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Construction of Symplectic Runge-Kutta Methods for Stochastic Hamiltonian Systems

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Communications in computational Physics 2017年第1期21卷 237-270页

作者： Peng Wang Jialin Hong Dongsheng Xu Institute of Mathematics Jilin UniversityChangchun 130012P.R.China State Key Laboratory of Scientific and Engineering Computing Institute of ComputationalMathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of Sciences100080 BeijingP.R.China University of Chinese Academy of Sciences P.R.China

We study the construction of symplectic Runge-Kutta methods for stochastic Hamiltonian systems(SHS).Three types of systems,SHS with multiplicative noise,special separable Hamiltonians and multiple additive noise,respectively,are considered in this *** Runge-Kutta(SRK)methods for these systems are investigated,and the corresponding conditions for SRK methods to preserve the symplectic property are *** on the weak/strong order and symplectic conditions,some effective schemes are *** particular,using the algebraic computation,we obtained two classes of high weak order symplectic Runge-Kutta methods for SHS with a single multiplicative noise,and two classes of high strong order symplectic Runge-Kutta methods for SHS with multiple multiplicative and additive noise,*** numerical case studies confirm that the symplectic methods are efficient computational tools for long-term simulations.

关键词： Stochastic differential equation Stochastic Hamiltonian system symplectic integration Runge-Kutta method order condition

Non-linear fitting with joint spatial regularization in Arterial Spin Labeling

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arXiv 2020年

作者： Maier, Oliver Spann, Stefan M. Pinter, Daniela Gattringer, Thomas Hinteregger, Nicole Thallinger, Gerhard G. Enzinger, Christian Pfeuffer, Josef Bredies, Kristian Stollberger, Rudolf Institute of Medical Engineering Graz University of Technology Stremayrgasse 16/III Graz8010 Austria Department of Neurology Division of General Neurology Medical University of Graz Auenbruggerplatz 22 Graz8036 Austria Division of Neuroradiology Vascular and Interventional Radiology Department of Radiology Medical University of Graz Auenbruggerplatz 22 Graz8036 Austria Institute of Biomedical Informatics Graz University of Technology Stremayrgasse 16/I Graz8010 Austria BioTechMed-Graz Mozartgasse 12/II Graz8010 Austria Application Development Siemens Healthcare Henkestraße 127 Erlangen91052 Germany Institute of Mathematics and Scientific Computing University of Graz Heinrichstraße 36 Graz8010 Austria

Multi-Delay single-shot arterial spin labeling (ASL) imaging provides accurate cerebral blood flow (CBF) and, in addition, arterial transit time (ATT) maps but the inherent low SNR can be challenging. Especially standard fitting using non-linear least squares often fails in regions with poor SNR, resulting in noisy estimates of the quantitative maps. State-of-the-art fitting techniques improve the SNR by incorporating prior knowledge in the estimation process which typically leads to spatial blurring. To this end, we propose a new estimation method with a joint spatial total generalized variation regularization on CBF and ATT. This joint regularization approach utilizes shared spatial features across maps to enhance sharpness and simultaneously improves noise suppression in the final estimates. The proposed method is evaluated at three levels, first on synthetic phantom data including pathologies, followed by in vivo acquisitions of healthy volunteers, and finally on patient data following an ischemic stroke. The quantitative estimates are compared to two reference methods, non-linear least squares fitting and a stateof-the-art ASL quantification algorithm based on Bayesian inference. The proposed joint regularization approach outperforms the reference implementations, substantially increasing the SNR in CBF and ATT while maintaining sharpness and quantitative accuracy in the *** Codes 92C55, 68U10, 94A12 Copyright © 2020, The Authors. All rights reserved.

关键词： Hospital data processing

QCaMP: A 4-Week Summer Camp Introducing High School Students to Quantum Information Science and Technology

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arXiv 2025年

作者： Ivory, Megan Balewski, Jan Bettale, Alisa Brewer, Jaden Boren, Rachel Camps, Daan Hackett, Lisa Juarez, Martin Kononov, Alina Lee, Kan-Heng Long, Maryanne Mounce, Andy Mniszewski, Susan Naik, Ravi K. Pakin, Scott Sanchez, Ernesto Sandia National Laboratories AlbuquerqueNM United States National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA United States Office of Government and Community Relations Lawrence Berkeley National Laboratory BerkeleyCA United States Quantum Photonics Lab Northern Arizona University FlagstaffAZ United States College of Health Education and Social Transformation New Mexico State University Las CrucesNM United States Bourns College of Engineering University of California Riverside RiversideCA United States Quantum Algorithms and Applications Collaboratory Sandia National Laboratories AlbuquerqueNM United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA United States Center for Integrated Nanotechnology Sandia National Laboratories AlbuquerqueNM United States Los Alamos National Laboratory Los AlamosNM United States Applied Computer Science Los Alamos National Laboratory Los AlamosNM United States

The 2024 Quantum computing, Math and Physics Camp (QCaMP) for Students was a 4-week long summer camp aimed at introducing high school students to quantum concepts and careers, including applications spanning quantum computing, sensing, and communication. The program ran for 7 hours/day, Monday–Friday, July 1–26, and included hands-on modules and activities, professional development, and project-based learning. Here we provide details on the camp curriculum and outcomes based on pre and post knowledge and attitudes assessments. © 2025, CC BY.

关键词： Qubits

FAIR for AI: An interdisciplinary and international community building perspective

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arXiv 2022年

作者： Huerta, E.A. Blaiszik, Ben Brinson, L. Catherine Bouchard, Kristofer E. Diaz, Daniel Doglioni, Caterina Duarte, Javier M. Emani, Murali Foster, Ian Fox, Geoffrey Harris, Philip Heinrich, Lukas Jha, Shantenu Katz, Daniel S. Kindratenko, Volodymyr Kirkpatrick, Christine R. Lassila-Perini, Kati Madduri, Ravi K. Neubauer, Mark S. Psomopoulos, Fotis E. Roy, Avik Rübel, Oliver Zhao, Zhizhen Zhu, Ruike Data Science and Learning Division Argonne National Laboratory LemontIL60439 United States Department of Computer Science University of Chicago ChicagoIL60637 United States Globus University of Chicago ChicagoIL60637 United States Department of Mechanical Engineering and Materials Science Duke University DurhamNC27708 United States Scientific Data Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Biological Systems & Engineering Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Helen Wills Neuroscience Institute University of California Berkeley BerkeleyCA94720 United States Department of Physics University of California La Jolla San DiegoCA92093 United States Lund University Department of Physics Box 118 Lund221 00 Sweden School of Physics & Astronomy The University of Manchester ManchesterM13 9PL United Kingdom Leadership Computing Facility Argonne National Laboratory LemontIL60439 United States Biocomplexity Institute Department of Computer Science University of Virginia CharlottesvilleVA22904 United States Department of Physics Massachusetts Institute of Technology CambridgeMA02139 United States Technical University Munich Arcisstraße 21 München80333 Germany Computational Science Initiative Brookhaven National Laboratory UptonNY11973 United States Electrical and Computer Engineering Rutgers The State University of New Jersey PiscatawayNJ08854 United States National Center for Supercomputing Applications University of Illinois Urbana-Champaign UrbanaIL61801 United States Department of Computer Science University of Illinois at Urbana-Champaign UrbanaIL61801 United States Department of Electrical & Computer Engineering University of Illinois at Urbana-Champaign UrbanaIL61801 United States School of Information Sciences University of Illinois at Urbana-Champaign UrbanaIL61801 United States San Diego Supercomputer Center University of California La Jolla San DiegoCA

A foundational set of findable, accessible, interoperable, and reusable (FAIR) principles were proposed in 2016 as prerequisites for proper data management and stewardship, with the goal of enabling the reusability of scholarly data. The principles were also meant to apply to other digital assets, at a high level, and over time, the FAIR guiding principles have been reinterpreted or extended to include the software, tools, algorithms, and workflows that produce data. FAIR principles are now being adapted in the context of AI models and datasets. Here, we present the perspectives, vision, and experiences of researchers from different countries, disciplines, and backgrounds who are leading the definition and adoption of FAIR principles in their communities of practice, and discuss outcomes that may result from pursuing and incentivizing FAIR AI research. The material for this report builds on the FAIR for AI Workshop held at Argonne National Laboratory on June 7, 2022. Copyright © 2022, The Authors. All rights reserved.

关键词： Information management

Linear Stability of Hyperbolic Moment Models for Boltzmann Equation

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高等学校计算数学学报（英文版） 2017年第2期10卷 255-277页

作者： Yana Di Yuwei Fan Ruo Li Lingchao Zheng LSEC Institute of Computational Mathematics and Scientific/Engineering Computing NCMIS AMSS Chinese Academy of Sciences Beijing 100190China School of Mathematical Sciences Peking University Beijing 100871 China HEDPS & CAPT LMAM & School of Mathematical SciencesPeking University Beijing 100871 China

Grad's moment models for Boltzmann equation were recently regularized to globally hyperbolic systems and thus the regularized models attain local wellposedness for Cauchy *** hyperbolic regularization is only related to the convection term in Boltzmann *** in this paper studied the regularized models with the presentation of collision *** is proved that the regularized models are linearly stable at the local equilibrium and satisfy Yong's first stability condition with commonly used approximate collision terms,and particularly with Boltzmann's binary collision model.

关键词： Boltzmann equation Grad's moment method hyperbolic moment equation linear stability

Plane wave methods for quantum eigenvalue problems of incommensurate systems

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arXiv 2018年

作者： Zhou, Yuzhi Chen, Huajie Zhou, Aihui Institute of Applied Physics and Computational Mathematics Bejing100088 China School of Mathematical Sciences Beijing Normal University Beijing100875 China 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

We propose a novel numerical algorithm for computing the electronic structure related eigenvalue problem of incommensurate systems. Unlike the conventional practice that approximates the system by a large commensurate supercell, our algorithm directly discretizes the eigenvalue problem under the framework of a plane wave method. The emerging ergodicity and the interpretation from higher dimensions give rise to many unique features compared to what we have been familiar with in the periodic system. The numerical results of 1D and 2D quantum eigenvalue problems are presented to show the reliability and efficiency of our scheme. Furthermore, the extension of our algorithm to full Kohn-Sham density functional theory calculations are discussed. Copyright © 2018, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

Versatile stabilized finite element formulations for nearly and fully incompressible solid mechanics

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arXiv 2019年

作者： Karabelas, Elias Haase, Gundolf Plank, Gernot Augustin, Christoph M. Institute for Mathematics and Scientific Computing NAWI Graz University of Graz Graz Austria Gottfried Schatz Research Center Division of Biophysics Medical University of Graz Graz Austria BioTechMed-Graz Graz Austria Department of Mechanical Engineering University of California Berkeley BerkeleyCA United States /IV Graz8010 Austria

computational formulations for large strain, polyconvex, nearly incompressible elasticity have been extensively studied, but research on enhancing solution schemes that offer better tradeoffs between accuracy, robustness, and computational efficiency remains to be highly relevant. In this paper, we present two methods to overcome locking phenomena, one based on a displacement-pressure formulation using a stable finite element pairing with bubble functions, and another one using a simple pressure-projection stabilized P1 − P1 finite element pair. A key advantage is the versatility of the proposed methods: with minor adjustments they are applicable to all kinds of finite elements and generalize easily to transient dynamics. The proposed methods are compared to and verified with standard benchmarks previously reported in the literature. Benchmark results demonstrate that both approaches provide a robust and computationally efficient way of simulating nearly and fully incompressible materials. Copyright © 2019, The Authors. All rights reserved.

关键词： Finite element method

Assessing Trustworthy AI in Times of COVID-19: Deep Learning for Predicting a Multiregional Score Conveying the Degree of Lung Compromise in COVID-19 Patients

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IEEE Transactions on Technology and Society

IEEE Transactions on Technology and Society 2022年第4期3卷 272-289页

作者： Allahabadi, Himanshi Amann, Julia Balot, Isabelle Beretta, Andrea Binkley, Charles Bozenhard, Jonas Bruneault, Frederick Brusseau, James Candemir, Sema Cappellini, Luca Alessandro Chakraborty, Subrata Cherciu, Nicoleta Cociancig, Christina Coffee, Megan Ek, Irene Espinosa-Leal, Leonardo Farina, Davide Fieux-Castagnet, Genevieve Frauenfelder, Thomas Gallucci, Alessio Giuliani, Guya Golda, Adam Van Halem, Irmhild Hildt, Elisabeth Holm, Sune Kararigas, Georgios Krier, Sebastien A. Kuhne, Ulrich Lizzi, Francesca Madai, Vince I. Markus, Aniek F. Masis, Serg Mathez, Emilie Wiinblad Mureddu, Francesco Neri, Emanuele Osika, Walter Ozols, Matiss Panigutti, Cecilia Parent, Brendan Pratesi, Francesca Moreno-Sanchez, Pedro A. Sartor, Giovanni Savardi, Mattia Signoroni, Alberto Sormunen, Hanna-Maria Spezzatti, Andy Srivastava, Adarsh Stephansen, Annette F. Theng, Lau Bee Tithi, Jesmin Jahan Tuominen, Jarno Umbrello, Steven Vaccher, Filippo Vetter, Dennis Westerlund, Magnus Wurth, Renee Zicari, Roberto V. Ey Netherlands Enterprise Intelligence Department Amsterdam1083 HP Netherlands Eth Zurich Health Ethics and Policy Lab Department of Health Sciences and Technology Zürich8092 Switzerland Center for Diplomatic and Strategic Studies Postgraduate Studies in Diplomacy and International Relations Paris75015 France Pisa56124 Italy Hackensack Meridian Health Bioethics Center EdisonNJ08820 United States University of Oxford Faculty of Philosophy OxfordOX2 6GG United Kingdom Collège André- Laurendeau Philosophie Department MontrealQCH8N 2J4 Canada Université du Québec À Montréal École des Médias MontrealQCH2L 2C4 Canada Pace University Philosophy Department New YorkNY10038 United States The Ohio State University Wexner Medical Center Department of Radiology ColumbusOH43210 United States Humanitas Research Hospital Department of Radiology Milan20089 Italy Humanitas University Department of Biomedical Sciences Milan20089 Italy University of New England Faculty of Science Agriculture Business and Law ArmidaleNSW2351 Australia University of Technology Sydney Faculty of Engineering and Information Technology SydneyNSW2007 Australia Scuola Superiore Sant'Anna European Centre of Excellence on the Regulation of Robotics and Ai Pisa56127 Italy University of Bremen Group of Computer Architecture Bremen28359 Germany New York University Grossman School of Medicine Division of Infectious Diseases and Immunology Department of Medicine New YorkNY10016 United States Digital Institute Ai Research Section Stockholm16731 Sweden Arcada University of Applied Sciences Department of Business Management and Analytics Helsinki00550 Finland University of Brescia Radiological Sciences and Public Health Department of Medical and Surgical Specialties Brescia25121 Italy Sncf Reseau Sa Ethique Groupe La Plaine93418 France Institute of Diagnostic and Interventional Radiology University Hospital Zurich Zürich8091 Switzerland Eindhoven University of Tech

This article's main contributions are twofold: 1) to demonstrate how to apply the general European Union's High-Level Expert Group's (EU HLEG) guidelines for trustworthy AI in practice for the domain of healthcare and 2) to investigate the research question of what does 'trustworthy AI' mean at the time of the COVID-19 pandemic. To this end, we present the results of a post-hoc self-assessment to evaluate the trustworthiness of an AI system for predicting a multiregional score conveying the degree of lung compromise in COVID-19 patients, developed and verified by an interdisciplinary team with members from academia, public hospitals, and industry in time of pandemic. The AI system aims to help radiologists to estimate and communicate the severity of damage in a patient's lung from Chest X-rays. It has been experimentally deployed in the radiology department of the ASST Spedali Civili clinic in Brescia, Italy, since December 2020 during pandemic time. The methodology we have applied for our post-hoc assessment, called Z-Inspection®, uses sociotechnical scenarios to identify ethical, technical, and domain-specific issues in the use of the AI system in the context of the pandemic. © 2020 IEEE.

关键词： COVID-19

Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics

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arXiv 2019年

作者： Fleeter, Casey M. Geraci, Gianluca Schiavazzi, Daniele E. Kahn, Andrew M. Marsden, Alison L. Institute for Computational and Mathematical Engineering Stanford University StanfordCA United States Center for Computing Research Sandia National Laboratories AlbuquerqueNM United States Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN United States Department of Medicine University of California San Diego San diegoCA United States Departments of Pediatrics and Bioengineering Stanford University StanfordCA United States

Standard approaches for uncertainty quantification in cardiovascular modeling pose challenges due to the large number of uncertain inputs and the significant computational cost of realistic three-dimensional simulations. We propose an efficient uncertainty quantification framework utilizing a multilevel multifidelity Monte Carlo (MLMF) estimator to improve the accuracy of hemodynamic quantities of interest while maintaining reasonable computational cost. This is achieved by leveraging three cardiovascular model fidelities, each with varying spatial resolution to rigorously quantify the variability in hemodynamic outputs. We employ two low-fidelity models (zero- and one-dimensional) to construct several different estimators. Our goal is to investigate and compare the efficiency of estimators built from combinations of these two low-fidelity model alternatives and our high-fidelity three-dimensional models. We demonstrate this framework on healthy and diseased models of aortic and coronary anatomy, including uncertainties in material property and boundary condition parameters. Our goal is to demonstrate that for this application it is possible to accelerate the convergence of the estimators by utilizing a MLMF paradigm. Therefore, we compare our approach to single fidelity Monte Carlo estimators and to a multilevel Monte Carlo approach based only on three-dimensional simulations, but leveraging multiple spatial resolutions. We demonstrate significant, on the order of 10 to 100 times, reduction in total computational cost with the MLMF estimators. We also examine the differing properties of the MLMF estimators in healthy versus diseased models, as well as global versus local quantities of interest. As expected, global quantities such as outlet pressure and flow show larger reductions than local quantities, such as those relating to wall shear stress, as the latter rely more heavily on the highest fidelity model evaluations. Similarly, healthy models show larger reducti

关键词： Monte Carlo methods