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At least 1,513 records · Page 84

Polynomial meta-models with canonical low-rank approximations: Numerical insights and comparison to sparse polynomial chaos expansions

The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide statistically-equivalent analytical representations based on relatively few evaluations of the original model. Polynomial chaos expansions (PCE) have proven a powerful tool for developing meta-models in a wide range of applications; the key idea thereof is to expand the model response onto a basis made of multivariate polynomials obtained as tensor products of appropriate univariate polynomials. The classical PCE approach nevertheless faces the “curse of dimensionality”, namely the exponential increase of the basis size with increasing input dimension. To address this limitation, the sparse PCE technique has been proposed, in which the expansion is carried out on only a few relevant basis terms that are automatically selected by a suitable algorithm. An alternative for developing meta-models with polynomial functions in high-dimensional problems is offered by the newly emerged low-rank approximations (LRA) approach. By exploiting the tensor–product structure of the multivariate basis, LRA can provide polynomial representations in highly compressed formats. Through extensive numerical investigations, we herein first shed light on issues relating to the construction of canonical LRA with a particular greedy algorithm involving a sequential updating of the polynomial coefficients along separate dimensions. Specifically, we examine the selection of optimal rank, stopping criteria in the updating of the polynomial coefficients and error estimation. In the sequel, we confront canonical LRA to sparse PCE in structural-mechanics and heat-conduction applications based on finite-element solutions. Canonical LRA exhibit smaller errors than sparse PCE in cases when the number of available model evaluations is small with respect to the input dimension, a situation that is often encountered in real-life problems. By introducing the conditional generalization error, we further demonstrate that canonical LRA tend to outperform sparse PCE in the prediction of extreme model responses, which is critical in reliability analysis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Evaluation of Digital Image Recognition Methods for Mass Spectrometry Imaging Data Analysis

Analyzing mass spectrometry imaging data can be laborious and time consuming, and as the size and complexity of datasets grow, so does the need for robust automated processing methods. We here present a method for comprehensive, semi-targeted discovery of molecular distributions of interest from mass spectrometry imaging data, using widely available image similarity scoring algorithms to rank images by spatial correlation. A fast and powerful batch search method using a MATLAB implementation of structural similarity (SSIM) index scoring with a pre-selected reference distribution is demonstrated for two sample imaging datasets, a plant metabolite study using Artemisia annua leaf, and a drug distribution study using maraviroc-dosed macaque tissue. .

97 MATHEMATICS AND COMPUTING↗

Acoustic cloaking: Geometric transform, homogenization and a genetic algorithm

A general process is proposed to experimentally design anisotropic inhomogeneous metamaterials obtained through a change of coordinates in the Helmholtz equation. The method is applied to the case of a cylindrical transformation that allows cloaking to be performed. To approximate such complex metamaterials we apply results of the theory of homogenization and combine them with a genetic algorithm. To illustrate the power of our approach, we design three types of cloaks composed of isotropic concentric layers structured with three types of perforations: curved rectangles, split rings and crosses. These cloaks have parameters compatible with existing technology and they mimic the behavior of the transformed material. Numerical simulations have been performed to qualitatively and quantitatively study the cloaking efficiency of these metamaterials.

36 MATERIALS SCIENCE↗

HIGH-RESOLUTION LINEAR POLARIMETRIC IMAGING FOR THE EVENT HORIZON TELESCOPE

Images of the linear polarizations of synchrotron radiation around active galactic nuclei (AGNs) highlight their projected magnetic field lines and provide key data for understanding the physics of accretion and outflow from supermassive black holes. The highest-resolution polarimetric images of AGNs are produced with Very Long Baseline Interferometry (VLBI). Because VLBI incompletely samples the Fourier transform of the source image, any image reconstruction that fills in unmeasured spatial frequencies will not be unique and reconstruction algorithms are required. In this paper, we explore some extensions of the Maximum Entropy Method (MEM) to linear polarimetric VLBI imaging. In contrast to previous work, our polarimetric MEM algorithm combines a Stokes I imager that only uses bispectrum measurements that are immune to atmospheric phase corruption, with a joint Stokes Q and U imager that operates on robust polarimetric ratios. We demonstrate the effectiveness of our technique on 7 and 3 mm wavelength quasar observations from the VLBA and simulated 1.3 mm Event Horizon Telescope observations of Sgr A* and M87. Consistent with past studies, we find that polarimetric MEM can produce superior resolution compared to the standard CLEAN algorithm, when imaging smooth and compact source distributions. As an imaging framework, MEM is highly adaptable, allowing a range of constraints on polarization structure. Polarimetric MEM is thus an attractive choice for image reconstruction with the EHT.

79 ASTRONOMY AND ASTROPHYSICS↗

A self-learning disturbance observer for nonlinear systems in feedback-error learning scheme

Here this paper represents a novel online self-learning disturbance observer (SLDO) by benefiting from the combination of a type-2 neuro-fuzzy structure (T2NFS), feedback-error learning scheme and sliding mode control (SMC) theory. The SLDO is developed within a framework of feedback-error learning scheme in which a conventional estimation law and a T2NFS work in parallel. In this scheme, the latter learns uncertainties and becomes the leading estimator whereas the former provides the learning error to the T2NFS for learning system dynamics. A learning algorithm established on SMC theory is derived for an interval type-2 fuzzy logic system. In addition to the stability of the learning algorithm, the stability of the SLDO and the stability of the overall system are proven in the presence of time-varying disturbances. Thanks to learning process by the T2NFS, the simulation results show that the SLDO is able to estimate time-varying disturbances precisely as distinct from the basic nonlinear disturbance observer (BNDO) so that the controller based on the SLDO ensures robust control performance for systems with time-varying uncertainties, and maintains nominal performance in the absence of uncertainties.

42 ENGINEERING↗

Stochastic Dual Algorithm for Voltage Regulation in Distribution Networks with Discrete Loads

This paper considers power distribution networks with distributed energy resources and designs an incentive-based algorithm that allows the network operator and customers to pursue given operational and economic objectives while concurrently ensuring that voltages are within prescribed limits. Heterogeneous DERs with continuous and discrete control commands are considered. We address four major challenges: discrete decision variables, non-convexity due to a Stackelberg game structure, unavailability of private information from customers, and asynchronous operation. Starting from a non-convex setting, we develop a distributed stochastic dual algorithm that solves a relaxed problem, and prove that the proposed algorithm achieves the global optimal solution of the original problem on average. Feasible values for discrete decision variables are also recovered. Stability of the algorithm is analytically established and numerically corroborated.

24 POWER TRANSMISSION AND DISTRIBUTION↗

First Annual Report on Pulsed Thermal Tomography Nondestructive Evaluation of Additively Manufactured Reactor Materials and Components: Pulsed Thermal Tomography Nondestructive Examination of Additively Manufactured Reactor Materials and Components

Additive manufacturing (AM, or 3D printing) for commercial nuclear energy applications is an emerging method for cost-efficient manufacturing aimed at replacing aging nuclear reactor parts and reducing costs for new construction. Because of the geometry of metallic structures of interest for nuclear applications, which consist of planar primitives with no symmetry of revolution, limited options are available for nondestructive evaluation (NDE), either during or post manufacturing. Known material flaws in AM include low-density regions consisting of non-sintered powder, which have to be detected to ensure the safety of long-term performance nuclear reactor components. As a solution to NDE of AM, we are developing pulsed thermal tomography (PTT) models and depth inversion algorithms for 3D imaging. PTT has many advantages because the method is non-contact and allows for in-service, NDE of AM nuclear reactor parts. By analyzing transients of surface temperature response due to internal thermal resistances, one can obtain 3D reconstructions of material effusivity using a unique inversion algorithm developed at Argonne. This report provides results of preliminary performance evaluation of PTT capability in detection of flaws in metallic structures, as well imaging complex geometry AM structures. Performance of PTT was investigated through modeling and experiments, Computer models of PTT were developed using COMSOL Heat Transfer module. Defects were modeled as cylindrical flat bottom holes (FBH), which is a common model of calibrated material flaws in thermal tomography experiments. Materials considered in this study include stainless steel 316 (SS316), stainless steel 304 (SS304), and Inconel 718. Theoretical analyses were conducted to validate inversion of simulated PTT data with COMSOL for a plate. Subsequently, 3D reconstructions were performed on COMSOL simulations for FBH, revealing a decrease in spatial resolution over depth due to thermal diffusion. The results of this study show that the performance of the inversion algorithm for detecting smaller defects depends strongly on the depth of the defect as well as the incident heat flux. The size of detectable defect was estimated by fitting a Gaussian function to surface temperature profile. The criteria for detectability was taken as 20mK noise equivalent temperature difference (NETD), which is currently the sensitivity limit of high-performance infrared cameras. It was determined through computer simulations that the smallest detectable FBH in SS316 has a 50µm diameter and is located 0.5mm below the plate surface. Preliminary experimental studies were performed to evaluate PTT performance in detecting calibrated flaws using metallic specimens with AM defects simulated as drilled-in FBH’s. High strength Stainless Steel 316 and Inconel 718 alloys were considered, as well as lower grade Stainless Steel 304, Nickel 200, and Hastelloy C276. Specimens investigated in this report consisted of approximately 1/4in-thick plates made out of these alloys using conventional manufacturing methods. The diameters of FBH’s varied from 1mm to 8mm, and their depths below the plate flat surface varied between 1mm and 6mm. The size of the smallest FBH was limited to 1mm because conventional mechanical drills were used for creating the holes. PTT imaging results have shown that 1mm-diameter FBH located 1mm and 2mm below the surface were detectable. Larger size FBH were detectable at greater depth. For example, 6mm-diameter FBH could be detected at 8mm depth. Image contrast varied slightly between the specimens, with the best reconstructions obtained in SS316 and C276 plates. Finally, PTT capability in imaging several AM structures fabricated from Inconel 718 (IN718) powder feedstock was investigated. The AM structures have complex geometry, but do not have calibrated internal defects. The objective is to determine PTT settings, such as the total integration time, for imaging of representative AM structures. A new FLIR X8500sc IR camera with higher spatial resolution (1280x1024 at 181Hz frame rate) was integrated into the PTT laboratory setup. Software tools were developed to ensure compatibility of new camera files with legacy effusivity reconstruction codes. The new camera was used to obtain 3-D reconstructions of AM IN718 nozzle plate and a particle filter plate. It was shown that PTT can scan through 2/3in-thick Inconel 718 plates in approximately 15s. Several modes of 3-D data visualization were explored, including using ImageJ and MATLAB software packages. The results demonstrate the capability of PTT in 3-D imaging of complex geometry AM structures. Intermediate results demonstrated in this report will be developed further to investigate detection of flaws in AM specimens.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Entropic formation of a thermodynamically stable colloidal quasicrystal with negligible phason strain

Quasicrystals have been discovered in a variety of materials ranging from metals to polymers. Yet, why and how they form is incompletely understood. In situ transmission electron microscopy of alloy quasicrystal formation in metals suggests an error-and-repair mechanism, whereby quasiperiodic crystals grow imperfectly with phason strain present, and only perfect themselves later into a high-quality quasicrystal with negligible phason strain. The growth mechanism has not been investigated for other types of quasicrystals, such as dendrimeric, polymeric, or colloidal quasicrystals. Soft-matter quasicrystals typically result from entropic, rather than energetic, interactions, and are not usually grown (either in laboratories or in silico) into large-volume quasicrystals. Consequently, it is unknown whether soft-matter quasicrystals form with the high degree of structural quality found in metal alloy quasicrystals. Here, we investigate the entropically driven growth of colloidal dodecagonal quasicrystals (DQCs) via computer simulation of systems of hard tetrahedra, which are simple models for anisotropic colloidal particles that form a quasicrystal. Using a pattern recognition algorithm applied to particle trajectories during DQC growth, we analyze phason strain to follow the evolution of quasiperiodic order. As in alloys, we observe high structural quality; DQCs with low phason strain crystallize directly from the melt and only require minimal further reduction of phason strain. Finally, we also observe transformation from a denser approximant to the DQC via continuous phason strain relaxation. Our results demonstrate that soft-matter quasicrystals dominated by entropy can be thermodynamically stable and grown with high structural quality––just like their alloy quasicrystal counterparts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Flexible machine-learning interatomic potential for simulating structural disordering behavior of Li 7 La 3 Zr 2 O 12 solid electrolytes

Batteries based on solid-state electrolytes, including Li 7 La 3 Zr 2 O 12 (LLZO), promise improved safety and increased energy density; however, atomic disorder at grain boundaries and phase boundaries can severely deteriorate their performance. Machine-learning (ML) interatomic potentials offer a uniquely compelling solution for simulating chemical processes, rare events, and phase transitions associated with these complex interfaces by mixing high scalability with quantum-level accuracy, provided that they can be trained to properly address atomic disorder. To this end, we report the construction and validation of an ML potential that is specifically designed to simulate crystalline, disordered, and amorphous LLZO systems across a wide range of conditions. The ML model is based on a neural network algorithm and is trained using ab initio data. Performance tests prove that the developed ML potential can predict accurate structural and vibrational characteristics, elastic properties, and Li diffusivity of LLZO comparable to ab initio simulations. As a demonstration of its applicability to larger systems, we show that the potential can correctly capture grain boundary effects on diffusivity, as well as the thermal transition behavior of LLZO. Here these examples show that the ML potential enables simulations of transitions between well-defined and disordered structures with quantum-level accuracy at speeds thousands of times faster than ab initio methods.

25 ENERGY STORAGE↗

On the elimination of the electronic structure bottleneck in on the fly nonadiabatic dynamics for small to moderate sized (10-15 atom) molecules using fit diabatic representations based solely on ab initio electronic structure data: The photodissociation of phenol

In this work, we demonstrate that for moderate sized systems, here a system with 13 atoms, global coupled potential energy surfaces defined for several electronic states over a wide energy range and for distinct regions of nuclear coordinate space characterized by distinct electron configurations, can be constructed with precise energetics and an excellent description of non-adiabatic interactions in all regions. This is accomplished using a recently reported algorithm for constructing quasi-diabatic representations, H{sup d}, of adiabatic electronic states coupled by conical intersections. In this work, the algorithm is used to construct an H{sup d} to describe the photodissociation of phenol from its first and second excited electronic states. The representation treats all 33 internal degrees of freedom in an even handed manner. The ab initio adiabatic electronic structure data used to construct the fit are obtained exclusively from multireference configuration interaction with single and double excitation wave functions comprised of 88 × 10{sup 6} configuration state functions, at geometries determined by quasi-classical trajectories. Since the algorithm uses energy gradients and derivative couplings in addition to electronic energies to construct H{sup d}, data at only 7379 nuclear configurations are required to construct a representation, which describes all nuclear configurations involved in H atom photodissociation to produce the phenoxyl radical in its ground or first excited electronic state, with a mean unsigned energy error of 202.9 cm{sup −1} for electronic energies <60 000 cm{sup −1}.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Synergies between asteroseismology and three-dimensional simulations of stellar turbulence

Turbulent mixing of chemical elements by convection has fundamental effects on the evolution of stars. The standard algorithm at present, mixing-length theory (MLT), is intrinsically local, and must be supplemented by extensions with adjustable parameters. As a step toward reducing this arbitrariness, we compare asteroseismically inferred internal structures of two Kepler slowly pulsating B stars (SPBs; M∼3.25M{sub ⊙}) to predictions of 321D turbulence theory, based upon well-resolved, truly turbulent three-dimensional simulations that include boundary physics absent from MLT. We find promising agreement between the steepness and shapes of the theoretically predicted composition profile outside the convective region in 3D simulations and in asteroseismically constrained composition profiles in the best 1D models of the two SPBs. The structure and motion of the boundary layer, and the generation of waves, are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗

Measurement of exclusive dijet production in diffractive DIS with the ZEUS detector at HERA

The exclusive production of dijets in diffractive deep inelastic lepton–proton scattering has been measured with the ZEUS detector at HERA with an integrated luminosity of 372 pb{sup −1}. Jets have been reconstructed in the photon–Pomeron rest frame using the exclusive k{sub T} algorithm. The shape of the differential cross-section as a function of the angle between the plane spanned by the incoming and scattered lepton momenta and the plane spanned by the virtual photon and jets momenta is presented. The shape is determined by the jet production mechanism and provides information about the Pomeron structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Q4Q: Quantum Computation for Quantum Prediction of Materials and Molecular Properties

We aim at exploring the potential of quantum computation to solve practical problems that are currently targeted by “traditional” high performance computing (HPC). Along the way, we will develop theoretical frameworks and algorithmic strategies. We propose computational research activities that will advance the application of quantum computers to selected materials/molecular properties: (1) Band structure of solids; (2) Molecular electronic/vibronic properties; (3) Free energies and phase transitions.

36 MATERIALS SCIENCE↗

Turbomole

Turbomole is a highly optimized software package for large‐scale quantum chemical simulations of molecules, clusters, and periodic solids. Turbomole uses G aussian basis sets and specializes on predictive electronic structure methods with excellent cost to performance characteristics, such as (time‐dependent) density functional theory ( TDDFT ), second‐order M øller– P lesset theory, and explicitly correlated coupled cluster ( CC ) methods. These methods are combined with ultraefficient and numerically stable algorithms such as integral‐direct and Laplace transform methods, resolution‐of‐the‐identity, pair natural orbitals, fast multipole, and low‐order scaling techniques. Apart from energies and structures, a variety of optical, electric, and magnetic properties are accessible from analytical energy derivatives for electronic ground and excited states. Recent additions include post‐ K ohn– S ham calculations within the random phase approximation, periodic calculations, spin–orbit couplings, explicitly correlated CC singles doubles and perturbative triples methods, CC singles doubles excitation energies, and nonadiabatic molecular dynamics simulations using TDDFT . A dedicated graphical user interface and a user support network are also available. This article is categorized under: Software > Quantum Chemistry

Furche, Filipp↗

Information Transformation Algorithms in Echo-Holography

The filtering of optical signals and the transformation of information using stimulated echo-holography is examined in the case where it is excited by an information-carrying object laser pulse and a pulse that serves as a frequency filter. It is shown that the shape of the response of the stimulated echo hologram depends on the duration, amplitude, area, and temporal structure of the exciting pulses. This can be used for logical operations with signals.

42 ENGINEERING↗

State Preparation of Antisymmetrized Geminal Power on a Quantum Computer without Number Projection

The antisymmetrized geminal power (AGP) is equivalent to the number projected Bardeen–Cooper–Schrieffer (PBCS) wave function. It is also an elementary symmetric polynomial (ESP) state. We generalize previous research on deterministically implementing the Dicke state to a state preparation algorithm for an ESP state, or equivalently AGP, on a quantum computer. Our method is deterministic and has polynomial cost, and it does not rely on number symmetry breaking and restoration. We also show that our circuit is equivalent to a disentangled unitary paired coupled cluster operator and a layer of unitary Jastrow operator acting on a single Slater determinant. Here, the method presented herein highlights the ability of disentangled unitary coupled cluster to capture nontrivial entanglement properties that are hardly accessible with traditional Hartree–Fock based electronic structure methods.

97 MATHEMATICS AND COMPUTING↗

Scalable generalized screening for high-order terms in the many-body expansion: Algorithm, open-source implementation, and demonstration

The many-body expansion lies at the heart of numerous fragment-based methods that are intended to sidestep the nonlinear scaling of ab initio quantum chemistry, making electronic structure calculations feasible in large systems. In principle, inclusion of higher-order n-body terms ought to improve the accuracy in a controllable way, but unfavorable combinatorics often defeats this in practice and applications with n ≥ 4 are rare. Here, we outline an algorithm to overcome this combinatorial bottleneck, based on a bottom-up approach to energy-based screening. This is implemented within a new open-source software application (“Fragme∩t”), which is integrated with a lightweight semi-empirical method that is used to cull subsystems, attenuating the combinatorial growth of higher-order terms in the graph that is used to manage the calculations. This facilitates applications of unprecedented size, and we report four-body calculations in (H2O)64 clusters that afford relative energies within 0.1 kcal/mol/monomer of the supersystem result using less than 10% of the unique subsystems. We also report n-body calculations in (H2O)20 clusters up to n = 8, at which point the expansion terminates naturally due to screening. These are the largest n-body calculations reported to date using ab initio electronic structure theory, and they confirm that high-order n-body terms are mostly artifacts of basis-set superposition error.

Chemistry↗

Tail queues: A multi-threaded matching architecture

As we approach exascale, computational parallelism will have to drastically increase in order to meet throughput targets. Many–core architectures have exacerbated this problem by trading reduced clock speeds, core complexity, and computation throughput for increasing parallelism. This presents two major challenges for communication libraries such as MPI: the library must leverage the performance advantages of thread level parallelism and avoid the scalability problems associated with increasing the number of processes to that scale. Hybrid programming models, such as MPI+X, have been proposed to address these challenges. MPI THREAD MULTIPLE is MPI's thread safe mode. While there has been work to optimize it, it largely remains non–performant in most implementations. While current applications avoid MPI multithreading due to performance concerns, it is expected to be utilized in future applications. One of the major synchronous data structures required by MPI is the matching engine. In this paper, we present a parallel matching algorithm that can improve MPI matching for multithreaded applications. We then perform a feasibility study to demonstrate the performance benefit of the technique.

97 MATHEMATICS AND COMPUTING↗