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arXiv 2017年

作者： Osborn, Sarah Zulian, Patrick Benson, Thomas Villa, Umberto Krause, Rolf Vassilevski, Panayot S. Center for Applied Scientific Computing Lawrence Livermore National Laboratory P.O. Box 808 L-561 LivermoreCA94551 United States Institute of Computational Science Università della Svizzera italiana Lugano6900 Switzerland Institute for Computational Engineering and Sciences University of Texas AustinTX Fariborz Maseeh Department of Mathematics and Statistics Portland State University PortlandOR

This work describes a domain embedding technique between two non-matching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is to apply the multilevel Monte Carlo (MLMC) method for the quantification of output uncertainties of PDEs with random input coefficients on general, unstructured computational domains. We propose a highly scalable, hierarchical sampling method to generate realizations of a Gaussian random field on a given unstructured mesh by solving a reaction-diffusion PDE with a stochastic right-hand side. The stochastic PDE is discretized using the mixed finite element method on an embedded domain with a structured mesh, and then the solution is projected onto the unstructured mesh. This work describes implementation details on how to efficiently transfer data from the structured and unstructured meshes at coarse levels, assuming this can be done efficiently on the finest level. We investigate the efficiency and parallel scalability of the technique for the scalable generation of Gaussian random fields in three dimensions. An application of the MLMC method is presented for quantifying uncertainties of subsurface flow problems. We demonstrate the scalability of the sampling method with non-matching mesh embedding, coupled with a parallel forward model problem solver, for large-scale 3D MLMC simulations with up to 1.9 · *** Codes 65C05, 60H15, 35R60, 65N30, Copyright © 2017, The Authors. All rights reserved.

关键词： Uncertainty analysis

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Author Correction: Federated learning enables big data for rare cancer boundary detection

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Nature communications 2023年第1期14卷 436页

作者： Sarthak Pati Ujjwal Baid Brandon Edwards Micah Sheller Shih-Han Wang G Anthony Reina Patrick Foley Alexey Gruzdev Deepthi Karkada Christos Davatzikos Chiharu Sako Satyam Ghodasara Michel Bilello Suyash Mohan Philipp Vollmuth Gianluca Brugnara Chandrakanth J Preetha Felix Sahm Klaus Maier-Hein Maximilian Zenk Martin Bendszus Wolfgang Wick Evan Calabrese Jeffrey Rudie Javier Villanueva-Meyer Soonmee Cha Madhura Ingalhalikar Manali Jadhav Umang Pandey Jitender Saini John Garrett Matthew Larson Robert Jeraj Stuart Currie Russell Frood Kavi Fatania Raymond Y Huang Ken Chang Carmen Balaña Jaume Capellades Josep Puig Johannes Trenkler Josef Pichler Georg Necker Andreas Haunschmidt Stephan Meckel Gaurav Shukla Spencer Liem Gregory S Alexander Joseph Lombardo Joshua D Palmer Adam E Flanders Adam P Dicker Haris I Sair Craig K Jones Archana Venkataraman Meirui Jiang Tiffany Y So Cheng Chen Pheng Ann Heng Qi Dou Michal Kozubek Filip Lux Jan Michálek Petr Matula Miloš Keřkovský Tereza Kopřivová Marek Dostál Václav Vybíhal Michael A Vogelbaum J Ross Mitchell Joaquim Farinhas Joseph A Maldjian Chandan Ganesh Bangalore Yogananda Marco C Pinho Divya Reddy James Holcomb Benjamin C Wagner Benjamin M Ellingson Timothy F Cloughesy Catalina Raymond Talia Oughourlian Akifumi Hagiwara Chencai Wang Minh-Son To Sargam Bhardwaj Chee Chong Marc Agzarian Alexandre Xavier Falcão Samuel B Martins Bernardo C A Teixeira Flávia Sprenger David Menotti Diego R Lucio Pamela LaMontagne Daniel Marcus Benedikt Wiestler Florian Kofler Ivan Ezhov Marie Metz Rajan Jain Matthew Lee Yvonne W Lui Richard McKinley Johannes Slotboom Piotr Radojewski Raphael Meier Roland Wiest Derrick Murcia Eric Fu Rourke Haas John Thompson David Ryan Ormond Chaitra Badve Andrew E Sloan Vachan Vadmal Kristin Waite Rivka R Colen Linmin Pei Murat Ak Ashok Srinivasan J Rajiv Bapuraj Arvind Rao Nicholas Wang Ota Yoshiaki Toshio Moritani Sevcan Turk Joonsang Lee Snehal Prabhudesai Fanny Morón Jacob Mandel Konstantinos Kamnitsas Ben Glocker Luke V M Dixon Matthew Williams Peter Zamp Center for Biomedical Image Computing and Analytics (CBICA) University of Pennsylvania Philadelphia PA USA. Department of Radiology Perelman School of Medicine University of Pennsylvania Philadelphia PA USA. Department of Pathology and Laboratory Medicine Perelman School of Medicine University of Pennsylvania Philadelphia PA USA. Department of Informatics Technical University of Munich Munich Bavaria Germany. Intel Corporation Santa Clara CA USA. Department of Neuroradiology Heidelberg University Hospital Heidelberg Germany. Clinical Cooperation Unit Neuropathology German Cancer Consortium (DKTK) within the German Cancer Research Center (DKFZ) Heidelberg Germany. Department of Neuropathology Heidelberg University Hospital Heidelberg Germany. Division of Medical Image Computing German Cancer Research Center Heidelberg Germany. Pattern Analysis and Learning Group Department of Radiation Oncology Heidelberg University Hospital Heidelberg Germany. Neurology Clinic Heidelberg University Hospital Heidelberg Germany. Department of Radiology & Biomedical Imaging University of California San Francisco San Francisco CA USA. Symbiosis Center for Medical Image Analysis Symbiosis International University Pune Maharashtra India. Department of Neuroimaging and Interventional Radiology National Institute of Mental Health and Neurosciences Bangalore Karnataka India. Department of Radiology School of Medicine and Public Health University of Wisconsin Madison WI USA. Department of Medical Physics School of Medicine and Public Health University of Wisconsin Madison WI USA. Leeds Teaching Hospitals Trust Department of Radiology Leeds UK. Department of Radiology Brigham and Women's Hospital Harvard Medical School Boston MA USA. Athinoula A. Martinos Center for Biomedical Imaging Massachusetts General Hospital Charlestown MA USA. Catalan Institute of Oncology Badalona Spain. Consorci MAR Parc de Salut de Barcelona Catalonia Spain. Department of Radiology (IDI

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Acceleration of weak Galerkin methods for the Laplacian eigenvalue problem

arXiv

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arXiv 2017年

作者： Zhai, Qilong Xie, Hehu Zhang, Ran Zhang, Zhimin Department of Mathematics Jilin University Changchun130012 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Beijing Computational Science Research Center Beijing100193 China Department of Mathematics Wayne State University DetroitMI48202 United States

Recently, we proposed a weak Galerkin finite element method for the Laplace eigenvalue problem. In this paper, we present two-grid and two-space skills to accelerate the weak Galerkin method. By choosing parameters properly, the two-grid and two-space weak Galerkin method not only doubles the convergence rate, but also maintains the asymptotic lower bounds property of the weak Galerkin method. Some numerical examples are provided to validate our theoretical ***, 65N30, 65N15, 65N12, 74N20, Secondary, 35B45, 35J50, 35J35 Copyright © 2017, The Authors. All rights reserved.

关键词： Galerkin methods

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From atomistic model to the Peierls-Nabarro model with g-surface for dislocations

arXiv

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arXiv 2017年

作者： Luo, Tao Ming, Pingbing Xiang, Yang Department of Mathematics Hong Kong University of Science and Technology Clear Water Bay Kowloon Hong Kong LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences No. 55 East Road Zhong-Guan-Cun Beijing100190 China

The Peierls-Nabarro (PN) model for dislocations is a hybrid model that incorporates the atomistic information of the dislocation core structure into the continuum theory. In this paper, we study the convergence from a full atomisticmodel to the PNmodel with g-surface for the dislocation in a bilayer system (e.g. bilayer graphene). We prove that the displacement field of and the total energy of the dislocation solution of the PN model are asymptotically close to those of the full atomistic model. Our work can be considered as a generalization of the analysis of the convergence from atomistic model to Cauchy-Born rule for crystals without defects in the literature. Copyright © 2017, The Authors. All rights reserved.

关键词： Continuum mechanics

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Recent developments in the PySCF program package

arXiv

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arXiv 2020年

作者： Sun, Qiming Zhang, Xing Banerjee, Samragni Bao, Peng Barbry, Marc Blunt, Nick S. Bogdanov, Nikolay A. Booth, George H. Chen, Jia Cui, Zhi-Hao Eriksen, Janus Juul Gao, Yang Guo, Sheng Hermann, Jan Hermes, Matthew R. Koh, Kevin Koval, Peter Lehtola, Susi Li, Zhendong Liu, Junzi Mardirossian, Narbe McClain, James D. Motta, Mario Mussard, Bastien Pham, Hung Q. Pulkin, Artem Purwanto, Wirawan Robinson, Paul J. Ronca, Enrico Sayfutyarova, Elvira Scheurer, Maximilian Schurkus, Henry F. Smith, James E.T. Sun, Chong Sun, Shi-Ning Upadhyay, Shiv Wagner, Lucas K. Wang, Xiao White, Alec Whitfield, James Daniel Williamson, Mark J. Wouters, Sebastian Yang, Jun Yu, Jason M. Zhu, Tianyu Berkelbach, Timothy C. Sharma, Sandeep Sokolov, Alexander Yu. Chan, Garnet Kin-Lic AxiomQuant Investment Management LLC Shanghai200120 China Division of Chemistry and Chemical Engineering California Institute of Technology PasadenaCA91125 United States Department of Chemistry and Biochemistry The Ohio State University ColumbusOH43210 United States Beijing National Laboratory for Molecular Sciences State Key Laboratory for Structural Chemistry of Unstable and Stable Species Institute of Chemistry Chinese Academy of Sciences Beijing100190 China Simbeyond B.V. P.O. Box 513 EindhovenNL-5600 MB Netherlands Department of Chemistry Lensfield Road CambridgeCB2 1EW United Kingdom Max Planck Institute for Solid State Research Heisenbergstraße 1 Stuttgart70569 Germany Department of Physics King's College London Strand LondonWC2R 2LS United Kingdom Department of Physics University of Florida GainesvilleFL32611 United States Quantum Theory Project University of Florida GainesvilleFL32611 United States School of Chemistry University of Bristol Cantock's Close BristolBS8 1TS United Kingdom Division of Engineering and Applied Science California Institute of Technology PasadenaCA91125 United States Google Inc. Mountain ViewCA94043 United States FU Berlin Department of Mathematics and Computer Science Arnimallee 6 Berlin14195 Germany TU Berlin Machine Learning Group Marchstr. 23 Berlin10587 Germany Department of Chemistry Chemical Theory Center Supercomputing Institute University of Minnesota 207 Pleasant Street SE MinneapolisMN55455 United States Department of Chemistry and Biochemistry The University of Notre Dame du Lac 251 Nieuwland Science Hall Notre DameIN46556 United States Simune Atomistics S.L. Avenida Tolosa 76 Donostia-San Sebastian Spain HelsinkiFI-00014 Finland Key Laboratory of Theoretical and Computational Photochemistry Ministry of Education College of Chemistry Beijing Normal University Beijing100875 China Department of Chemistry The Johns Hopkins University BaltimoreMD21218 United States AMGEN

PYSCF is a Python-based general-purpose electronic structure platform that both supports first-principles simulations of molecules and solids, as well as accelerates the development of new methodology and complex computational workflows. The present paper explains the design and philosophy behind PYSCF that enables it to meet these twin objectives. With several case studies, we show how users can easily implement their own methods using PYSCF as a development environment. We then summarize the capabilities of PYSCF for molecular and solid-state simulations. Finally, we describe the growing ecosystem of projects that use PYSCF across the domains of quantum chemistry, materials science, machine learning and quantum information science. Copyright © 2020, The Authors. All rights reserved.

关键词： Python

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A note on optimal decay rates for the axisymmetric D-solutions to the steady Navier-Stokes equations

arXiv

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arXiv 2017年

作者： Weng, Shangkun Xie, Chunjing School of Mathematics and Statistics Computational Science Hubei Key Laboratory Wuhan University Wuhan Hubei Province430072 China Department of Mathematics Institute of Natural Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China

In this paper, we investigate the decay properties of an axisymmetric D-solutions to stationary incompressible Navier-Stokes systems in R3. We obtain the optimal decay rate |u(x)| | xC|+1 for axisymmetric flows without swirl. Furthermore, we find a dichotomy for the decay rates of the swirl component ua, that is, either O(+11) +1or |ue(r,z)| (C1r)3, where p = Vr2+ z2. In the latter case, we can further deduce that the other two components of the velocity field also attain the optimal decay rates: |ur(r, z)| + |uz(r, z)| C+1-. We do not require any small assumptions on the forcing *** Codes 76D05 Copyright © 2017, The Authors. All rights reserved.

关键词： Navier Stokes equations

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A Laguerre homotopy method for optimal control of nonlinear systems in semi-infinite interval

arXiv

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arXiv 2017年

作者： Yu, Haijun Nik, Hassan Saberi School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Institute of Computational Mathematics and Scientific/Engineering Computing Ncmis and Lsec Academy of Mathematics and Systems Science Beijing100190 China Department of Mathematics Neyshabur Branch Islamic Azad University Neyshabur Iran

This paper presents a Laguerre homotopy method for optimal control problems in semi-infinite intervals (LaHOC), with particular interests given to nonlinear interconnected large-scale dynamic systems. In LaHOC, spectral homotopy analysis method is used to derive an iterative solver for the nonlinear two-point boundary value problem derived from Pontryagins maximum principle. A proof of local convergence of the LaHOC is provided. Numerical comparisons are made between the LaHOC, Matlab BVP5C generated results and results from literature for two nonlinear optimal control problems. The results show that LaHOC is superior in both accuracy and efficiency. Copyright © 2017, The Authors. All rights reserved.

关键词： Optimal control systems

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A Hele-Shaw-Cahn-Hilliard model for incompressible two-phase flows with different densities

arXiv

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arXiv 2017年

作者： Dedè, Luca Garcke, Harald Lam, Kei Fong CMCS Chair of Modeling and Scientific Computing MATHICSE Mathematics Institute of Computational Science and Engineering EPFL École Polytechnique Fédérale de Lausanne Station 8 Lausanne1015 Switzerland Fakultät für Mathematik Universität Regensburg Regensburg93040 Germany

Topology changes in multi-phase fluid flows are difficult to model within a traditional sharp interface theory. Diffuse interface models turn out to be an attractive alternative to model two-phase flows. Based on a Cahn-Hilliard-Navier-Stokes model introduced by Abels, Garcke and Grün (math. Models Methods Appl. Sci. 2012), which uses a volume averaged velocity, we derive a diffuse interface model in a Hele-Shaw geometry, which in the case of non-matched densities, simplifies an earlier model of Lee, Lowengrub and Goodman (Phys. Fluids 2002). We recover the classical Hele-Shaw model as a sharp interface limit of the diffuse interface model. Furthermore, we show the existence of weak solutions and present several numerical computations including situations with rising bubbles and fingering *** Codes 35Q35, 76D27, 76D45, 76T99, 76S05, 35D30 Copyright © 2017, The Authors. All rights reserved.

关键词： Two phase flow

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Convergence analysis of a finite element approximation of minimum action methods

arXiv

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arXiv 2017年

作者： Wan, Xiaoliang Yu, Haijun Zhai, Jiayu Department of Mathematics and Center for Computation and Technology Louisiana State University Baton Rouge70803 United States School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China NCMIS and LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China

In this work, we address the convergence of a finite element approximation of the minimizer of the Freidlin-Wentzell (F-W) action functional for non-gradient dynamical systems perturbed by small noise. The F-W theory of large deviations is a rigorous mathematical tool to study small-noise-induced transitions in a dynamical system. The central task in the application of F-W theory of large deviations is to seek the minimizer and minimum of the F-W action functional. We discretize the F-W action functional using linearfinite elements, and establish the convergence of the approximation through Γ-convergence.65M60, 65P40, 65K10 Copyright © 2017, The Authors. All rights reserved.

关键词： Dynamical systems

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On the ideal interpolation operator in algebraic multigrid methods

arXiv

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arXiv 2017年

作者： Xu, Xuefeng Zhang, Chen-Song LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China LSEC & NCMIS Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

Various algebraic multigrid algorithms have been developed for solving problems in scientific and engineering computation over the past decades. They have been shown to be well-suited for solving discretized partial differential equations on unstructured girds in practice. One key ingredient of algebraic multigrid algorithms is a strategy for constructing an effective prolongation operator. Among many questions on constructing a prolongation, an important question is how to evaluate its quality. In this paper, we establish new characterizations (including sufficient condition, necessary condition, and equivalent condition) of the so-called ideal interpolation operator. Our result suggests that, compared with common wisdom, one has more room to construct an ideal interpolation, which can provide new insights for designing algebraic multigrid algorithms. Moreover, we derive a new expression for a class of ideal interpolation operators.65F10, 65F15, 65N55 Copyright © 2017, The Authors. All rights reserved.

关键词： Coarsening

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