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arXiv 2019年

作者： Huang, Daniel Z. Pazner, Will Persson, Per-Olof Zahr, Matthew J. Institute for Computational and Mathematical Engineering Stanford University United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory United States Department of Mathematics University of California Berkeley United States Department of Aerospace and Mechanical Engineering University of Notre Dame United States

We present an arbitrarily high-order, conditionally stable, partitioned spectral deferred correction (SDC) method for solving multiphysics problems using a sequence of pre-existing single-physics solvers. This method extends the work in [1, 2], which used implicit-explicit Runge-Kutta methods (IMEX) to build high-order, partitioned multiphysics solvers. We consider a generic multiphysics problem modeled as a system of coupled ordinary differential equations (ODEs), coupled through coupling terms that can depend on the state of each subsystem;therefore the method applies to both a semi-discretized system of partial differential equations (PDEs) or problems naturally modeled as coupled systems of ODEs. The sufficient conditions to build arbitrarily high-order partitioned SDC schemes are derived. Based on these conditions, various of partitioned SDC schemes are designed. The stability of the first-order partitioned SDC scheme is analyzed in detail on a coupled, linear model problem. We show that the scheme is conditionally stable, and under conditions on the coupling strength, the scheme can be unconditionally stable. We demonstrate the performance of the proposed partitioned solvers on several classes of multiphysics problems including a simple linear system of ODEs, advection-diffusion-reaction systems, and fluid-structure interaction problems with both incompressible and compressible flows, where we verify the design order of the SDC schemes and study various stability properties. We also directly compare the accuracy, stability, and cost of the proposed partitioned SDC solver with the partitioned IMEX method in [1, 2] on this suite of test problems. The results suggest that the high-order partitioned SDC solvers are more robust than the partitioned IMEX solvers for the numerical examples considered in this work, while the IMEX methods require fewer implicit solves. Copyright © 2019, The Authors. All rights reserved.

关键词： Stability

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Leveraging randomized compiling for the QITE algorithm

arXiv

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arXiv 2021年

作者： Ville, Jean-Loup Morvan, Alexis Hashim, Akel Naik, Ravi K. Lu, Marie Mitchell, Bradley Kreikebaum, John-Mark O’Brien, Kevin P. Wallman, Joel J. Hincks, Ian Emerson, Joseph Smith, Ethan Younis, Ed Iancu, Costin Santiago, David I. Siddiqi, Irfan Quantum Nanoelectronics Laboratory Dept. of Physics University of California at Berkeley BerkeleyCA94720 United States Computational Research Division Lawrence Berkeley National Lab BerkeleyCA94720 United States Materials Sciences Division Lawrence Berkeley National Lab BerkeleyCA94720 United States Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology CambridgeMA02139 United States Inst. for Quantum Computing Dept. of Applied Mathematics University of Waterloo WaterlooONN2L 3G1 Canada Quantum Benchmark Inc. KitchenerONN2H 5G5 Canada

The success of the current generation of Noisy Intermediate-Scale Quantum (NISQ) hardware shows that quantum hardware may be able to tackle complex problems even without error correction. One outstanding issue is that of coherent errors arising from the increased complexity of these devices. These errors can accumulate through a circuit, making their impact on algorithms hard to predict and mitigate. Iterative algorithms like Quantum Imaginary Time Evolution are susceptible to these errors. This article presents the combination of both noise tailoring using Randomized Compiling and error mitigation with a purification. We also show that Cycle Benchmarking gives an estimate of the reliability of the purification. We apply this method to the Quantum Imaginary Time Evolution of a Transverse Field Ising Model and report an energy estimation and a ground state infidelity both below 1%. Our methodology is general and can be used for other algorithms and platforms. We show how combining noise tailoring and error mitigation will push forward the performance of NISQ devices. © 2021, CC BY.

关键词： Benchmarking

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Deep nitsche method: Deep ritz method with essential boundary conditions

arXiv

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arXiv 2019年

作者： Liao, Yulei Ming, Pingbing LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences No. 55 East Road Zhong-Guan-Cun Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

We propose a new method to deal with the essential boundary conditions encountered in the deep learning-based numerical solvers for partial differential equations. The trial functions representing by deep neural networks are non-interpolatory, which makes the enforcement of the essential boundary conditions a nontrivial matter. Our method resorts to Nitsche's variational formulation to deal with this difficulty, which is consistent, and does not require significant extra computational costs. We prove the error estimate in the energy norm and illustrate the method on several representative problems posed in at most 100 dimension. Copyright © 2019, The Authors. All rights reserved.

关键词： Deep neural networks

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Lattice studies of Sp(2N) gauge theories using GRID

arXiv

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arXiv 2023年

作者： Forzano, Niccolò Bennett, Ed Boyle, Peter Del Debbio, Luigi Hong, Deog Ki Lee, Jong-Wan Lenz, Julian Lin, C.-J. David Lucini, Biagio Lupo, Alessandro Piai, Maurizio Vadacchino, Davide Swansea Academy of Advanced Computing Swansea University Bay Campus Fabian Way Wales SwanseaSA1 8EN United Kingdom School of Physics and Astronomy University of Edinburgh EdinburghEH9 3FD United Kingdom Physics Department Brookhaven National Laboratory Upton NY11973 United States Higgs Centre for Theoretical Physics School of Physics and Astronomy The University of Edinburgh Peter Guthrie Tait Road EdinburghEH9 3FD United Kingdom Department of Physics Faculty of Science and Engineering Swansea University Singleton Park Wales SwanseaSA2 8PP United Kingdom Department of Physics Pusan National University Busan46241 Korea Republic of Institute for Extreme Physics Pusan National University Busan46241 Korea Republic of Daejeon34126 Korea Republic of Institute of Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu30010 Taiwan Centre for High Energy Physics Chung-Yuan Christian University Chung-Li32023 Taiwan Centre for Theoretical and Computational Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu30010 Taiwan Department of Mathematics Faculty of Science and Engineering Swansea University Bay Campus Fabian Way Wales SwanseaSA1 8EN United Kingdom Centre for Mathematical Sciences University of Plymouth PlymouthPL4 8AA United Kingdom

Four-dimensional gauge theories based on symplectic Lie groups provide elegant realisations of the microscopic origin of several new physics models. Numerical studies pursued on the lattice provide quantitative information necessary for phenomenological applications. To this purpose, we implemented Sp(2N) gauge theories using Monte Carlo techniques within Grid, a performant framework designed for the numerical study of quantum field theories on the lattice. We show the first results obtained using this library, focusing on the case-study provided by the Sp(4) theory coupled to Nas = 4 Wilson-Dirac fermions transforming in the 2-index antisymmetric representation. In particular, we discuss preliminary tests of the algorithm and we test some of its main functionalities. © 2023, CC BY.

关键词： Monte Carlo methods

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A CASCADIC MULTIGRID METHOD FOR EIGENVALUE PROBLEM

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Journal of computational mathematics 2017年第1期35卷 74-90页

作者： Xiaole Han Hehu Xie Fei Xu IAPCM Institute of Applied Physics and Computational Mathematics Beijing 100093 China LSEC NCMIS Institute of Computational Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China Beijing Institute for Scientific and Engineering Computing Beijing University of Technology Beijing 100124 China

A cascadic multigrid method is proposed for eigenvalue problems based on the multilevel correction scheme. With this new scheme, an eigenvalue problem on the finest space can be solved by linear smoothing steps on a series of multilevel finite element spaces and nonlinear correcting steps on special coarsest spaces. Once the sequence of finite element spaces and the number of smoothing steps are appropriately chosen, the optimal convergence rate with the optimal computational work can be obtained. Some numerical experiments are presented to validate our theoretical analysis.

关键词： Eigenvalue problem Cascadic multigrid Multilevel correction scheme Finiteelement method.

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Double parameters full-waveform inversion for velocity and density in the time domain

Double parameters full-waveform inversion for velocity and d...

引用

CPS/SEG北京2018国际地球物理会议暨展览

作者： Wensheng Zhang UCAS LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences

In this paper, the double parameters full-waveform inversion for velocity and density simultaneously in the time domain is investigated. Comparing with the single parameter inversion, the double parameters inversion is more difficult because of the interactive influences between velocity and density. The forward is solved by the efficient staggered-grid difference scheme with the perfectly matched absorbing layer. The inversion is an optimization iterative process based on LBFGS algorithm. The combination of L2 regularization and TV regularization and the stepwise inversion strategy from low frequency to high frequency are applied to overcome the ill-posedness. Moreover, the adaptive regularization parameter is adopted to improve inversion precision. The double parameters inversion for Marmousi model is completed. The numerical results show the double parameters inversion can yield good inversion results of velocity and density even in the case of noisy data. The numerical computations show the correctness and effectiveness of the method in this paper.

关键词： FWI Double parameters full-waveform inversion for velocity and density in the time domain

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Symplectic lattice gauge theories in the grid framework: Approaching the conformal window

引用

Physical Review D 2023年第9期108卷 094508-094508页

作者： Ed Bennett Peter A. Boyle Luigi Del Debbio Niccolò Forzano Deog Ki Hong Jong-Wan Lee Julian Lenz C.-J. David Lin Biagio Lucini Alessandro Lupo Maurizio Piai Davide Vadacchino Swansea Academy of Advanced Computing Swansea University (Bay Campus) Fabian Way SA1 8EN Swansea Wales United Kingdom School of Physics and Astronomy University of Edinburgh Edinburgh EH9 3FD United Kingdom Physics Department Brookhaven National Laboratory Upton New York 11973 USA Higgs Centre for Theoretical Physics School of Physics and Astronomy The University of Edinburgh Peter Guthrie Tait Road Edinburgh EH9 3FD United Kingdom Department of Physics Faculty of Science and Engineering Swansea University Singleton Park SA2 8PP Swansea Wales United Kingdom Department of Physics Pusan National University Busan 46241 Korea Institute for Extreme Physics Pusan National University Busan 46241 Korea Particle Theory and Cosmology Group Center for Theoretical Physics of the Universe Institute for Basic Science (IBS) Daejeon 34126 Korea Institute of Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu 30010 Taiwan Centre for High Energy Physics Chung-Yuan Christian University Chung-Li 32023 Taiwan Centre for Theoretical and Computational Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu 30010 Taiwan Department of Mathematics Faculty of Science and Engineering Swansea University (Bay Campus) Fabian Way SA1 8EN Swansea Wales United Kingdom Centre for Mathematical Sciences University of Plymouth Plymouth PL4 8AA United Kingdom

Symplectic gauge theories coupled to matter fields lead to symmetry enhancement phenomena that have potential applications in such diverse contexts as composite Higgs, top partial compositeness, strongly interacting dark matter, and dilaton-Higgs models. These theories are also interesting on theoretical grounds, for example in reference to the approach to the large-N limit. A particularly compelling research aim is the determination of the extent of the conformal window in gauge theories with symplectic groups coupled to matter, for different groups and for field content consisting of fermions transforming in different representations. Such determination would have far-reaching implications, but requires overcoming huge technical challenges. Numerical studies based on lattice field theory can provide the quantitative information necessary to this endeavor. We developed new software to implement symplectic groups in the Monte Carlo algorithms within the Grid framework. In this paper, we focus most of our attention on the Sp(4) lattice gauge theory coupled to four (Wilson-Dirac) fermions transforming in the 2-index antisymmetric representation, as a case study. We discuss an extensive catalog of technical tests of the algorithms and present preliminary measurements to set the stage for future large-scale numerical investigations. We also include the scan of parameter space of all asymptotically free Sp(4) lattice gauge theories coupled to varying number of fermions transforming in the antisymmetric representation.

关键词： Lattice field theory Lattice gauge theory Monte Carlo methods

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Why is the Winner the Best?

Why is the Winner the Best?

引用

Conference on Computer Vision and Pattern Recognition (CVPR)

作者： M. Eisenmann A. Reinke V. Weru M. D. Tizabi F. Isensee T. J. Adler S. Ali V. Andrearczyk M. Aubreville U. Baid S. Bakas N. Balu S. Bano J. Bernal S. Bodenstedt A. Casella V. Cheplygina M. Daum M. De Bruijne A. Depeursinge R. Dorent J. Egger D. G. Ellis S. Engelhardt M. Ganz N. Ghatwary G. Girard P. Godau A. Gupta L. Hansen K. Harada M. Heinrich N. Heller A. Hering A. Huaulmé P. Jannin A. E. Kavur O. Kodym M. Kozubek J. Li H. Li J. Ma C. Martín-Isla B. Menze A. Noble V. Oreiller N. Padoy S. Pati K. Payette T. Rädsch J. Rafael-Patiño V. Singh Bawa S. Speidel C. H. Sudre K. Van Wijnen M. Wagner D. Wei A. Yamlahi M. H. Yap C. Yuan M. Zenk A. Zia D. Zimmerer D. Aydogan B. Bhattarai L. Bloch R. Brüngel J. Cho C. Choi Q. Dou I. Ezhov C. M. Friedrich C. Fuller R. R. Gaire A. Galdran Á. García Faura M. Grammatikopoulou S. Hong M. Jahanifar I. Jang A. Kadkhodamohammadi I. Kang F. Kofler S. Kondo H. Kuijf M. Li M. Luu T. Martinčič P. Morais M. A. Naser B. Oliveira D. Owen S. Pang J. Park S. Park S. Płotka E. Puybareau N. Rajpoot K. Ryu N. Saeed A. Shephard P. Shi D. Štepec R. Subedi G. Tochon H. R. Torres H. Urien J. L. Vilaça K. A. Wahid H. Wang J. Wang L. Wang X. Wang B. Wiestler M. Wodzinski F. Xia J. Xie Z. Xiong S. Yang Y. Yang Z. Zhao K. Maier-Hein P. F. Jäger A. Kopp-Schneider L. Maier-Hein Division of Intelligent Medical Systems German Cancer Research Center (DKFZ) Heidelberg Germany Helmholtz Imaging German Cancer Research Center (DKFZ) Heidelberg Germany Faculty of Mathematics and Computer Science Heidelberg University Heidelberg Germany Division of Biostatistics German Cancer Research Center (DKFZ) Heidelberg Germany Division of Medical Image Computing German Cancer Research Center (DKFZ) Heidelberg Germany Faculty of Engineering and Physical Sciences School of Computing University of Leeds Leeds UK Institute of Informatics School of Management HES-SO Valais-Wallis University of Applied Sciences and Arts Western Switzerland Sierre Switzerland Department of Nuclear Medicine and Molecular Imaging Lausanne University Hospital Lausanne Switzerland Technische Hochschule Ingolstadt Ingolstadt Germany Center for Artificial Intelligence and Data Science for Integrated Diagnostics (AI2D) and Center for Biomedical Image Computing and Analytics (CBICA) University of Pennsylvania Philadelphia PA USA Department of Pathology and Laboratory Medicine Perelman School of Medicine University of Pennsylvania Philadelphia PA USA Department of Radiology Perelman School of Medicine University of Pennsylvania Philadelphia PA USA Department of Radiology University of Washington Seattle WA USA Department of Computer Science Wellcome/EPSRC Centre for Interventional and Surgical Sciences (WEISS) University College London London UK Universitat Autònoma de Barcelona & Computer Vision Center Barcelona Spain Division of Translational Surgical Oncology National Center for Tumor Diseases (NCT/UCC) Dresden Dresden Germany Department of Advanced Robotics Istituto Italiano di Tecnologia Italy Department of Electronics Information and Bioengineering Politecnico di Milano Milan Italy IT University of Copenhagen Copenhagen Denmark Department of General Visceral and Transplantation Surgery Heidelberg University Hospital Heidelberg Germany Department of Radiology and Nuc

International benchmarking competitions have become fundamental for the comparative performance assessment of image analysis methods. However, little attention has been given to investigating what can be learnt from these competitions. Do they really generate scientific progress? What are common and successful participation strategies? What makes a solution superior to a competing method? To address this gap in the literature, we performed a multicenter study with all 80 competitions that were conducted in the scope of IEEE ISBI 2021 and MICCAI 2021. Statistical analyses performed based on comprehensive descriptions of the submitted algorithms linked to their rank as well as the underlying participation strategies revealed common characteristics of winning solutions. These typically include the use of multi-task learning (63%) and/or multi-stage pipelines (61%), and a focus on augmentation (100%), image preprocessing (97%), data curation (79%), and post-processing (66%). The “typical” lead of a winning team is a computer scientist with a doctoral degree, five years of experience in biomedical image analysis, and four years of experience in deep learning. Two core general development strategies stood out for highly-ranked teams: the reflection of the metrics in the method design and the focus on analyzing and handling failure cases. According to the organizers, 43% of the winning algorithms exceeded the state of the art but only 11% completely solved the respective domain problem. The insights of our study could help researchers (1) improve algorithm development strategies when approaching new problems, and (2) focus on open research questions revealed by this work.

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Scalability of high-performance PDE solvers

arXiv

引用

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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Automated detection of corrosion in used nuclear fuel dry storage canisters using residual neural networks

arXiv

引用

arXiv 2020年

作者： Papamarkou, Theodore Guy, Hayley Kroencke, Bryce Miller, Jordan Robinette, Preston Schultz, Daniel Hinkle, Jacob Pullum, Laura Schuman, Catherine Renshaw, Jeremy Chatzidakis, Stylianos Computational Sciences and Engineering Division Oak Ridge National Laboratory Oak RidgeTN United States Department of Mathematics North Carolina State University RaleighNC United States Department of Computer Science University of California DavisCA United States Center for Cognitive Ubiquitous Computing Arizona State University TempeAZ United States Presbyterian College ClintonSC United States Innovative Computing Laboratory University of Tennessee KnoxvilleTN United States Computer Science and Mathematics Division Oak Ridge National Laboratory Oak RidgeTN United States Electric Power Research Institute Palo AltoCA United States Reactor and Nuclear Systems Division Oak Ridge National Laboratory Oak RidgeTN United States

Nondestructive evaluation methods play an important role in ensuring component integrity and safety in many industries. Operator fatigue can play a critical role in the reliability of such methods. This is important for inspecting high value assets or assets with a high consequence of failure, such as aerospace and nuclear components. Recent advances in convolution neural networks can support and automate these inspection efforts. This paper proposes using residual neural networks (ResNets) for real-time detection of corrosion, including iron oxide discoloration, pitting and stress corrosion cracking, in dry storage stainless steel canisters housing used nuclear fuel. The proposed approach crops nuclear canister images into smaller tiles, trains a ResNet on these tiles, and classifies images as corroded or intact using the per-image count of tiles predicted as corroded by the ResNet. The results demonstrate that such a deep learning approach allows to detect the locus of corrosion via smaller tiles, and at the same time to infer with high accuracy whether an image comes from a corroded canister. Thereby, the proposed approach holds promise to automate and speed up nuclear fuel canister inspections, to minimize inspection costs, and to partially replace human-conducted onsite inspections, thus reducing radiation doses to personnel. Copyright © 2020, The Authors. All rights reserved.

关键词： Deep learning

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