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Functional a posteriori error estimates for boundary element methods

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arXiv 2019年

作者： Kurz, Stefan Pauly, Dirk Praetorius, Dirk Repin, Sergey Sebastian, Daniel TU Wien Institute for Analysis and Scientific Computing Wiedner Hauptstraße 8-10/E101/4 Vienna1040 Austria TU Darmstadt Centre for Computational Engineering Dolivostraße 15 Darmstadt64293 Germany Universität Duisburg-Essen Fakultät für Mathematik Thea-Leymann-Straße 9 Essen45141 Germany University of Jyväskylä Building Agora Mattilanniemi 2 Jyväskylä40100 Finland Russian Academy of Sciences Steklov Institute of Mathematics 191011 Fontanka 27 St. Petersburg Russia

Functional error estimates are well-estabilished tools for a posteriori error estimation and related adaptive mesh-refinement for the finite element method (FEM). The present work proposes a first functional error estimate for the boundary element method (BEM). One key feature is that the derived error estimates are independent of the BEM discretization and provide guaranteed lower and upper bounds for the unknown error. In particular, our analysis covers Galerkin BEM as well as collocation, which makes our approach of particular interest for people working in engineering. Numerical experiments for the Laplace problem confirm the theoretical *** Codes 65N38, 65N15, 65N50 Copyright © 2019, The Authors. All rights reserved.

关键词： Boundary element method

Corrigendum to “High order positivity-preserving discontinuous Galerkin schemes for radiative transfer equations on triangular meshes” [J. Comput. Phys. 397 (2019) 108811]

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Journal of computational Physics 2020年 406卷

作者： Min Zhang Juan Cheng Jianxian Qiu School of Mathematical Sciences Xiamen University Xiamen Fujian 361005 PR China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing 100088 PR China Center for Applied Physics and Technology Peking University Beijing 100871 PR China School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University Xiamen Fujian 361005 PR China

Randomized compiling for scalable quantum computing on a noisy superconducting quantum processor

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arXiv 2020年

作者： Hashim, Akel Naik, Ravi K. Morvan, Alexis Ville, Jean-Loup Mitchell, Bradley Kreikebaum, John Mark Davis, Marc Smith, Ethan Iancu, Costin O'Brien, Kevin P. Hincks, Ian Wallman, Joel J. Emerson, Joseph Siddiqi, Irfan Quantum Nanoelectronics Laboratory Department of Physics University of California at Berkeley BerkeleyCA94720 United States Graduate Group in Applied Science and Technology 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 CambridgeMA United States Quantum Benchmark Inc. KitchenerONN2H 5G5 Canada Institute for Quantum Computing and Department of Applied Mathematics University of Waterloo WaterlooONN2L 3G1 Canada

The successful implementation of algorithms on quantum processors relies on the accurate control of quantum bits (qubits) to perform logic gate operations. In this era of noisy intermediate-scale quantum (NISQ) computing, systematic miscalibrations, drift, and crosstalk in the control of qubits can lead to a coherent form of error which has no classical analog. Coherent errors severely limit the performance of quantum algorithms in an unpredictable manner, and mitigating their impact is necessary for realizing reliable quantum computations. Moreover, the average error rates measured by randomized benchmarking and related protocols are not sensitive to the full impact of coherent errors, and therefore do not reliably predict the global performance of quantum algorithms, leaving us unprepared to validate the accuracy of future large-scale quantum computations. Randomized compiling is a protocol designed to overcome these performance limitations by converting coherent errors into stochastic noise, dramatically reducing unpredictable errors in quantum algorithms and enabling accurate predictions of algorithmic performance from error rates measured via cycle benchmarking. In this work, we demonstrate significant performance gains under randomized compiling for the four-qubit quantum Fourier transform algorithm and for random circuits of variable depth on a superconducting quantum processor. Additionally, we accurately predict algorithm performance using experimentally-measured error rates. Our results demonstrate that randomized compiling can be utilized to leverage and predict the capabilities of modern-day noisy quantum processors, paving the way forward for scalable quantum computing. Copyright © 2020, The Authors. All rights reserved.

关键词： Benchmarking

Variational regularization of inverse problems for manifold-valued data

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arXiv 2018年

作者： Storath, Martin Weinmann, Andreas Image Analysis and Learning Group Interdisciplinary Center for Scientific Computing Universität Heidelberg Germany Department of Mathematics and Natural Sciences Hochschule Darmstadt Institute of Computational Biology Helmholtz Zentrum München Germany

In this paper, we consider the variational regularization of manifold-valued data in the inverse problems setting. In particular, we consider TV and TGV regularization for manifoldvalued data with indirect measurement operators. We provide results on the well-posedness and present algorithms for a numerical realization of these models in the manifold setup. Further, we provide experimental results for synthetic and real data to show the potential of the proposed schemes for *** Codes 94A08, 68U10, 90C90, 53B99, 65K10 Copyright © 2018, The Authors. All rights reserved.

关键词： Differential equations

Quantum Simulation for High-Energy Physics

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PRX Quantum 2023年第2期4卷 027001-027001页

作者： Christian W. Bauer Zohreh Davoudi A. Baha Balantekin Tanmoy Bhattacharya Marcela Carena Wibe A. de Jong Patrick Draper Aida El-Khadra Nate Gemelke Masanori Hanada Dmitri Kharzeev Henry Lamm Ying-Ying Li Junyu Liu Mikhail Lukin Yannick Meurice Christopher Monroe Benjamin Nachman Guido Pagano John Preskill Enrico Rinaldi Alessandro Roggero David I. Santiago Martin J. Savage Irfan Siddiqi George Siopsis David Van Zanten Nathan Wiebe Yukari Yamauchi Kübra Yeter-Aydeniz Silvia Zorzetti Physics Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA Department of Physics Maryland Center for Fundamental Physics and the NSF Institute for Robust Quantum Simulation University of Maryland College Park Maryland 20742 USA Department of Physics University of Wisconsin Madison Wisconsin 53706 USA T-2 Los Alamos National Laboratory Los Alamos New Mexico 87545 USA Fermi National Accelerator Laboratory Batavia Illinois 60510 USA Enrico Fermi Institute University of Chicago Chicago Illinois 60637 USA Kavli Institute for Cosmological Physics University of Chicago Chicago Illinois 60637 USA Department of Physics University of Chicago Chicago Illinois 60637 USA Department of Physics and Illinois Center for the Advanced Study of the Universe and Illinois Quantum Information Science and Technology Center University of Illinois Urbana Illinois 61801 USA QuEra Computing Inc Boston Massachusetts 02135 USA Department of Mathematics University of Surrey Guildford Surrey GU2 7XH United Kingdom Center for Nuclear Theory Department of Physics and Astronomy Stony Brook University New York 11794-3800 USA Department of Physics Brookhaven National Laboratory Upton New York 11973 USA Peng Huanwu Center for Fundamental Theory Hefei Anhui 230026 China Interdisciplinary Center for Theoretical Study University of Science and Technology of China Hefei Anhui 230026 China Pritzker School of Molecular Engineering Chicago Quantum Exchange and Kadanoff Center for Theoretical Physics University of Chicago Illinois 60637 USA qBraid Co. Harper Court 5235 Chicago Illinois 60615 USA Department of Physics Harvard University Cambridge Massachusetts 02138 USA Department of Physics and Astronomy University of Iowa Iowa City Iowa 52242 USA Duke Quantum Center Duke University Durham North Carolina 27701 USA Department of Electrical and Computer Engineering Duke University Durham North Carolina 27708 USA Department of Physics Duke University

It is for the first time that quantum simulation for high-energy physics (HEP) is studied in the U.S. decadal particle-physics community planning, and in fact until recently, this was not considered a mainstream topic in the community. This fact speaks of a remarkable rate of growth of this subfield over the past few years, stimulated by the impressive advancements in quantum information sciences (QIS) and associated technologies over the past decade, and the significant investment in this area by the government and private sectors in the U.S. and other countries. High-energy physicists have quickly identified problems of importance to our understanding of nature at the most fundamental level, from tiniest distances to cosmological extents, that are intractable with classical computers but may benefit from quantum advantage. They have initiated, and continue to carry out, a vigorous program in theory, algorithm, and hardware co-design for simulations of relevance to the HEP mission. This Roadmap is an attempt to bring this exciting and yet challenging area of research to the spotlight, and to elaborate on what the promises, requirements, challenges, and potential solutions are over the next decade and beyond.

关键词： Quantum simulation

A reduction method for Riccati-based control of the Fokker-Planck equation

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IFAC-PapersOnLine 2017年第1期50卷 1631-1636页

作者： Breiten T. Kunisch K. Pfeiffer L. Institute for Mathematics and Scientific Computing Karl-Franzens-Universität Heinrichstrasse 36 Graz A8010 Austria Johann Radon Institute for Computational and Applied Mathematics (RICAM) Austrian Academy of Sciences Altenbergerstrasse 69 Linz A4040 Austria

A control strategy which allows to speed up the convergence of a bilinear system governed by the Fokker-Planck equation to its stationary distribution is developed. After linearization of the state equation, a linear feedback control is computed by solving the Riccati equation associated with the linearized problem. A reduction method for approximating this feedback is proposed. From a numerical point of view, this method avoids the resolution of a high-dimensional Riccati equation. Numerical results are provided for a double-well potential and the efficiency of the reduction method is demonstrated. © 2017

关键词： bilinear systems control of partial differential equations Fokker-Planck equation Output feedback control Riccati equation

Corrigendum to: A convergent adaptive finite element method for elliptic Dirichlet boundary control problems

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IMA Journal of Numerical Analysis 2020年第1期40卷 800-800页

作者： Gong, Wei Liu, Wenbin Tan, Zhiyu Yan, Ningning National Center for Mathematics and Interdisciplinary Sciences Chinese Academy of Sciences Beijing China The State Key Laboratory of Scientific and Engineering Computing Chinese Academy of Sciences Beijing China Institute of Computational Mathematics Chinese Academy of Sciences Beijing China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Kent Business School University of Kent Kent UK Department of Mathematics Hong Kong Baptist University Kowloon Tong Hong Kong SAR NCMIS Chinese Academy of Sciences Beijing China LSEC Chinese Academy of Sciences Beijing China Institute of Systems Science Chinese Academy of Sciences Beijing China

A monotone scheme for sparsity optimization in lp with p Є (0,1]

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IFAC-PapersOnLine 2017年第1期50卷 494-499页

作者： Ghilli D. Kunisch K. Institute of Mathematics and Scientific Computing Karl-Franzens-Universitaät Heinrichstrasse 36 Graz A8010 Austria Johann Radon Institute for Computational and Applied Mathematics(RICAM) Austrian Academy of Sciences Altenbergerstrasse 69 Linz A4040 Austria

Nonsmooth nonconvex optimization problems are considered in infinite dimensional sequence spaces lp with p Є (0,1]. Our starting points are necessary optimality conditions in the form of a complementary system and a monotonically convergent algorithm for a regularized version of the original problem. We propose an algorithm for solving the necessary optimality condition based on a combination of the monotone scheme and an active-set strategy. Numerical results for different test cases are provided, e.g. for optimal control problems and microscopy image reconstruction. © 2017

关键词： active-set method image reconstruction monotone algorithm nonsmooth nonconvex optimization optimal control problems sparsity optimization

AbdomenCT-1K: Is abdominal organ segmentation a solved problem?

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arXiv 2020年

作者： Ma, Jun Zhang, Yao Gu, Song Zhu, Cheng Ge, Cheng Zhang, Yichi An, Xingle Wang, Congcong Wang, Qiyuan Liu, Xin Cao, Shucheng Zhang, Qi Liu, Shangqing Wang, Yunpeng Li, Yuhui He, Jian Yang, Xiaoping Department of Mathematics Nanjing University of Science and Technology China Institute of Computing Technology Chinese Academy of Sciences University of Chinese Academy of Sciences China AI Lab Lenovo Research School of Automation Nanjing University of Information Science and Technology China Shenzhen Haichuang Medical CO. LTD. China Institute of Bioinformatics and Medical Engineering Jiangsu University of Technology China School of Biological Science and Medical Engineering Beihang University China Beijing Infervision Technology CO. LTD. China School of Computer Science and Engineering Tianjin University of Technology China Department of Computer Science Norwegian University of Science and Technology Norway School of Electronic Science and Engineering Nanjing University China Suzhou LungCare Medical Technology Co. Ltd China Bioengineering Biological and Environmental Science and Engineering Division King Abdullah University of Science and Technology Saudi Arabia Department of Computer and Information Science Faculty of Science and Technology University of Macau China School of Biomedical Engineering Southern Medical University China Institutes of Biomedical Sciences Fudan University China Computational Biology University of Southern California United States Department of Radiology Nanjing Drum Tower Hospital The Affiliated Hospital Nanjing University Medical School China Department of Mathematics Nanjing University China

With the unprecedented developments in deep learning, automatic segmentation of main abdominal organs seems to be a solved problem as state-of-the-art (SOTA) methods have achieved comparable results with inter-rater variability on many benchmark datasets. However, most of the existing abdominal datasets only contain single-center, single-phase, single-vendor, or single-disease cases, and it is unclear whether the excellent performance can generalize on diverse datasets. This paper presents a large and diverse abdominal CT organ segmentation dataset, termed AbdomenCT-1K, with more than 1000 (1K) CT scans from 12 medical centers, including multi-phase, multi-vendor, and multi-disease cases. Furthermore, we conduct a large-scale study for liver, kidney, spleen, and pancreas segmentation and reveal the unsolved segmentation problems of the SOTA methods, such as the limited generalization ability on distinct medical centers, phases, and unseen diseases. To advance the unsolved problems, we further build four organ segmentation benchmarks for fully supervised, semi-supervised, weakly supervised, and continual learning, which are currently challenging and active research topics. Accordingly, we develop a simple and effective method for each benchmark, which can be used as out-of-the-box methods and strong baselines. We believe the AbdomenCT-1K dataset will promote future in-depth research towards clinical applicable abdominal organ segmentation methods. © 2020, CC BY-NC-SA.

关键词： Computerized tomography