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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

Determining system Hamiltonian from eigenstate measurements without correlation functions

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arXiv 2019年

作者： Hou, Shi-Yao Cao, Ningping Lu, Sirui Shen, Yi Poon, Yiu-Tung Zeng, Bei College of Physics and Electronic Engineering Center for Computational Sciences Sichuan Normal University Chengdu610068 China Center for Quantum Computing Peng Cheng Laboratory Shenzhen518055 China Shenzhen Institute for Quantum Science and Engineering Southern University of Science and Technology Shenzhen518055 China Department of Mathematics & Statistics University of Guelph GuelphONN1G 2W1 Canada Institute for Quantum Computing University of Waterloo WaterlooONN2L 3G1 Canada Department of Physics Tsinghua University Beijing100084 China Department of Statistics and Actuarial Science University of Waterloo WaterlooON Canada Department of Mathematics Iowa State University AmesIA50011 United States Department of Physics Hong Kong University of Science and Technology Clear Water Bay Kowloon Hong Kong

Local Hamiltonians arise naturally in physical systems. Despite its seemingly 'simple' local structure, exotic features such as nonlocal correlations and topological orders exhibit in eigenstates of these systems. Previous studies for recovering local Hamiltonians from measurements on an eigenstate |ψ〉 require information of nonlocal correlation functions. In this work, we develop an algorithm to determine local Hamiltonians from only local measurements on |ψ〉, by reformulating the task as an unconstrained optimization problem of certain target function of Hamiltonian parameters, with only polynomial number of parameters in terms of system size. We also develop a machine learning-based-method to solve the first-order gradient used in the algorithm. Our method is tested numerically for randomly generated local Hamiltonians and returns promising reconstruction in the desired accuracy. Our result shed light on the fundamental question on how a single eigenstate can encode the full system Hamiltonian, indicating a somewhat surprising answer that only local measurements are enough without additional assumptions, for generic cases. Copyright © 2019, The Authors. All rights reserved.

关键词： Hamiltonians

A decoupling two-grid method for the time-dependent poisson-nernst-planck equations

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arXiv 2018年

作者： Shen, Ruigang Shu, Shi Yang, Ying Lu, Benzhuo School of Mathematics and Computational Science Xiangtan University Xiangtan Hunan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan411105 China School of Mathematics and Computational Science Guangxi Colleges Universities Key Laboratory of Data Analysis and Computation Guangxi Key Laboratory of Cryptography and information Security Guilin University of Electronic Technology Guilin Guangxi541004 China Institute of Computational Mathematics and Scientific/Engineering Computing National Center for Mathematics and Interdisciplinary Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

We study a two-grid strategy for decoupling the time-dependent Poisson-Nernst-Planck equations describing the mass concentration of ions and the electrostatic potential. The computational system is decoupled to smaller systems by using coarse space solutions at each time level, which can speed up the solution process compared with the finite element method combined with the Gummel iteration. We derive the optimal error estimates in L2 norm for both semi- and fully discrete finite element approximations. Based on the a priori error estimates, the error estimates in H1 norm are presented for the two-grid algorithm. The theoretical results indicate this decoupling method can retain the same accuracy as the finite element method. Numerical experiments including the Poisson-Nernst-Planck equations for an ion channel show the efficiency and effectiveness of the decoupling two-grid method. Copyright © 2018, The Authors. All rights reserved.

关键词： Finite element method

Learning from learning machines: A new generation of AI technology to meet the needs of science

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arXiv 2021年

作者： Pion-Tonachini, Luca Bouchard, Kristofer Martin, Hector Garcia Peisert, Sean Holtz, W. Bradley Aswani, Anil Dwivedi, Dipankar Wainwright, Haruko Pilania, Ghanshyam Nachman, Benjamin Marrone, Babetta L. Falco, Nicola Prabhat Arnold, Daniel Wolf-Yadlin, Alejandro Powers, Sarah Climer, Sharlee Jackson, Quinn Carlson, Ty Sohn, Michael Zwart, Petrus Kumar, Neeraj Justice, Amy Tomlin, Claire Jacobson, Daniel Micklem, Gos Gkoutos, Georgios V. Bickel, Peter J. Cazier, Jean-Baptiste Müller, Juliane Webb-Robertson, Bobbie-Jo Stevens, Rick Anderson, Mark Kreutz-Delgado, Ken Mahoney, Michael W. Brown, James B. Pattern Computer Inc. Friday HarborWA98250 United States Biosciences Area Lawrence Berkeley National Lab BerkeleyCA94803 United States Computational Research Division Lawrence Berkeley National Lab BerkeleyCA94720 United States Helen Wils Neuroscience Institute Redwood Center for Theoretical Neuroscience Uc Berkeley BerkeleyCA94720 United States Doe Agile BioFoundry Lawrence Berkeley National Laboratory BerkeleyCA94803 United States Joint BioEnergy Institute Lawrence Berkeley National Laboratory BerkeleyCA94803 United States Bcam Basque Center for Applied Mathematics Bilbao48009 Spain Computer Science University of California Davis DavisCA95616 United States Cenic La MiradaCA90638 United States Health Informatics University of California Davis School of Medicine SacramentoCA95817 United States Berkeley Institute for Data Science University of California Berkeley BerkeleyCA94720 United States Industrial Engineering and Operations Research University of California Berkeley BerkeleyCA94720 United States Environmental & Earth Sciences Area Lawrence Berkeley National Laboratory BerkeleyCA94803 United States Nuclear Engineering University of California Berkeley BerkeleyCA94720 United States Materials Science and Technology Division Los Alamos National Laboratory Los AlamosNM87545 United States Physics Division Lawrence Berkeley National Lab BerkeleyCA94720 United States Bioscience Division Los Alamos National Laboratory Los AlamosNM87545 United States Earth and Environmental Sciences Area Lawrence Berkeley National Lab BerkeleyCA94803 United States Energy Technologies Area Lawrence Berkeley National Lab BerkeleyCA94803 United States Computing and Computational Sciences Oak Ridge National Laboratory Oak RidgeTN37831 United States Industrial & Systems Engineering The University of Tennessee KnoxvilleTN37996 United States Department of Computer Science University of Missouri-Saint Louis St. LouisMO63121 United

We outline emerging opportunities and challenges to enhance the utility of AI for scientific discovery. The distinct goals of AI for industry versus the goals of AI for science create tension between identifying patterns in data versus discovering patterns in the world from data. If we address the fundamental challenges associated with "bridging the gap" between domain-driven scientific models and data-driven AI learning machines, then we expect that these AI models can transform hypothesis generation, scientific discovery, and the scientific process itself. © 2021, CC BY.

关键词： Learning systems

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

Quasi-potential calculation and minimum action method for limit cycle

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arXiv 2018年

作者： Lin, Ling Yu, Haijun Zhou, Xiang School of Mathematics Sun Yat-sen University Guangzhou510275 China School of Mathematical Sciences University of Chinese Academy of Sciences NCMIS and LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China Department of Mathematics City University of Hong Kong Tat Chee Ave Kowloon Hong Kong

We study the noise-induced escape from a stable limit cycle of a non-gradient dynamical system driven by a small additive noise. The fact that the optimal transition path in this case is infinitely long imposes a severe numerical challenge to resolve it in the minimum action method. We first consider the landscape of the quasi-potential near the limit cycle, which characterizes the minimal cost of the noise to drive the system far away form the limit cycle. We derive and compute the quadratic approximation of this quasi-potential near the limit cycle in the form of a positive definite solution to a matrix-valued periodic Riccati differential equation on the limit cycle. We then combine this local approximation in the neighbourhood of the limit cycle with the minimum action method applied outside of the neighbourhood. The neighbourhood size is selected to be compatible with the path discretization error. By several numerical examples, we show that this strategy effectively improve the minimum action method to compute the spiral optimal escape path from limit cycles in various *** 65K05, Secondary 82B05 Copyright © 2018, The Authors. All rights reserved.

关键词： Numerical methods

Lattice QCD and Particle Physics

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arXiv 2022年

作者： Kronfeld, Andreas S. Bhattacharya, Tanmoy Blum, Thomas Christ, Norman H. DeTar, Carleton Detmold, William Edwards, Robert Hasenfratz, Anna Lin, Huey-Wen Mukherjee, Swagato Orginos, Konstantinos Brower, Richard Cirigliano, Vincenzo Davoudi, Zohreh Jóo, Bálint Jung, Chulwoo Lehner, Christoph Meinel, Stefan Neil, Ethan T. Petreczky, Peter Richards, David G. Bazavov, Alexei Catterall, Simon Dudek, Jozef J. El-Khadra, Aida X. Engelhardt, Michael Fleming, George T. Giedt, Joel Gupta, Rajan Hansen, Maxwell T. Izubuchi, Taku Karsch, Frithjof Laiho, Jack Liu, Keh-Fei Meyer, Aaron S. Rinaldi, Enrico Savage, Martin Schaich, David Shanahan, Phiala E. Sharpe, Stephen R. Sufian, Raza Syritsyn, Sergey Van de Water, Ruth S. Wagman, Michael L. Weinberg, Evan Witzel, Oliver Aubin, Christopher Boyle, Peter Chandrasekharan, Shailesh Cloët, Ian C. Constantinou, Martha Cushman, Kimmy DeGrand, Thomas Fodor, Zoltan Foreman, Sam Gottlieb, Steven Hoying, Daniel Jang, Yong-Chull Jay, William I. Jin, Xiao-Yong Kelly, Christopher Kuti, Julius Lamm, Henry Lin, Meifeng Lin, Yin Lytle, Andrew T. Mackenzie, Paul Mandula, Jeffrey Meurice, Yannick Monahan, Christopher Morningstar, Colin Osborn, James C. Park, Sungwoo Simone, James N. Strelchenko, Alexei Tomii, Masaaki Vaquero, Alejandro Vranas, Pavlos Wang, Bigeng Wilcox, Walter Yoon, Boram Zhao, Yong Theory Division Fermi National Accelerator Laboratory BataviaIL60510 United States Group T-2 Los Alamos National Laboratory Los AlamosNM87545 United States Department of Physics University of Connecticut StorrsCT06269 United States RIKEN BNL Research Center Brookhaven National Laboratory UptonNY11973 United States Department of Physics Columbia University New YorkNY10027 United States Department of Physics and Astronomy University of Utah Salt Lake CityUT84112 United States Center for Theoretical Physics Massachusetts Institute of Technology CambridgeMA02139 United States The NSF Institute for Artificial Intelligence and Fundamental Interactions Theory Center Thomas Jefferson National Accelerator Facility Newport NewsVA23606 United States Department of Physics University of Colorado BoulderCO80309 United States Department of Physics and Astronomy Michigan State University East LansingMI48824 United States Physics Department Brookhaven National Laboratory UptonNY11973 United States Department of Physics College of William & Mary WilliamsburgVA23187 United States Department of Physics Center for Computational Science Boston University BostonMA02215 United States Institute of Nuclear Theory University of Washington SeattleWA98195 United States Department of Physics Maryland Center for Fundamental Physics University of Maryland College ParkMD20742 United States Oak Ridge Leadership Computing Facility Oak Ridge National Laboratory Oak RidgeTN37831 United States Fakultät für Physik Universität Regensburg RegensburgD-93040 Germany Department of Physics University of Arizona TucsonAZ85721 United States Department of Computational Mathematics Science and Engineering Michigan State University East LansingMI48824 United States Department of Physics Syracuse University SyracuseNY13244 United States Department of Physics University of Illinois Urbana-Champaign UrbanaIL61801 United States Department of Physics New Mexic

Lattice field theory provides a mathematically rigorous definition of quantum field theory, including gauge theories. The rigor provides a platform for computation of strongly-coupled gauge theories, not only quantum chromodynamics (QCD) at long-distances but also strongly-coupled sectors that might lie beyond the Standard Model (BSM) of particle physics. Indeed, the interpretation of many experiments in particle physics, nuclear physics, and astrophysics relies, often crucially, on results from lattice QCD or BSM. In quark-flavor physics, lattice QCD is essential for grounding theoretical predictions. Together with experimental measurements, lattice QCD is used to determine many of the fundamental parameters of the Standard Model's flavor sector: five out of six quark masses and the three mixing angles and CP-violating phase of the Cabibbo-Kobayashi-Maskawa (CKM) matrix. Further Standard-Model predictions requiring lattice QCD are for processes that could reveal signatures of new physics. This area of lattice QCD has become a precision science, as has the determination of the strong coupling, αs, which is key in many areas, for example for understanding Higgs-boson decay to gluons. Lattice-QCD calculations of the hadronic contributions to the anomalous magnetic moment of the muon are another area for which precision is both mandatory and achievable. While these contributions can be estimated via a combination of certain measurements and general theoretical concepts, a direct ab initio calculation from QCD is desirable to confirm robustly the tantalizingly large discrepancy between experiment and the Standard Model. Other indirect searches for new physics are complementary to quark-flavor physics and the muon anomalous magnetic moment. Lattice QCD is an essential tool for understanding newly discovered hadrons with quark content different from the usual baryons and mesons. Lattice-QCD calculations are needed to interpret bounds on electric dipole moments, proton dec

关键词： Calculations

A new estimate for a quantity involving the Chebyshev polynomials of the first kind

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arXiv 2018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

In this paper, we establish a new estimate (including lower and upper bounds) for an important quantity involved in the convergence analysis of smoothed aggregation algebraic multigrid methods. The new upper bound imp... 详细信息

关键词： Polynomials

Numerical approximation of elliptic problems with log-normal random coefficients

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arXiv 2018年

作者： Wan, Xiaoliang Yu, Haijun Department of Mathematics Center for Computation and Technology Louisiana State University Baton RougeLA70803 United States NCMIS & LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In this work, we consider a non-standard preconditioning strategy for the numerical approximation of the classical elliptic equations with log-normal random coefficients. In [45], a Wick-type elliptic model was proposed by modeling the random flux through the Wick product. Due to the lower-triangular structure of the uncertainty propagator, this model can be approximated efficiently using the Wiener chaos expansion in the probability space. Such a Wick-type model provides, in general, a second-order approximation of the classical one in terms of the standard deviation of the underlying Gaussian process. Furthermore, when the correlation length of the underlying Gaussian process goes to infinity, the Wick-type model yields the same solution as the classical one. These observations imply that the Wick-type elliptic equation can provide an effective preconditioner for the classical random elliptic equation under appropriate conditions. We use the Wick-type elliptic model to accelerate the Monte Carlo method and the stochastic Galerkin finite element method. Numerical results are presented and discussed.60H35, 65N30 Copyright © 2018, The Authors. All rights reserved.

关键词： Stochastic systems