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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 OSTI2010

Phase retrieval of diffraction from highly strained crystals

An important application of phase retrieval methods is to invert coherent x-ray diffraction measurements to obtain real-space images of nanoscale crystals. The phase information is currently recovered from reciprocal-space amplitude measurements by the application of iterative projective algorithms that solve the nonlinear and nonconvex optimization problem. Various algorithms have been developed each of which apply constraints in real and reciprocal space on the reconstructed object. In general, these methods rely on experimental data that is oversampled above the Nyquist frequency. To date, support-based methods have worked well, but are less successful for highly strained structures, defined as those which contain (real-space) phase information outside the range of {+-}{pi}/2. As a direct result the acquired experimental data is, in general, inadvertently subsampled below the Nyquist frequency. In recent years, a new theory of 'compressive sensing' has emerged, which dictates that an appropriately subsampled (or compressed) signal can be recovered exactly through iterative reconstruction and various routes to minimizing the l{sub 1} norm or total variation in that signal. This has proven effective in solving several classes of convex optimization problems. Here we report on a 'density-modification' phase reconstruction algorithm that applies the principles of compressive sensing to solve the nonconvex phase retrieval problem for highly strained crystalline materials. The application of a nonlinear operator in real-space minimizes the l{sub 1} norm of the amplitude by a promotion-penalization (or 'propenal') operation that confines the density bandwidth. This was found to significantly aid in the reconstruction of highly strained nanocrystals. We show how this method is able to successfully reconstruct phase information that otherwise could not be recovered.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Image Reconstruction from Under sampled Fourier Data Using the Polynomial Annihilation Transform

Fourier samples are collected in a variety of applications including magnetic resonance imaging and synthetic aperture radar. The data are typically under-sampled and noisy. In recent years, l 1 regularization has received considerable attention in designing image reconstruction algorithms from under-sampled and noisy Fourier data. The underlying image is assumed to have some sparsity features, that is, some measurable features of the image have sparse representation. The reconstruction algorithm is typically designed to solve a convex optimization problem, which consists of a fidelity term penalized by one or more l 1 regularization terms. The Split Bregman Algorithm provides a fast explicit solution for the case when TV is used for the l1l1 regularization terms. Due to its numerical efficiency, it has been widely adopted for a variety of applications. A well known drawback in using TV as an l 1 regularization term is that the reconstructed image will tend to default to a piecewise constant image. This issue has been addressed in several ways. Recently, the polynomial annihilation edge detection method was used to generate a higher order sparsifying transform, and was coined the “polynomial annihilation (PA) transform.” This paper adapts the Split Bregman Algorithm for the case when the PA transform is used as the l 1 regularization term. In so doing, we achieve a more accurate image reconstruction method from under-sampled and noisy Fourier data. Our new method compares favorably to the TV Split Bregman Algorithm, as well as to the popular TGV combined with shearlet approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Quantifying Dynamic Signal Spread in Real-Time High-Energy X-ray Diffraction

Abstract Measured intensity in high-energy monochromatic X-ray diffraction (HEXD) experiments provides information regarding the microstructure of the crystalline material under study. The location of intensity on an areal detector is determined by the lattice spacing and orientation of crystals so that changes in the heterogeneity of these quantities are reflected in the spreading of diffraction peaks over time. High temporal resolution of such dynamics can now be experimentally observed using technologies such as the mixed-mode pixel array detector (MM-PAD) which facilitates in situ dynamic HEXD experiments to study plasticity and its underlying mechanisms. In this paper, we define and demonstrate a feature computed directly from such diffraction time series data quantifying signal spread in a manner that is correlated with plastic deformation of the sample. A distinguishing characteristic of the analysis is the capability to describe the evolution from the distinct diffraction peaks of an undeformed alloy sample through to the non-uniform Debye–Scherrer rings developed upon significant plastic deformation. We build on our previous work modeling data using an overcomplete dictionary by treating temporal measurements jointly to improve signal spread recovery. We demonstrate our approach in simulations and on experimental HEXD measurements captured using the MM-PAD. Our method for characterizing the temporal evolution of signal spread is shown to provide an informative means of data analysis that adds to the capabilities of existing methods. Our work draws on ideas from convolutional sparse coding and requires solving a coupled convex optimization problem based on the alternating direction method of multipliers.

Engineering↗
DOE OSTI2018

Observer-based H{sub ∞} control for nonlinear Markovian jump systems with time-delay and input saturation

This paper focus on the problem of observer-based H{sub ∞} control for uncertain nonlinear Markovian jump systems with time-delay and actuator saturation. A delay-dependent sufficient condition is proposed which guarantees that the uncertain nonlinear Markovian jump system with time-delay and input saturation is stochastically stable via Lyapunov theory and linear matrix inequality (LMI) approach. Then, with this condition, the estimation of stability region and the design method of observer-based H{sub ∞} controller are given by solving LMIs and convex optimization problems. Finally, numerical examples are exploited to illustrate the effectiveness of the proposed method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Robust H{sub ∞} control for singular time-delay systems with saturating actuators via static output feedback

The problem of H{sub ∞} robust exponential stability and static output feedback stabilization of uncertain singular time-delay systems with saturating actuators are investigated. First, the delay-dependent condition is given to guarantee that the singular time-delay systems are not only exponential admissible, but also satisfies H{sub ∞} performance γ. Moreover, the estimation of stability region and the design method of H{sub ∞} static output feedback controller are given by solving a convex optimization problem. Some simulation examples are provided to demonstrate the merit of the proposed design methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Extended Newton-type method for nonlinear functions with values in a cone

In this paper, we consider the problem of finding solutions of nonlinear inclusion problems in Banach space. Using convex optimization techniques introduced by Robinson (Numer Math 19:341–347, 1972), a convergence theorem for Kantorovich-like methods is given, which improves the results of Yamamoto (Jpn J Appl Math 3(2):295–313, 1986; Numer Math 51(5):545–557, 1987) and Robinson (Numer Math 19:341–347, 1972). The result is compared with previously known results. Numerical examples further justify the theoretical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Data-driven learning of nonlocal physics from high-fidelity synthetic data

A key challenge to nonlocal models is the analytical complexity of deriving them from first principles, and frequently their use is justified a posteriori. Here, we extract nonlocal models from data, circumventing these challenges and providing data-driven justification for the resulting model form. Extracting data-driven surrogates is a major challenge for machine learning (ML) approaches, due to nonlinearities and lack of convexity — it is particularly challenging to extract surrogates which are provably well-posed and numerically stable. Our scheme not only yields a convex optimization problem, but also allows extraction of nonlocal models whose kernels may be partially negative while maintaining well-posedness even in small-data regimes. To achieve this, based on established nonlocal theory, we embed in our algorithm sufficient conditions on the non-positive part of the kernel that guarantee well-posedness of the learnt operator. These conditions are imposed as inequality constraints to meet the requisite conditions of the nonlocal theory. We demonstrate this workflow for a range of applications, including reproduction of manufactured nonlocal kernels; numerical homogenization of Darcy flow associated with a heterogeneous periodic microstructure; nonlocal approximation to high-order local transport phenomena; and approximation of globally supported fractional diffusion operators by truncated kernels.

42 ENGINEERING↗
DOE OSTI2023

Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustness

In this article, full waveform inversion (FWI) infers the subsurface structure information from seismic waveform data by solving a non-convex optimization problem. Data-driven FWI has been increasingly studied with various neural network architectures to improve accuracy and computational efficiency. Nevertheless, the applicability of pre-trained neural networks is severely restricted by potential discrepancies between the source function used in the field survey and the one utilized during training. Here, we develop a Fourier-enhanced deep operator network (Fourier-DeepONet) for FWI with the generalization of seismic sources, including the frequencies and locations of sources. Specifically, we employ the Fourier neural operator as the decoder of DeepONet, and we utilize source parameters as one input of Fourier-DeepONet, facilitating the resolution of FWI with variable sources. To test Fourier-DeepONet, we develop three new and realistic FWI benchmark datasets (FWI-F, FWI-L, and FWI-FL) with varying source frequencies, locations, or both. Our experiments demonstrate that compared with existing data-driven FWI methods, Fourier-DeepONet obtains more accurate predictions of subsurface structures in a wide range of source parameters. Moreover, the proposed Fourier-DeepONet exhibits superior robustness when handling data with Gaussian noise or missing traces and sources with Gaussian noise, paving the way for more reliable and accurate subsurface imaging across diverse real conditions.

42 ENGINEERING↗
DOE OSTI2023

Projective embedding of dynamical systems: Uniform mean field equations

Herein we study embeddings of continuous dynamical systems in larger dimensions via projector operators. We call this technique PEDS, projective embedding of dynamical systems, as the stable fixed point of the original system dynamics are recovered via projection from the higher dimensional space. In this paper we provide a general definition and prove that for a particular type of rank-1 projector operator, the uniform mean field projector, the equations of motion become a mean field approximation of the dynamical system. While in general the embedding depends on a specified variable ordering, the same is not true for the uniform mean field projector. We prove a variety of results on the relationship between the spectrum of the Jacobian for fixed points in the original and in the embedded system. Direct applications of PEDS can be non-convex optimization and machine learning.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Rapid data-driven model reduction of nonlinear dynamical systems including chemical reaction networks using ℓ 1 -regularization

We develop a new data-driven paradigm for efficient model reduction of a broad class of nonlinear dynamical systems. Our model reduction method directly enables the interpretation of key components of the dynamical system, unlike traditional projection-based model reduction methods that focus on reducing computational complexity more than interpretability. Our method is not application specific and is simple to implement on nonlinear dynamical systems arising from a variety of different fields. It requires minimal parameterization using a single parameter to trade-off between model complexity and estimation error. We use a data-driven paradigm to formulate model reduction as an efficient convex optimization problem that scales polynomially in the original size of the complex system, enabling systems with as many as thousands of components to be reduced in a matter of minutes.

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

Ptychographic phase retrieval by proximal algorithms

We derive a set of ptychography phase-retrieval iterative engines based on proximal algorithms originally developed in convex optimization theory, and discuss their connections with existing ones. The use of proximal operator creates a simple frame work that allows us to incorporate the effect of noise from a maximum-likelihood (ML) principle. We focus on three particular algorithms, namely proximal minimization, alternating direction method of multiplier and accelerated proximal gradient (APG). We benchmark their performance with numerical simulations, and discuss their optimal conditions for convergence and accuracy. An experimental dataset is used to demonstrate their effectiveness as well, in which case an array of cubic Au nanoparticles with a size of 50 nm is imaged. We show that with the presence of Poisson noise, a dataset with photon counts up to 10 4 at one detector pixel already requires ML-based methods to achieve a stable convergence. Among the three algorithms derived in this work, APG method is reported first time for its application in ptychographic reconstruction and shows superior performance in terms of both accuracy and convergence rate with a noisy dataset.

36 MATERIALS SCIENCE↗
DOE OSTI2017

SkyFACT: high-dimensional modeling of gamma-ray emission with adaptive templates and penalized likelihoods

We present SkyFACT (Sky Factorization with Adaptive Constrained Templates), a new approach for studying, modeling and decomposing diffuse gamma-ray emission. Like most previous analyses, the approach relies on predictions from cosmic-ray propagation codes like GALPROP and DRAGON. However, in contrast to previous approaches, we account for the fact that models are not perfect and allow for a very large number (∼> 10{sup 5}) of nuisance parameters to parameterize these imperfections. We combine methods of image reconstruction and adaptive spatio-spectral template regression in one coherent hybrid approach. To this end, we use penalized Poisson likelihood regression, with regularization functions that are motivated by the maximum entropy method. We introduce methods to efficiently handle the high dimensionality of the convex optimization problem as well as the associated semi-sparse covariance matrix, using the L-BFGS-B algorithm and Cholesky factorization. We test the method both on synthetic data as well as on gamma-ray emission from the inner Galaxy, |ℓ|<90{sup o} and | b |<20{sup o}, as observed by the Fermi Large Area Telescope. We finally define a simple reference model that removes most of the residual emission from the inner Galaxy, based on conventional diffuse emission components as well as components for the Fermi bubbles, the Fermi Galactic center excess, and extended sources along the Galactic disk. Variants of this reference model can serve as basis for future studies of diffuse emission in and outside the Galactic disk.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Sparse Bayesian mass mapping with uncertainties: hypothesis testing of structure

ABSTRACT A crucial aspect of mass mapping, via weak lensing, is quantification of the uncertainty introduced during the reconstruction process. Properly accounting for these errors has been largely ignored to date. We present a new method to reconstruct maximum a posteriori (MAP) convergence maps by formulating an unconstrained Bayesian inference problem with Laplace-type l1-norm sparsity-promoting priors, which we solve via convex optimization. Approaching mass mapping in this manner allows us to exploit recent developments in probability concentration theory to infer theoretically conservative uncertainties for our MAP reconstructions, without relying on assumptions of Gaussianity. For the first time, these methods allow us to perform hypothesis testing of structure, from which it is possible to distinguish between physical objects and artefacts of the reconstruction. Here, we present this new formalism, and demonstrate the method on simulations, before applying the developed formalism to two observational data sets of the Abell 520 cluster. Initial reconstructions of the Abell 520 catalogues reported the detection of an anomalous ‘dark core’ – an overdense region with no optical counterpart – which was taken to be evidence for self-interacting dark matter. In our Bayesian framework, it is found that neither Abell 520 data set can conclusively determine the physicality of such dark cores at $99{{\ \rm per\ cent}}$ confidence. However, in both cases the recovered MAP estimators are consistent with both sets of data.

Price, M. A.↗
DOE OSTI2011

Estimation of many-body quantum Hamiltonians via compressive sensing

We develop an efficient and robust approach for quantum measurement of nearly sparse many-body quantum Hamiltonians based on the method of compressive sensing. This work demonstrates that with only O(sln(d)) experimental configurations, consisting of random local preparations and measurements, one can estimate the Hamiltonian of a d-dimensional system, provided that the Hamiltonian is nearly s sparse in a known basis. The classical postprocessing is a convex optimization problem on the total Hilbert space which is generally not scalable. We numerically simulate the performance of this algorithm for three- and four-body interactions in spin-coupled quantum dots and atoms in optical lattices. Furthermore, we apply the algorithm to characterize Hamiltonian fine structure and unknown system-bath interactions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Network-Cognizant Design of Decentralized Volt/VAR Controllers

This paper considers the problem of designing decentralized Volt/VAR controllers for distributed energy resources (DERs). The voltage-reactive power characteristics of individual DERs are obtained by solving a convex optimization problem, where given performance objectives (e.g., minimization of the voltage deviations from a given profile) are specified and stability constraints are enforced. The resultant Volt/VAR characteristics are network-cognizant, in the sense that they embed information on the location of the DERs and, consequently, on the effect of reactive-power adjustments on the voltages throughout the feeder. Bounds on the maximum voltage deviation incurred by the controllers are analytically established. Numerical results are reported to corroborate the technical findings.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Matrix Completion Using Alternating Minimization for Distribution System State Estimation

This paper examines the problem of state estimation in power distribution systems under low-observability conditions. The recently proposed constrained matrix completion method which combines the standard matrix completion method and power flow constraints has been shown to be effective in estimating voltage phasors under low-observability conditions using single-snapshot information. However, the method requires solving a semidefinite programming (SDP) problem, which becomes computationally infeasible for large systems and if multiple-snapshot (time-series) information is used. This paper proposes an efficient algorithm to solve the constrained matrix completion problem with time-series data. This algorithm is based on reformulating the matrix completion problem as a bilinear (non-convex) optimization problem, and applying the alternating minimization algorithm to solve this problem. This paper proves the summable convergence of the proposed algorithm, and demonstrates its efficacy and scalability via IEEE 123-bus system and a real utility feeder system. This paper also explores the value of adding more data from the history in terms of computation time and estimation accuracy.

41 EE - Solar Energy Technologies Office (EE-4S)↗
DOE OSTI2019

Resilient Reinforcement in Secure State Estimation against Sensor Attacks with a priori Information

This paper deals with the state estimation problem in the presence of malicious sensor attacks. Unlike the existing work, in this paper, we address the problem with a priori information of the state to be estimated. Specifically, we address three prior knowledge: the sparsity information, (alpha, n_0)-sparsity information, and side information, and in each scenario, we show that the state can be reconstructed even if more sensors are compromised. This implies that the prior information reinforces the system resilience against sensor attacks. Then, an estimator under sensor attacks considering the information is developed and, under a certain condition, the estimator can be relaxed into a tractable convex optimization problem. Further, we extend this analysis to systems in presence of measurement noises, and it is shown that the prior information reduces the state-estimation error caused by the noise. Here, the numerical simulations in a diffusion process finally illustrate the reinforcement and error-reduction results with the information.

24 POWER TRANSMISSION AND DISTRIBUTION↗