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Outcomes from the DOE workshop on turbulent flow simulation at the exascale 46

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Outcomes from the DOE workshop on turbulent flow simulation ...

46th AIAA Fluid Dynamics Conference, 2016

作者： Sprague, Michael A. Boldyrev, Stanislav Chang, Choong-Seock Fischer, Paul Grout, Ray Gustafson, William I. Hittinger, Jeffrey A. F. Merzari, Elia Moser, Robert National Renewable Energy Laboratory 15013 DenverWest Parkway GoldenCO80401 United States University of Wisconsin-Madison MadisonWI53706 United States Princeton University PrincetonNJ08543 United States University of Illinois at Urbana-Champaign UrbanaIL61801 United States National Renewable Energy Laboratory GoldenCO80401 United States Pacific Northwest National Laboratory RichlandWA99352 United States Lawrence Livermore National Laboratory LivermoreCA94551 United States Argonne National Laboratory ArgonneIL60439 United States University of Texas at Austin AustinTX78712 United States Computational Science Center 15013 DenverWest Parkway United States Physics Department 1150 University Avenue United States Princeton Plasma Physics Laboratory P.O. Box 451 United States Department of Computer Science 201 North Goodwin Avenue United States Computational Science Center 5013 Denver West Parkway United States Atmospheric Sciences and Global Change Division P.O. Box 999 K9-30 United States Scientific Computing Group Center for Applied Scientific Computing PO Box 808 L-561 United States Mathematics and Computer Science 9700 S. Cass Avenue United States Institute for Computational Engineering and Sciences and Department of Mechanical Engineering 201 East 24th United States

ISBN: (数字)9781624104367

ISBN: (纸本)9781624104367

This paper summarizes the outcomes from the Turbulent Flow Simulation at the Exascale: Opportunities and Challenges Workshop, which was held 4-5 August 2015, and was sponsored by the U.S. Department of Energy (DOE) Office of Advanced Scientific Computing Research (ASCR). The workshop objectives were to define and describe the challenges and opportunities that computing at the exascale will bring to turbulent-flow simulations in applied science and technology. The need for accurate simulation of turbulent flows is evident across the DOE applied-science and engineering portfolios, including combustion, plasma physics, nuclear-reactor physics, wind energy, and atmospheric science. The work-shop brought together experts in turbulent-flow simulation, computational mathematics, and high-performance computing. Building upon previous ASCR workshops on exascale computing, participants defined a research agenda and path forward that will enable scientists and engineers to continually leverage, engage, and direct advances in computational systems on the path to exascale computing. © 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.

关键词： Turbulent flow

Visualizing structure and transitions in high-dimensional biological data (vol 54, pg 781, 2019)

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NATURE BIOTECHNOLOGY 2020年第1期38卷 108-108页

作者： Moon, Kevin R. van Dijk, David Wang, Zheng Gigante, Scott Burkhardt, Daniel B. Chen, William S. Yim, Kristina van den Elzen, Antonia Hirn, Matthew J. Coifman, Ronald R. Ivanova, Natalia B. Wolf, Guy Krishnaswamy, Smita Department of Mathematics and Statistics Utah State University Logan USA Cardiovascular Research Center section Cardiology Department of Internal Medicine Yale University New Haven USA Department of Computer Science Yale University New Haven USA School of Basic Medicine Qingdao University Qingdao China Yale Stem Cell Center Department of Genetics Yale University New Haven USA Computational Biology and Bioinformatics Program Yale University New Haven USA Department of Genetics Yale University New Haven USA Department of Computational Mathematics Science and Engineering Michigan State University East Lansing USA Department of Mathematics Michigan State University East Lansing USA Applied Mathematics Program Yale University New Haven USA Department of Genetics Center for Molecular Medicine University of Georgia Athens USA Department of Mathematics and Statistics Université de Montréal Montréal Canada Mila—Quebec Artificial Intelligence Institute Montréal Canada

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

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Unbiased Estimation Using a Class of Diffusion Processes

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SSRN

SSRN 2022年

We study the problem of unbiased estimation of expectations with respect to (w.r.t.) π a given, general probability measure on (Rd,B(Rd)) that is absolutely continuous with respect to a standard Gaussian measure. We focus on simulation associated to a particular class of diffusion processes, sometimes termed the Schrödinger-Föllmer Sampler, which is a simulation technique that approximates the law of a particular diffusion bridge process {Xt}t∈[0,1] on Rd, d ∈ N0. This latter process is constructed such that, starting at X0 = 0, one has X1 ∼ π. Typically, the drift of the diffusion is intractable and, even if it were not, exact sampling of the associated diffusion is not possible. As a result, [10, 15] consider a stochastic Euler-Maruyama scheme that allows the development of biased estimators for expectations w.r.t. π. We show that for this methodology to achieve a mean square error of O(Ε2), for arbitrary Ε > 0, the associated cost is O(Ε−5). We then introduce an alternative approach that provides unbiased estimates of expectations w.r.t. π, that is, it does not suffer from the time discretization bias or the bias related with the approximation of the drift function. We prove that to achieve a mean square error of O(Ε2), the associated cost is, with high probability, O(Ε−2|log(Ε)|2+δ), for any δ > 0. We implement our method on several examples including Bayesian inverse problems. © 2022, The Authors. All rights reserved.

关键词： Diffusion

A spacetime finite elements method to solve the dirac equation

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arXiv 2021年

作者： Sundermann, Rylee Lim, Hyun Waybright, Jace Kimn, Jung-Han Department of Mathematics and Statistics South Dakota State University BrookingsSD57007 United States Computational Physics and Methods Group Los Alamos National Laboratory Los AlamosNM87545 United States Center for Theoretical Astrophysics Los Alamos National Laboratory Los AlamosNM87545 United States Applied Computer Science Group Los Alamos National Laboratory Los AlamosNM87545 United States Princeton Plasma Physics Laboratory Princeton University PrincetonNJ08543 United States

In this work, a fully implicit numerical approach based on space-time finite element method is presented to solve the Dirac equation in 1 (space) + 1 (time), 2 + 1, and 3 + 1 dimensions. We utilize PETSc/Tao library to implement our linear system and for using Krylov subspace based solvers such as GMRES. We demonstrate our method by analyzing several different cases including plane wave solution, Zitterbewegung, and Klein paradox. Parallel performance of this implementation is also presented. © 2021, CC BY.

关键词： Finite element method

Author Correction: Hysteresis control of epithelial-mesenchymal transition dynamics conveys a distinct program with enhanced metastatic ability

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Nature communications 2019年第1期10卷 527页

作者： Toni Celià-Terrassa Caleb Bastian Daniel D Liu Brian Ell Nicole M Aiello Yong Wei Jose Zamalloa Andres M Blanco Xiang Hang Dmitriy Kunisky Wenyang Li Elizabeth D Williams Herschel Rabitz Yibin Kang Department of Molecular Biology Princeton University Princeton NJ 08544 USA. Cancer Program IMIM (Hospital del Mar Medical Research Institute) 08003 Barcelona Spain. Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA. cbastian@princeton.edu. Lewis-Sigler Institute of Integrative Genomics Princeton University Princeton NJ 08544 USA. Department of Mathematics Princeton University Princeton NJ 08544 USA. School of Biomedical Sciences Translational Research Institute Queensland University of Technology (QUT) Brisbane QLD 4102 Australia. Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA. Department of Chemistry Princeton University Princeton NJ 08544 USA. Department of Molecular Biology Princeton University Princeton NJ 08544 USA. ykang@princeton.edu.

The original version of this Article contained an error in the spelling of the author Daniel D. Liu, which was incorrectly given as Daniel Liu. This has now been corrected in both the PDF and HTML versions of the Arti...

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Constraining reionization with the first measurement of the cross-correlation between the CMB optical-depth fluctuations and the Compton y-map

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arXiv 2021年

作者： Namikawa, Toshiya Roy, Anirban Sherwin, Blake D. Battaglia, Nicholas Spergel, David N. Department of Applied Mathematics and Theoretical Physics University of Cambridge Wilberforce Road CambridgeCB3 0WA United Kingdom Department of Astronomy Cornell University IthacaNY14853 United States Department of Applied Mathematics and Theoretical Physics University of Cambridge Wilberforce Road CambridgeCB3 0WA United Kingdom Kavli Institute for Cosmology University of Cambridge Madingley Road CambridgeCB3 OHA United Kingdom Center for Computational Astrophysics Flatiron Institute 162 Fifth Avenue New YorkNY10010 United States Department of Astrophysical Sciences Princeton University Peyton Hall PrincetonNJ08544 United States

We propose a new reionization probe that uses cosmic microwave background (CMB) observations;the cross-correlation between fluctuations in the CMB optical depth which probes the integrated electron density, δτ, and the Compton y-map which probes the integrated electron pressure. This cross-correlation is much less contaminated than the y-map power spectrum by late-time cluster contributions. In addition, this cross-correlation can constrain the temperature of ionized bubbles while the optical-depth fluctuations and kinetic SZ effect can not. We measure this new observable using a Planck y-map as well as a map of optical-depth fluctuations that we reconstruct from Planck CMB temperature data. We use our measurements to derive a first CMB-only upper limit on the temperature inside ionized bubbles, Tb . 7.0 × 105 K (2 σ). We also present future forecasts, assuming a fiducial model with characteristic reionization bubble size Rb = 5 Mpc and Tb = 5 × 104 K. The signal-to-noise ratio of the fiducial cross-correlation using a signal dominated y-map from the Probe of Inflation and Cosmic Origins (PICO) becomes ' 7 with CMB-S4 δτ and ' 13 with CMB-HD δτ. For the fiducial model, we predict that the CMB-HD − PICO cross-correlation should achieve an accurate measurement of the reionization parameters;Tb ' 49800+4500−5100 K and Rb ' 5.09+0−0.6679 Mpc. Since the power spectrum of the electron density fluctuations is constrained by the δτ auto spectrum, the temperature constraints should be only weakly model-dependent on the details of the electron distributions and should be statistically representative of the temperature in ionized bubbles during reionization. This cross-correlation could, therefore, become an important observable for future CMB experiments. Copyright © 2021, The Authors. All rights reserved.

关键词： Cosmology

Algebraic constraints and algorithms for common lines in cryo-EM

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Biological imaging 2024年 4卷 e9页

作者： Tommi Muller Adriana L Duncan Eric J Verbeke Joe Kileel Mathematical Institute University of Oxford Oxford UK. Department of Mathematics University of Texas at Austin Austin TX USA. Program in Applied and Computational Mathematics Princeton University Princeton NJ USA. Oden Institute University of Texas at Austin Austin TX USA.

We revisit the topic of common lines between projection images in single-particle cryo-electron microscopy (cryo-EM). We derive a novel low-rank constraint on a certain 2 × matrix storing properly scaled basis vectors for the common lines between projection images of one molecular conformation. Using this algebraic constraint and others, we give optimization algorithms to denoise common lines and recover the unknown 3D rotations associated with the images. As an application, we develop a clustering algorithm to partition a set of noisy images into homogeneous communities using common lines, in the case of discrete heterogeneity in cryo-EM. We demonstrate the methods on synthetic and experimental datasets.

关键词： ADMM common lines cryo-electron microscopy discrete heterogeneity group synchronization low-rank matrix

Benchmarking the Immersed Boundary Method for Viscoelastic Flows

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arXiv 2023年

作者： Gruninger, Cole Barrett, Aaron Fang, Fuhui Forest, M. Gregory Griffith, Boyce E. Department of Mathematics University North Carolina Chapel HillNC United States Department of Mathematics University of Utah Salt Lake CityUT United States Department of Applied Physical Sciences University of North Carolina Chapel HillNC United States Department of Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina School of Medicine Chapel HillNC United States McAllister Heart Institute University of North Carolina School of Medicine Chapel HillNC United States

We present and analyze a series of benchmark tests regarding the application of the immersed boundary (IB) method to viscoelastic flows through and around non-trivial, stationary geometries. The IB method is widely used for the simulation of biological fluid dynamics and other modeling scenarios where a structure is immersed in a fluid. Although the IB method has been most commonly used to model systems with viscous incompressible fluids, it also can be applied to visoelastic fluids, and has enabled the study of a wide variety of dynamical problems including the settling of vesicles and the swimming of elastic filaments in fluids modeled by the Oldroyd-B constuitive equation. However, to date, relatively little work has explored the accuracy or convergence properties of the numerical scheme. Herein, we present benchmarking results for an IB solver applied to viscoelastic flows in and around non-trivial geometries using the idealized Oldroyd-B and more realistic, polymer-entanglement-based Rolie-Poly constitutive equations. We use two-dimensional numerical test cases along with results from rheology experiments to benchmark the IB method and compare it to more complex finite element and finite volume viscoelastic flow solvers. Additionally, we analyze different choices of regularized delta function and relative Lagrangian grid spacings which allow us to identify and recommend the key choices of these numerical parameters depending on the present flow regime. Copyright © 2023, The Authors. All rights reserved.

关键词： Benchmarking

Unbiased Estimation using a Class of Diffusion Processes

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arXiv 2022年

作者： Ruzayqat, Hamza Beskos, Alexandros Crisan, Dan Jasra, Ajay Kantas, Nikolas Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 KSA Saudi Arabia Department of Statistical Science University College London LondonWC1E 6BT United Kingdom Department of Mathematics Imperial College London LondonSW7 2AZ United Kingdom

We study the problem of unbiased estimation of expectations with respect to (w.r.t.) π a given, general probability measure on (d, B(d)) that is absolutely continuous with respect to a standard Gaussian measure. We focus on simulation associated to a particular class of diffusion processes, sometimes termed the Schrödinger-Föllmer Sampler, which is a simulation technique that approximates the law of a particular diffusion bridge process {Xt}tϵ[0,1]on d, d ϵ 0. This latter process is constructed such that, starting at X0= 0, one has X1∼ π. Typically, the drift of the diffusion is intractable and, even if it were not, exact sampling of the associated diffusion is not possible. As a result, [10, 16] consider a stochastic Euler-Maruyama scheme that allows the development of biased estimators for expectations w.r.t. π. We show that for this methodology to achieve a mean square error of O(ϵ2), for arbitrary ϵ > 0, the associated cost is O(ϵ-5). We then introduce an alternative approach that provides unbiased estimates of expectations w.r.t. π, that is, it does not suffer from the time discretization bias or the bias related with the approximation of the drift function. We prove that to achieve a mean square error of O(ϵ2), the associated cost (which is random) is, with high probability, O(ϵ-2| log(ϵ)|2+δ), for any δ > 0. We implement our method on several examples including Bayesian inverse *** Codes 60J60, 62D05, 65C40 © 2022, CC BY.

关键词： Diffusion