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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Deflation as a method of variance reduction for estimating the trace of a matrix inverse

Many fields require computing the trace of the inverse of a large, sparse matrix. The typical method used for such computations is the Hutchinson method which is a Monte Carlo (MC) averaging over matrix quadratures. To improve its convergence, several variance reductions techniques have been proposed. In this paper, we study the effects of deflating the near null singular value space. We make two main contributions. First, we analyze the variance of the Hutchinson method as a function of the deflated singular values and vectors. Although this provides good intuition in general, by assuming additionally that the singular vectors are random unitary matrices, we arrive at concise formulas for the deflated variance that include only the variance and mean of the singular values. We make the remarkable observation that deflation may increase variance for Hermitian matrices but not for non-Hermitian ones. This is a rare, if not unique, property where non-Hermitian matrices outperform Hermitian ones. The theory can be used as a model for predicting the benefits of deflation. Second, we use deflation in the context of a large scale application of "disconnected diagrams" in Lattice QCD. On lattices, Hierarchical Probing (HP) has previously provided an order of magnitude of variance reduction over MC by removing "error" from neighboring nodes of increasing distance in the lattice. Although deflation used directly on MC yields a limited improvement of 30% in our problem, when combined with HP they reduce variance by a factor of over 150 compared to MC. For this, we pre-computated 1000 smallest singular values of an ill-conditioned matrix of size 25 million. Furthermore, using PRIMME and a domain-specific Algebraic Multigrid preconditioner, we perform one of the largest eigenvalue computations in Lattice QCD at a fraction of the cost of our trace computation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Influence of Contrast Agent Dilution on Ballon Deflation Time and Visibility During Tracheal Balloon Dilation: A 3D Printed Phantom Study

PurposeTo determine the effect of contrast medium dilution during tracheal balloon dilation on balloon deflation time and visibility using a 3-dimensional (3D) printed airway phantom.Materials and MethodsA comparison study to investigate balloon deflation times and image quality was performed using two contrast agents with different viscosities, i.e., iohexol and ioxithalamate, and six contrast dilutions with a 3D printed airway phantom.ResultsCompared to 1:0 concentration, 3:1, 2:1, 1:1, 1:2, and 1:3, contrast/saline ratios resulted in a 46% (56.2 s), 59.8% (73.1 s), 74.9% (91.6 s), 81.7% (99.8 s), and 83.5% (102 s) reduction for iohexol, respectively, and a 51.8% (54.7 s), 63.8% (67.6 s), 74.7% (79.2 s), 80.5% (85.3 s), and 82.4% (87.4 s) reduction for ioxithalamate, respectively, in the mean balloon deflation time, although at the expense of decreased balloon opacity (3.5, 6.9, 11.1, 12.4, and 13.9%, for iohexol, respectively, and 3.2, 6, 9.6, 10.8, and 12.4%, for ioxithalamate, respectively).ConclusionsUse of a lower viscosity contrast agent and higher contrast dilution is considered to be able to reduce balloon deflation times and then simultaneously decrease visualization of balloons. The rapid balloon deflation time is likely to improve the safe performance of interventional procedures.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2020

Multigrid deflation for Lattice QCD

Computing the trace of the inverse of large matrices is typically addressed through statistical methods. Deflating out the lowest eigenvectors or singular vectors of the matrix reduces the variance of the trace estimator. This work summarizes our efforts to reduce the computational cost of computing the deflation space while achieving the desired variance reduction for Lattice QCD applications. Previous efforts computed the lower part of the singular spectrum of the Dirac operator by using an eigensolver preconditioned with a multigrid linear system solver. Despite the improvement in performance in those applications, as the problem size grows the runtime and storage demands of this approach will eventually dominate the stochastic estimation part of the computation. In this work, we propose to compute the deflation space in one of the following two ways. First, by using an inexact eigensolver on the Hermitian, but maximally indefinite, operator. Second, by exploiting the fact that the multigrid prolongator for this operator is rich in components toward the lower part of the singular spectrum. We show experimentally that the inexact eigensolver can approximate the lower part of the spectrum even for ill-conditioned operators. Also, the deflation based on the multigrid prolongator is more efficient to compute and apply, and, despite its limited ability to approximate the fine level spectrum, it obtains similar variance reduction on the trace estimator as deflating with approximate eigenvectors from the fine level operator.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Leveraging operator learning to accelerate convergence of the preconditioned conjugate gradient method

We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient (PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on eigenvector approximations or recycled Krylov subspaces, we generate the deflation subspaces using operator learning, specifically the Deep Operator Network (DeepONet). To this aim, we introduce two complementary approaches for assembling the deflation operators. The first approach approximates near-null space vectors of the discrete PDE operator using the basis functions learned by the DeepONet. The second approach directly leverages solutions predicted by the DeepONet. To further enhance convergence, we also propose several strategies for prescribing the sparsity pattern of the deflation operator. Here, a comprehensive set of numerical experiments encompassing steady-state, time-dependent, scalar, and vector-valued problems posed on both structured and unstructured geometries is presented and demonstrates the effectiveness of the proposed DeepONet-based deflated PCG method, as well as its generalization across a wide range of model parameters and problem resolutions.

Deflation↗
DOE OSTI2017

Disconnected Diagrams in Lattice QCD

In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called \disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagrams is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements of the nucleon at two different values of the lattice spacing. Finally, we employ these algorithms to do a high-precision study of strange sigma terms in light nuclei; to our knowledge this is the first calculation of its kind from Lattice QCD.

Gambhir, Arjun↗
DOE OSTI2017

Soft actuators and soft actuating devices

A soft buckling linear actuator is described, including: a plurality of substantially parallel bucklable, elastic structural components each having its longest dimension along a first axis; and a plurality of secondary structural components each disposed between and bridging two adjacent bucklable, elastic structural components; wherein every two adjacent bucklable, elastic structural components and the secondary structural components in-between define a layer comprising a plurality of cells each capable of being connected with a fluid inflation or deflation source; the secondary structural components from two adjacent layers are not aligned along a second axis perpendicular to the first axis; and the secondary structural components are configured not to buckle, the bucklable, elastic structural components are configured to buckle along the second axis to generate a linear force, upon the inflation or deflation of the cells. Methods of actuation using the same are also described.

42 ENGINEERING↗
DOE OSTI2017

Soft buckling actuators

A soft actuator is described, including: a rotation center having a center of mass; a plurality of bucklable, elastic structural components each comprising a wall defining an axis along its longest dimension, the wall connected to the rotation center in a way that the axis is offset from the center of mass in a predetermined direction; and a plurality of cells each disposed between two adjacent bucklable, elastic structural components and configured for connection with a fluid inflation or deflation source; wherein upon the deflation of the cell, the bucklable, elastic structural components are configured to buckle in the predetermined direction. A soft actuating device including a plurality of the soft actuators and methods of actuation using the soft actuator or soft actuating device disclosed herein are also described.

42 ENGINEERING↗
DOE OSTI2019

Soft actuators and soft actuating devices

A soft buckling linear actuator is described, including: a plurality of substantially parallel bucklable, elastic structural components each having its longest dimension along a first axis; and a plurality of secondary structural components each disposed between and bridging two adjacent bucklable, elastic structural components; wherein every two adjacent bucklable, elastic structural components and the secondary structural components in-between define a layer comprising a plurality of cells each capable of being connected with a fluid inflation or deflation source; the secondary structural components from two adjacent layers are not aligned along a second axis perpendicular to the first axis; and the secondary structural components are configured not to buckle, the bucklable, elastic structural components are configured to buckle along the second axis to generate a linear force, upon the inflation or deflation of the cells. Methods of actuation using the same are also described.

Yang, Dian↗
DOE OSTI2020

Soft buckling actuators

A soft actuator is described, including: a rotation center having a center of mass; a plurality of bucklable, elastic structural components each comprising a wall defining an axis along its longest dimension, the wall connected to the rotation center in a way that the axis is offset from the center of mass in a predetermined direction; and a plurality of cells each disposed between two adjacent bucklable, elastic structural components and configured for connection with a fluid inflation or deflation source; wherein upon the deflation of the cell, the bucklable, elastic structural components are configured to buckle in the predetermined direction. A soft actuating device including a plurality of the soft actuators and methods of actuation using the soft actuator or soft actuating device disclosed herein are also described.

42 ENGINEERING↗
DOE OSTI2016

A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems

Polynomial filtering can provide a highly effective means of computing all eigenvalues of a real symmetric (or complex Hermitian) matrix that are located in a given interval, anywhere in the spectrum. This paper describes a technique for tackling this problem by combining a thick-restart version of the Lanczos algorithm with deflation ("locking'') and a new type of polynomial filter obtained from a least-squares technique. Furthermore, the resulting algorithm can be utilized in a “spectrum-slicing” approach whereby a very large number of eigenvalues and associated eigenvectors of the matrix are computed by extracting eigenpairs located in different subintervals independently from one another.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Pushing memory bandwidth limitations through efficient implementations of Block-Krylov space solvers on GPUs

Lattice quantum chromodynamics simulations in nuclear physics have benefited from a tremendous number of algorithmic advances such as multigrid and eigenvector deflation. These improve the time to solution but do not alleviate the intrinsic memory-bandwidth constraints of the matrix-vector operation dominating iterative solvers. Batching this operation for multiple vectors and exploiting cache and register blocking can yield a super-linear speed up. Block-Krylov solvers can naturally take advantage of such batched matrix-vector operations, further reducing the iterations to solution by sharing the Krylov space between solves. However, practical implementations typically suffer from the quadratic scaling in the number of vector-vector operations. Here, using the QUDA library, we present an implementation of a block-CG solver on NVIDIA GPUs which reduces the memory-bandwidth complexity of vector-vector operations from quadratic to linear. We present results for the HISQ discretization, showing a 5x speedup compared to highly-optimized independent Krylov solves on NVIDIA's SaturnV cluster.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Optimizing shift selection in multilevel Monte Carlo for disconnected diagrams in lattice QCD

The calculation of disconnected diagram contributions to physical signals is a computationally expensive task in Lattice QCD. To extract the physical signal, the trace of the inverse Lattice Dirac operator, a large sparse matrix, must be stochastically estimated. Because the variance of the stochastic estimator is typically large, variance reduction techniques must be employed. Multilevel Monte Carlo (MLMC) methods reduce the variance of the trace estimator by utilizing a telescoping sequence of estimators. Frequency Splitting is one such method that uses a sequence of inverses of shifted operators to estimate the trace of the inverse lattice Dirac operator, however there is no a priori way to select the shifts that minimize the cost of the multilevel trace estimation. Here we present a sampling and interpolation scheme that is able to predict the variances associated with Frequency Splitting under displacements of the underlying space time lattice. The interpolation scheme is able to predict the variances to high accuracy and therefore chooses shifts that correspond to an approximate minimum of the cost for the trace estimation. We show that Frequency Splitting with the chosen shifts displays significant speedups over multigrid deflation, and that these shifts can be used for multiple configurations within the same ensemble with no penalty to performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Optimal design of solar-driven electrolytic hydrogen production systems within electricity markets

Hydrogen has the potential to be a key contributor toward a low-carbon economy. Generating hydrogen by electrolysis using renewable energy is one way to support a decarbonized economy; however, its cost is not typically competitive with the carbon-emitting incumbent technology, steam methane reforming. The ability of electrolysis to integrate with electricity markets presents a unique cost reduction opportunity due to the perceived future availability of low and zero-marginal cost renewable energy sources. Additionally, as renewables, and particularly, photovoltaics are installed on the grid, they have a value deflation effect. This work evaluates solar-electrolysis configurations using a mathematical programming framework to maximize system net present value. The framework has been tested with specific weather conditions and financial mechanisms in California. Our findings indicate that a spectrum of potential cost competitive solutions is available for systems that (i) have market configurations resembling hybrid retail/wholesale, resulting in a hydrogen production cost range of US$6.2 kg-1–US$6.6 kg-1, or full wholesale market participation, reducing production cost to US$2.6 kg-1–US$3.1 kg-1, and (ii) achieve projected future cost reductions.

08 HYDROGEN↗
DOE OSTI2018

A late Quaternary paleoenvironmental record in sand dunes of the northern Atacama Desert, Chile

This study reports a previously unidentified paleoenvironmental record found in sand dunes of the Atacama Desert, Chile. Long-term aeolian deflation by prevailing onshore winds has resulted in the deposition of sand on the irregular surface of a Miocene-aged anhydrite outcrop. Two deposits ~25 km apart, along the prevailing wind trajectory, were hand excavated then analyzed for vertical (and temporal) changes in physical and chemical composition. Radiocarbon ages of organic matter embedded within the deposits show that rapid accumulation of sediment began at the last glacial maximum and slowed considerably after the Pacific Ocean attained its present post-glacial level. Over this time period, grain sizes are seen to increase while accumulation rates simultaneously decrease, suggesting greater wind speeds and/or a change or decrease in sediment supply. Changes in δ 34 S values of sulfate in the sediment beginning ~10 ka indicate an increase in marine sources. Similarly, δ 2 H values from palmitic acid show a steady increase at ~10 ka, likely resulting from aridification of the region during the Holocene. Finally, due to the extreme aridity in the region, these sand dunes retain a well-preserved chemical record that reflects changes in elevation and coastal proximity after the last glacial maximum.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Are Contact Angle Measurements Useful for Oxide-Coated Liquid Metals?

This work establishes that static contact angles for gallium-based liquid metals have no utility despite the continued and common use of such angles in the literature. In the presence of oxygen, these metals rapidly form a thin (~1–3 nm) surface oxide “skin” that adheres to many surfaces and mechanically impedes its flow. This property is problematic for contact angle measurements, which presume the ability of liquids to flow freely to adopt shapes that minimize the interfacial energy. We show here that advancing angles for a metal are always high (>140°)—even on substrates to which it adheres—because the solid native oxide must rupture in tension to advance the contact line. The advancing angle for the metal depends subtly on the substrate surface chemistry but does not vary strongly with hydrophobicity of the substrate. During receding measurements, the metal droplet initially sags as the liquid withdraws from the “sac” formed by the skin and thus the contact area with the substrate initially increases despite its volumetric recession. Furthermore, the oxide pins at the perimeter of the deflated “sac” on all the surfaces are tested, except for certain rough surfaces. With additional withdrawal of the liquid metal, the pinned angle gets smaller until eventually the oxide “sac” collapses. Thus, static contact angles can be manipulated mechanically from 0° to >140° due to hysteresis and are therefore uninformative. We also provide recommendations and best practices for wetting experiments, which may find use in applications that use these alloys such as soft electronics, composites, and microfluidics.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Asymmetrically Stratified Beaufort Gyre: Mean State and Response to Decadal Forcing

Abstract Recent progress in understanding Beaufort Gyre (BG) dynamics reveals an important role of ice‐ocean stress in stabilizing BG freshwater content (FWC) over seasonal to interannual timescales. But how the BG's stratification and FWC respond to surface forcing over decadal timescales has not been fully explored. Using a global ocean‐sea ice model, we partition the BG into upper, middle (halocline), and lower (thermocline) layers and perform a volume budget analysis over 1948–2017. We find that the BG's asymmetric geometry (with steep and tight isohalines over continental slopes relative to the deep basin) is key in determining the mean volume transport balance. We further find that a net Ekman suction during 1983–1995 causes the upper and middle layers to deflate isopycnally, while an enhanced Ekman pumping during 1996–2017 causes these layers to inflate both isopycnally and diapycnally, the latter via anomalous flux from the upper to the middle layer.

Zhang, Jiaxu↗