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arXiv 2022年

作者： Sánchez, Hugo A. Castillo Jovanović, Mihailo R. Kumar, Satish Morozov, Alexander Shankar, V. Subramanian, Ganesh Wilson, Helen J. Department Of Applied Mathematics And Statistics Institute Of Mathematics And Computational Sciences University Of Sao Paulo Brazil Ming Hsieh Department Of Electrical And Computer Engineering University Of Southern California Los AngelesCA90089 United States Department Of Chemical Engineering And Materials Science University Of Minnesota MinneapolisMN55455 United States SUPA School Of Physics And Astronomy The University Of Edinburgh EdinburghEH9 3FD United Kingdom Department Of Chemical Engineering Indian Institute Of Technology Kanpur208016 India Engineering Mechanics Unit Jawaharlal Nehru Center For Advanced Scientific Research Bangalore560064 India Mathematics Department University College London Gower Street LondonWC1E 6BT United Kingdom

The Oldroyd-B model has been used extensively to predict a host of instabilities in shearing flows of viscoelastic fluids, often realized experimentally using polymer solutions. The present review, written on the occasion of the birth centenary of James Oldroyd, provides an overview of instabilities found across major classes of shearing flows. These comprise (i) the canonical rectilinear shearing flows including plane Couette, plane and pipe Poiseuille flows;(ii) viscometric shearing flows with curved streamlines such as those in the TaylorCouette, cone-and-plate and parallel-plate geometries;(iii) non-viscometric shearing flows with an underlying extensional flow topology such as the flow in a cross-slot device;and (iv) multilayer shearing flows. While the underlying focus in all these cases is on results obtained using the Oldroyd-B model, we also discuss their relation to the actual instability, and as to how the shortcomings of the Oldroyd-B model may be overcome by the use of more realistic constitutive models. All the three commonly used tools of stability analysis, viz., modal linear stability, nonmodal stability, and weakly nonlinear stability analyses are discussed, with supporting evidence from experiments and numerical simulations as appropriate. Despite only accounting for a shear-rate-independent viscosity and first normal stress coefficient, the Oldroyd-B model is able to qualitatively predict the majority of instabilities in the aforementioned shearing flows. The review also highlights, where appropriate, open questions in the area of viscoelastic stability. © 2022, CC BY.

关键词： Stability

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A Wall-time Minimizing Parallelization Strategy for Approximate Bayesian Computation

arXiv

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arXiv 2023年

作者： Alamoudi, Emad Reck, Felipe Bundgaard, Nils Graw, Frederik Brusch, Lutz Hasenauer, Jan Schälte, Yannik University of Bonn Life and Medical Sciences Institute Bonn53113 Germany Heidelberg University BioQuant - Center for Quantitative Biology Heidelberg69120 Germany Heidelberg University Interdisciplinary Center for Scientific Computing Heidelberg69120 Germany Friedrich-Alexander-University Erlangen-Nürnberg Department of Medicine 5 Erlangen91054 Germany Dresden01062 Germany Helmholtz Zentrum München Institute of Computational Biology Neuherberg85764 Germany Technische Universität München Center for Mathematics Garching85748 Germany

Approximate Bayesian Computation (ABC) is a widely applicable and popular approach to estimating unknown parameters of mechanistic models. As ABC analyses are computationally expensive, parallelization on high-performance infrastructure is often necessary. However, the existing parallelization strategies leave resources unused at times and thus do not optimally leverage them yet. We present look-ahead scheduling, a wall-time minimizing parallelization strategy for ABC Sequential Monte Carlo algorithms, which utilizes all available resources at practically all times by proactive sampling for prospective tasks. Our strategy can be integrated in e.g. adaptive distance function and summary statistic selection schemes, which is essential in practice. Evaluation of the strategy on different problems and numbers of parallel cores reveals speed-ups of typically 10-20% and up to 50% compared to the best established approach. Thus, the proposed strategy allows to substantially improve the cost and run-time efficiency of ABC methods on high-performance infrastructure. © 2023, CC BY-NC-ND.

关键词： Bayesian networks

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Weighted p-Rényi Entropy Power Inequality: Information Theory to Quantum Shannon Theory

arXiv

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arXiv 2023年

作者： Lee, Junseo Yeo, Hyeonjun Jeong, Kabgyun School of Electrical and Electronic Engineering Yonsei University Seoul03722 Korea Republic of Quantum Computing R&D Norma Inc. Seoul04799 Korea Republic of Department of Physics and Astronomy Seoul National University Seoul08826 Korea Republic of Research Institute of Mathematics Seoul National University Seoul08826 Korea Republic of School of Computational Sciences Korea Institute for Advanced Study Seoul02455 Korea Republic of

We study the p-Rényi entropy power inequality with a weight factor t on two independent continuous random variables X and Y . The extension essentially relies on a modulation on the sharp Young’s inequality due to Bobkov and Marsiglietti. Our research provides a key result that can be used as a fundamental research finding in quantum Shannon theory, as it offers a Rényi version of the entropy power inequality for quantum systems. Copyright © 2023, The Authors. All rights reserved.

关键词： Information theory

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Scalability of high-performance PDE solvers

arXiv

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arXiv 2020年

作者： Fischer, Paul Min, Misun Rathnayake, Thilina Dutta, Som Kolev, Tzanio Dobrev, Veselin Camier, Jean-Sylvain Kronbichler, Martin Warburton, Tim Swirydowicz, Kasia Brown, Jed Mathematics and Computer Science Argonne National Laboratory LemontIL60439 Department of Computer Science University of Illinois at Urbana-Champaign UrbanaIL61801 Department of Mechanical Science and Engineering University of Illinois at Urbana-Champaign UrbanaIL61801 Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA94550 Institute for Computational Mechanics Technical University of Munich Garching b. Muenchen85748 Germany Department of Computer Science University of Colorado BoulderCO80309 National Renewable Energy Laboratory LakewoodCO80401 Department of Mathematics Virginia Tech BlacksburgVA24061 Mechanical & Aerospace Engineering Utah State University UT84322

Performance tests and analyses are critical to effective HPC software development and are central components in the design and implementation of computational algorithms for achieving faster simulations on existing and future computing architectures for large-scale application problems. In this paper, we explore performance and space-time trade-offs for important compute-intensive kernels of large-scale numerical solvers for PDEs that govern a wide range of physical applications. We consider a sequence of PDE-motivated bake-off problems designed to establish best practices for efficient high-order simulations across a variety of codes and platforms. We measure peak performance (degrees of freedom per second) on a fixed number of nodes and identify effective code optimization strategies for each architecture. In addition to peak performance, we identify the minimum time to solution at 80% parallel efficiency. The performance analysis is based on spectral and p-type finite elements but is equally applicable to a broad spectrum of numerical PDE discretizations, including finite difference, finite volume, and h-type finite *** Codes 35-04 Copyright © 2020, The Authors. All rights reserved.

关键词： Computer architecture

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Disentangling quantum neural networks for unified estimation of quantum entropies and distance measures

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Physical Review A 2024年第6期110卷 062418-062418页

作者： Myeongjin Shin Seungwoo Lee Junseo Lee Mingyu Lee Donghwa Ji Hyeonjun Yeo Kabgyun Jeong School of Computing KAIST Daejeon 34141 South Korea Quantum AI Team Norma Inc. Seoul 04799 South Korea Department of Computer Science and Engineering Seoul National University Seoul 08826 South Korea College of Liberal Studies Seoul National University Seoul 08826 South Korea Department of Physics and Astronomy Seoul National University Seoul 08826 South Korea Research Institute of Mathematics Seoul National University Seoul 08826 South Korea School of Computational Sciences Korea Institute for Advanced Study Seoul 02455 South Korea

The estimation of quantum entropies and distance measures, such as von Neumann entropy, Rényi entropy, Tsallis entropy, trace distance, and fidelity-induced distances such as the Bures distance, has been a key area of research in quantum information science. In our study, we introduce the disentangling quantum neural network (DEQNN), designed to efficiently estimate various physical quantities in quantum information. Estimation algorithms for these quantities are generally tied to the size of the Hilbert space of the quantum state to be estimated. Our proposed DEQNN offers a unified dimensionality reduction methodology that can significantly reduce the size of the Hilbert space while preserving the values of diverse physical quantities. We provide an in-depth discussion of the physical scenarios and limitations in which our algorithm is applicable, as well as the learnability of the proposed quantum neural network.

关键词： Hilbert spaces

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Automatic Variationally Stable Analysis for Finite Element Computations: Transient Convection-Diffusion Problems

arXiv

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arXiv 2020年

作者： Valseth, Eirik Behnoudfar, Pouria Dawson, Clint Romkes, Albert Oden Institute for Computational Engineering and Sciences University of Texas at Austin AustinTX78712 United States The Department of Data Science The Norwegian University of Life Science Drøbakveien 31 Ås1433 Norway Department of Scientific Computing and Numerical Analysis Simula Research Laboratory Kristian Augusts gate 23 Oslo0164 Norway PerthWA6152 Australia Department of Mechanical Engineering South Dakota School of Mines & Technology Rapid CitySD57701 United States

We present an application of stable finite element (FE) approximations of convection-diffusion initial boundary value problems (IBVPs) using a weighted least squares FE method, the automatic variationally stable finite element (AVS-FE) method [1]. The transient convection-diffusion problem leads to issues in classical FE methods as the differential operator can be considered a singular perturbation in both space and time. The stability property of the AVS-FE method, allows us significant flexibility in the construction of FE approximations in both space and time. Thus, in this paper, we take two distinct approaches to the FE discretization of the convection-diffusion problem: i) considering a space-time approach in which the temporal discretization is established using finite elements, and ii) a method of lines approach in which we employ the AVS-FE method in space whereas the temporal domain is discretized using the generalized-α method. We also consider another space-time technique in which the temporal direction is partitioned, thereby leading to finite space-time"slices" in an attempt to reduce the computational cost of the space-time discretizations. We present numerical verifications for these approaches, including numerical asymptotic convergence studies highlighting optimal convergence properties. Furthermore, in the spirit of the discontinuous Petrov-Galerkin (DPG) method by Demkowicz and Gopalakrishnan [2–6], the AVS-FE method also leads to readily available a posteriori error estimates through a Riesz representer of the residual of the AVS-FE approximations. Hence, the norm of the resulting local restrictions of these estimates serve as error indicators in both space and time for which we present multiple numerical verifications in mesh adaptive *** Codes 65M60 65M12 65M20 65M50 Copyright © 2020, The Authors. All rights reserved.

关键词： Finite element method

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Multilevel monte carlo simulations of composite structures with uncertain manufacturing defects

arXiv

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arXiv 2019年

作者： Dodwell, T.J. Kynaston, S. Butler, R. Haftka, R.T. Kim, Nam H. Scheichl, R. College of Engineering Mathematics and Physical Sciences University of Exeter United Kingdom Alan Turing Institute LondonNW1 2DB United Kingdom Department of Mathematical Sciences University of Bath Bath United Kingdom Department of Mechanical Engineering University of Bath BathBA2 7AY United Kingdom Department of Mechanical and Aerospace Engineering University of Florida FL United States Interdisciplinary Center for Scientific Computing University of Heidelberg Germany

By adopting a Multilevel Monte Carlo (MLMC) framework, we show that only a handful of costly fine scale computations are needed to accurately estimate statistics of the failure of a composite structure, as opposed to the thousands typically needed in classical Monte Carlo analyses. We introduce the MLMC method, compare its theoretical complexity with classical Monte Carlo, and give a simple-to-implement algorithm which includes a simple extension called MLMC with selective refinement to efficiently calculated structural failure probabilities. To demonstrate the huge computational gains we present two benchmark problems in composites: (1) the effects of fibre waviness on the compressive strength of a composite material, (2) uncertain buckling performance of a composite panel with uncertain ply orientations. For our most challenging test case, estimating a rare (∼ 1/150) probability of buckling failure of a composite panel, we see a speed-up factor > 1000. Our approach distributed over 1024 processors reduces the computation time from 218 days to just 4.5 hours. This level of speed up makes stochastic simulations that would otherwise be unthinkable now possible. Copyright © 2019, The Authors. All rights reserved.

关键词： Monte Carlo methods

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Dislocation climb strengthening in systems with immobile obstacles: Three-dimensional level-set simulation study

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Physical Review B 2010年第5期81卷 054104-054104页

作者： Zi Chen Kevin T. Chu David J. Srolovitz Jeffrey M. Rickman Mikko P. Haataja Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08540 USA Princeton Institute for the Science and Technology of Materials (PRISM) Princeton University Princeton New Jersey 08540 USA Vitamin D Inc. Menlo Park California 94025 USA Institute of High Performance Computing Singapore Singapore Department of Materials Science and Engineering Lehigh University Bethlehem Pennsylvania 18015 USA Department of Physics Lehigh University Bethlehem Pennsylvania 18015 USA Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08540 USA

We employ a parallel, three-dimensional level-set code to simulate the dynamics of isolated dislocation lines and loops in an obstacle-rich environment. This system serves as a convenient prototype of those in which extended, one-dimensional objects interact with obstacles and the out-of-plane motion of these objects is key to understanding their pinning-depinning behavior. In contrast to earlier models of dislocation motion, we incorporate long-ranged interactions among dislocation segments and obstacles to study the effect of climb on dislocation dynamics in the presence of misfitting penetrable obstacles/solutes, as embodied in an effective climb mobility. Our main observations are as follows. First, increasing climb mobility leads to more effective pinning by the obstacles, implying increased strengthening. Second, decreasing the range of interactions significantly reduces the effect of climb. The dependence of the critical stress on obstacle concentration and misfit strength is also explored and compared with existing models. In particular, our results are shown to be in reasonable agreement with the Friedel-Suzuki theory. Finally, the limitations inherent in the simplified model employed here, including the neglect of some lattice effects and the use of a coarse-grained climb mobility, are discussed.

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AMG Preconditioners based on Parallel Hybrid Coarsening and Multi-objective Graph Matching

AMG Preconditioners based on Parallel Hybrid Coarsening and ...

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Euromicro Conference on Parallel, Distributed and Network-Based Processing

作者： Pasqua D'Ambra Fabio Durastante S M Ferdous Salvatore Filippone Mahantesh Halappanavar Alex Pothen National Research Council (CNR) Institute for Applied Computing “M. Picone” (IAC) Napoli Italy Department of Mathematics University of Pisa Pisa Italy Pacific Northwest National Laboratory Physical and Computational Sciences Richland WA USA Dept. of Civil and Computer Engineering University of Rome Tor-Vergata Rome Italy Computer Science Department Purdue University West Lafayette IN USA

We describe preliminary results from a multi-objective graph matching algorithm, in the coarsening step of an aggregation-based Algebraic MultiGrid (AMG) preconditioner, for solving large and sparse linear systems of equations on high-end parallel computers. We have two objectives. First, we wish to improve the convergence behavior of the AMG method when applied to highly anisotropic problems. Second, we wish to extend the parallel package PSCToolkit to exploit multi-threaded parallelism at the node level on multi-core processors. Our matching proposal balances the need to simultaneously compute high weights and large cardinalities by a new formulation of the weighted matching problem combining both these objectives using a parameter $\lambda$ . We compute the matching by a parallel $2/3-\varepsilon$ -approximation algorithm for maximum weight matchings. Results with the new matching algorithm show that for a suitable choice of the parameter $\lambda$ we compute effective preconditioners in the presence of anisotropy, i.e., smaller solve times, setup times, iterations counts, and operator complexity.

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Quantum solvers for plane-wave hamiltonians: Abridging virtual spaces through the optimization of pairwise correlations

arXiv

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arXiv 2020年

作者： Bylaska, Eric J. Song, Duo Bauman, Nicholas P. Kowalski, Karol Claudino, Daniel Humble, Travis S. Pacific Northwest National Laboratory RichlandWA99352 United States Quantum Computing Institute Oak Ridge National Laboratory Oak RidgeTN37831 United States Computer Science and Mathematics Oak Ridge National Laboratory Oak RidgeTN37831 United States Computational Sciences and Engineering Oak Ridge National Laboratory Oak RidgeTN37831 United States

For many-body methods such as MCSCF and CASSCF, in which the number of one-electron orbitals are optimized and independent of basis set used, there are no problems with using plane-wave basis sets. However, for methods currently used in quantum computing such as select configuration interaction (CI) and coupled cluster (CC) methods, it is necessary to have a virtual space that is able to capture a significant amount of electron-electron correlation in the system. The virtual orbitals in a pseudopotential plane-wave Hartree–Fock calculation, because of Coulomb repulsion, are often scattering states that interact very weakly with the filled orbitals. As a result, very little correlation energy is captured from them. The use of virtual spaces derived from the one-electron operators have also been tried, and while some correlation is captured, the amount is quite low. To overcome these limitations, we have been developing new classes of algorithms to define virtual spaces by optimizing orbitals from small pairwise CI Hamiltonians, which we term as correlation optimized virtual orbitals with the abbreviation COVOs. With these procedures we have been able to derive virtual spaces, containing only a few orbitals, that are able to capture a significant amount of correlation. Besides, using these derived basis sets for quantum computing calculations targeting full CI (FCI) quality-results, they can also be used in other many-body approaches, including CC and Møller–Plesset perturbation theories, and open up the door to many-body calculations for pseudopotential plane-wave basis set methods. For the H2 molecule, we were able to obtain good agreement with FCI/cc-pVTZ results with just 4 virtual orbitals, for both FCI and quantum simulations. Copyright © 2020, The Authors. All rights reserved.

关键词： Molecules

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