our results provide direct evidence for a link between microbial community structure, SOM composition, and thermal stability. This evidence demonstrates the relevance of soil microorganisms in building persistent SOM stocks.

Domeignoz-Horta, Luiz A. (ORCID:0000000346186253)↗
DOE OSTI2025

A Linear-Complexity Tensor Butterfly Algorithm for Compressing High-Dimensional Oscillatory Integral Operators

This paper presents a multilevel tensor compression algorithm called tensor butterfly algorithm for efficiently representing large-scale and high-dimensional oscillatory integral operators, including Green's functions for wave equations and integral transforms such as Radon transforms and Fourier transforms. The proposed algorithm leverages a tensor extension of the so-called complementary low-rank property of existing matrix butterfly algorithms. The algorithm partitions the discretized integral operator tensor into subtensors of multiple levels and factorizes each subtensor at the middle level as a Tucker-type interpolative decomposition, whose factor matrices are formed in a multilevel fashion. For a d-dimensional (d > 1) integral operator discretized into a 2d-mode tensor with n2d entries, the overall CPU time and memory requirement scale as O(nd), in stark contrast to the O(nd log n) complexity of existing matrix algorithms such as matrix butterfly algorithms and fast Fourier transforms (FFTs), where n is the number of points per direction. When comparing with other tensor algorithms such as quantized tensor train (QTT), the proposed algorithm also shows superior CPU and memory performance for tensor contraction. Remarkably, the tensor butterfly algorithm can efficiently model high-frequency Green's function interactions between two unit cubes, each spanning 512 wavelengths per direction, which represents problems of scale over 512× larger than that existing butterfly algorithms can handle, with the same amount of computation resources. On the other hand, for a problem representing 64 wavelengths per direction, which is the largest size existing algebraic matrix algorithms can handle, our tensor butterfly algorithm exhibits 200x speedups and 30× memory reduction compared with existing ones. Moreover, the tensor butterfly algorithm also permits O(nd)-complexity FFTs and Radon transforms up to d = 6 dimensions.

Kielstra, P Michael↗
DOE OSTI2021

Tensor force role in β decays analyzed within the Gogny-interaction shell model

The half-life of the famous C 14 β decay is anomalously long, with different mechanisms: the tensor force, cross-shell mixing, and three-body forces, proposed to explain the cancellations that lead to a small transition matrix element. In this study, we revisit and analyze the role of the tensor force for the β decay of C 14 as well as of neighboring isotopes. We add a tensor force to the Gogny interaction, and derive an effective Hamiltonian for shell-model calculations. The calculations were carried out in a p – s d model space to investigate cross-shell effects. Furthermore, we decompose the wave functions according to the total orbital angular momentum L in order to analyze the effects of the tensor force and cross-shell mixing. The inclusion of the tensor force significantly improves the shell-model calculations of the β -decay properties of carbon isotopes. In particular, the anomalously slow β decay of C 14 can be explained by the isospin T = 0 part of the tensor force, which changes the components of N 14 with the orbital angular momentum L = 0 , 1 , and results in a dramatic suppression of the Gamow-Teller transition strength. At the same time, the description of other nearby β decays are improved. Decomposition of wave function into L components illuminates how the tensor force modifies nuclear wave functions, in particular suppression of β -decay matrix elements. Cross-shell mixing also has a visible impact on the β -decay strength. Inclusion of the tensor force does not seem to significantly change, however, binding energies of the nuclei within the phenomenological interaction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Irradiation Effect on Noble Metal Particles in Water Using in situ Liquid Cell STEM Observation

During geologic disposal of spent nuclear fuel (SNF) in an engineered nuclear waste repository, once all other barriers have degraded, oxidizing may occur at the solid-water interface owing to a self-generated radiolytic field. The repository design includes large quantities of iron (Fe), that is anticipated to corrode under an anoxic environment, and generate hydrogen (H 2 ) gas. This H 2 gas is thought to be able to suppress the dissolution of SNF through a catalytic reaction with noble metal particles (NMP) that are pre-existing in the SNF. This interaction leads to the decomposition of the major oxidant, hydrogen peroxide (H 2 O 2 ). In conclusion, these processes are described in the Fuel Matrix Degradation (FMD) model that is being used to predict SNF degradation rates. The NMP, therefore, plays an important role within the FMD model.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

OR22-Neuromorphic Rad Detector-PD3Ra (Final Report)

In unattended monitoring scenarios, automated radiation detection algorithms must be able to detect low signal-to-noise ratio (SNR) anomalies in a potentially dynamic and noisy background and report these anomalies in a timely fashion. Dynamic and noisy backgrounds complicate the use of simple gross-counting algorithms because they can lead to either high false positive rates or low sensitivity. Algorithms that use the entire spectrum have been the most successful in this area; notable examples are the NSCRAD algorithm developed at Pacific Northwest National Laboratory and recently the nonnegative matrix factorization approach developed at Lawrence Berkeley National Laboratory (LBNL). These approaches use either spectral regions of interest or spectral decomposition to detect threat isotopes in the background.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Random projection using random quantum circuits

The random sampling task performed by Google's Sycamore processor gave us a glimpse of the “quantum supremacy era.” This has definitely shed some light on the power of random quantum circuits in this abstract task of sampling outputs from the (pseudo)random circuits. In this paper, we explore a practical near-term use of local random quantum circuits in dimensional reduction of large low-rank data sets. We make use of the well-studied dimensionality reduction technique called the random projection method. This method has been extensively used in various applications such as image processing, logistic regression, entropy computation of low-rank matrices, etc. We prove that the matrix representations of local random quantum circuits with sufficiently shorter depths [ ∼ O ( n ) ] serve as good candidates for random projection. We demonstrate numerically that their projection abilities are not far off from the computationally expensive classical principal components analysis on MNIST and CIFAR-100 image datasets. We also benchmark the performance of quantum random projection against the commonly used classical random projection in the tasks of dimensionality reduction of image data sets and computing von Neumann entropies of large low-rank density matrices. And finally, using variational quantum singular value decomposition, we demonstrate a near-term implementation of extracting the singular vectors with dominant singular values after quantum random projecting a large low-rank matrix to lower dimensions. All such numerical experiments unequivocally demonstrate the ability of local random circuits to randomize a large Hilbert space at sufficiently shorter depths with robust retention of properties of large data sets in reduced dimensions. Published by the American Physical Society 2024

Kumaran, Keerthi (ORCID:0009000949125721)↗
DOE OSTI2020

Localized Exponential Time Differencing Method for Shallow Water Equations: Algorithms and Numerical Study

Here, we explore the performance of the exponential time differencing (ETD) method applied to the rotating shallow water equations. Comparing with explicit time stepping of the same order accuracy in time, the ETD algorithms could reduce the computational time in many cases by allowing the use of large time step sizes while still maintaining numerical stability. To accelerate the ETD simulations, we propose a localized approach that synthesizes the ETD method and overlapping domain decomposition. By dividing the original problem into many subdomain problems of smaller sizes and solving them locally, the proposed approach could speed up the calculation of matrix exponential vector products. Several standard test cases for shallow water equations of one or multiple layers are considered. The results show great potential of the localized ETD method for high-performance computing because each subdomain problem can be naturally solved in parallel at every time step.

58 GEOSCIENCES↗