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Impact of subdominant modes on the interpretation of gravitational-wave signals from heavy binary black hole systems

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Physical Review D 2020年第12期101卷 124054-124054页

作者： Feroz H. Shaik Jacob Lange Scott E. Field Richard O’Shaughnessy Vijay Varma Lawrence E. Kidder Harald P. Pfeiffer Daniel Wysocki Department of Physics Department of Mathematics and the Center for Scientific Computing & Visualization Research University of Massachusetts Dartmouth Dartmouth Massachusetts 02747 USA Center for Computational Relativity and Gravitation Rochester Institute of Technology Rochester New York 14623 USA Department of Mathematics and the Center for Scientific Computing & Visualization Research University of Massachusetts Dartmouth Dartmouth Massachusetts 02747 USA Theoretical Astrophysics California Institute of Technology Pasadena California 91125 USA Cornell Center for Astrophysics and Planetary Science Cornell University Ithaca New York 14853 USA Max Planck Institute for Gravitational Physics (Albert Einstein Institute) Am Mühlenberg 1 14476 Potsdam Germany

Over the past year, a handful of new gravitational wave models have been developed to include multiple harmonic modes thereby enabling for the first time fully Bayesian inference studies including higher modes to be performed. Using one recently developed numerical relativity surrogate model, NRHybSur3dq8, we investigate the importance of higher modes on parameter inference of coalescing massive binary black holes. We focus on examples relevant to the current three-detector network of observatories, with a detector-frame mass set to 120 M⊙ and with signal amplitude values that are consistent with plausible candidates for the next few observing runs. We show that for such systems the higher mode content will be important for interpreting coalescing binary black holes, reducing systematic bias, and computing properties of the remnant object. Even for comparable-mass binaries and at low signal amplitude, the omission of higher modes can influence posterior probability distributions. We discuss the impact of our results on source population inference and self-consistency tests of general relativity. Our work can be used to better understand asymmetric binary black hole merger events, such as GW190412. Higher modes are critical for such systems, and their omission usually produces substantial parameter biases.

关键词： Gravitational waves

Effective Combined Method for Calculation of Excitation Dielectric Sphere with a Thin Coating

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Effective Combined Method for Calculation of Excitation Diel...

2019 Radiation and Scattering of Electromagnetic Waves, RSEMW 2019

作者： Kisel, N.N. Panychev, A.I. Alpatova, A.V. Kisel, D.V. Department of Antennas and Radio Transmitting Devices Southern Federal University Institute of Radio Engineering Systems and Management Taganrog Russia Scientific Researched Institute of Communication Taganrog Russia Faculty of Computational Mathematics and Cybernetics Lomonosov Moscow State University Moscow Russia

ISBN: (纸本)9781728106892

The method of calculation for thin coatings of dielectric sphere is proposed in this paper and the boundaries of applicability of the algorithm are estimated. Approximate boundary conditions for electric and magnetic fields are used to solve the problem of exciting a sphere covered with a thin coating (shell), the dielectric sphere is described by the exact method of eigenfunctions. This approach greatly simplifies the solution algorithm and practically does not reduce the accuracy and allows you to obtain a solution in an analytical form. © 2019 IEEE.

关键词： Eigenvalues and eigenfunctions

Epidemic analysis of COVID-19 in China by dynamical modeling

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arXiv 2020年

作者： Peng, Liangrong Yang, Wuyue Zhang, Dongyan Zhuge, Changjing Hong, Liu College of Mathematics and Data Science Minjiang University Fuzhou350108 Zhou Pei-Yuan Center for Applied Mathematics Tsinghua University Beijing100084 China Beijing Institute for Scientific and Engineering Computing College of Applied Sciences Beijing University of Technology Beijing100124

The outbreak of novel coronavirus-caused pneumonia (COVID-19) in Wuhan has attracted worldwide attention. Here, we propose a generalized SEIR model to analyze this epidemic. Based on the public data of National Health Commission of China from Jan. 20th to Feb. 9th, 2020, we reliably estimate key epidemic parameters and make predictions on the inflection point and possible ending time for 5 different regions. According to optimistic estimation, the epidemics in Beijing and Shanghai will end soon within two weeks, while for most part of China, including the majority of cities in Hubei province, the success of anti-epidemic will be no later than the middle of March. The situation in Wuhan is still very severe, at least based on public data until Feb. 15th. We expect it will end up at the beginning of April. Moreover, by inverse inference, we find the outbreak of COVID-19 in Mainland, Hubei province and Wuhan all can be dated back to the end of December 2019, and the doubling time is around two days at the early stage. Copyright © 2020, The Authors. All rights reserved.

关键词： Coronavirus

A real neural network state for quantum chemistry

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arXiv 2023年

作者： Wu, Yangjun Xu, Xiansong Poletti, Dario Fan, Yi Guo, Chu Shang, Honghui Institute of Computing Technology Chinese Academy of Sciences Beijing China Science Mathematics and Technology Cluster Singapore University of Technology and Design 8 Somapah Road 487372 Singapore College of Physics and Electronic Engineering Center for Computational Sciences Sichuan Normal University Chengdu610068 China EPD Pillar Singapore University of Technology and Design 8 Somapah Road 487372 Singapore University of Science and Technology of China Hefei China Henan Key Laboratory of Quantum Information and Cryptography Henan Zhengzhou450000 China Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education Department of Physics Synergetic Innovation Center for Quantum Effects and Applications Hunan Normal University Changsha410081 China

The restricted Boltzmann machine (RBM) has been successfully applied to solve the many-electron Schrödinger equation. In this work we propose a single-layer fully connected neural network adapted from RBM and apply it to study ab initio quantum chemistry problems. Our contribution is two-fold: 1) our neural network only uses real numbers to represent the real electronic wave function, while we obtain comparable precision to RBM for various prototypical molecules;2) we show that the knowledge of the Hartree-Fock reference state can be used to systematically accelerate the convergence of the variational Monte Carlo algorithm as well as to increase the precision of the final energy. © 2023, CC BY.

关键词： Wave functions

An a posteriori error estimator for the spectral fractional power of the Laplacian

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arXiv 2022年

作者： Bulle, Raphaël Barrera, Olga Bordas, Stéphane P.A. Chouly, Franz Hale, Jack S. Institute of Computational Engineering University of Luxembourg 6 Avenue de la Fonte Esch-sur-Alzette4362 Luxembourg Université Bourgogne Franche-Comté Institut de Mathématiques de Bourgogne Dijon21078 France Center for Mathematical Modeling Department of Mathematical Engineering University of Chile IRL 2807 - CNRS Santiago Chile School of Engineering Computing and Mathematics Oxford Brookes University Oxford United Kingdom Department of Engineering Science University of Oxford Oxford United Kingdom Department of Medical Research China Medical University Hospital China Medical University Taichung Taiwan Departamento de Ingenería Matématica CI2MA Universidad de Concepción Casilla 160-C Concepción Chile

We develop a novel a posteriori error estimator for the L2 error committed by the finite element discretization of the solution of the fractional Laplacian. Our a posteriori error estimator takes advantage of the semi-discretization scheme using rational approximations which allow to reformulate the fractional problem into a family of non-fractional parametric problems. The estimator involves applying the implicit Bank-Weiser error estimation strategy to each parametric non-fractional problem and reconstructing the fractional error through the same rational approximation used to compute the solution to the original fractional problem. In addition we propose an algorithm to adapt both the finite element mesh and the rational scheme in order to balance the discretization errors. We provide several numerical examples in both two and three-dimensions demonstrating the effectivity of our estimator for varying fractional powers and its ability to drive an adaptive mesh refinement *** Codes 65N15, 65N30 © 2022, CC BY-NC-ND.

关键词： Finite element method

Analysis and approximations of dirichlet boundary control of stokes flows in the energy space

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arXiv 2020年

作者： Gong, Wei Mateos, Mariano Singler, John R. Zhang, Yangwen State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics National Center for Mathematics and Interdisciplinary Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Dpto. de Matemáticas Universidad de Oviedo Campus de Gijón Spain Department of Mathematics and Statistics Missouri University of Science and Technology RollaMO United States Department of Mathematical Science University of Delaware NewarkDE United States

We study Dirichlet boundary control of Stokes flows in 2D polygonal domains. We consider cost functionals with two different boundary control regularization terms: the L2 norm and an energy space seminorm. We prove well-posedness and regularity results for both problems, develop finite element discretizations for both problems, and prove finite element error estimates for the latter problem. The motivation to study the energy space problem follows from our analysis: we prove that the choice of the control space L2(Γ) can lead to an optimal control with discontinuities at the corners, even when the domain is convex. We observe this phenomenon in numerical experiments. This behavior does not occur in Dirichlet boundary control problems for the Poisson equation on convex polygonal domains, and may not be desirable in real applications. For the energy space problem, we derive the first order optimality conditions, and show that the solution of the control problem is more regular than the solution of the problem with the L2(Γ) regularization. We also prove a priori error estimates for the control in the energy norm, and present several numerical experiments for both control problems on convex and nonconvex domains. © 2020, CC0.

关键词： Poisson equation

Position: Bayesian deep learning is needed in the age of large-scale AI 24

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Position: Bayesian deep learning is needed in the age of lar...

Proceedings of the 41st International Conference on Machine Learning

作者： Theodore Papamarkou Maria Skoularidou Konstantina Palla Laurence Aitchison Julyan Arbel David Dunson Maurizio Filippone Vincent Fortuin Philipp Hennig José Miguel Hernández-Lobato Aliaksandr Hubin Alexander Immer Theofanis Karaletsos Mohammad Emtiyaz Khan Agustinus Kristiadi Yingzhen Li Stephan Mandt Christopher Nemeth Michael A. Osborne Tim G. J. Rudner David Rügamer Yee Whye Teh Max Welling Andrew Gordon Wilson Ruqi Zhang Department of Mathematics The University of Manchester Manchester UK Eric and Wendy Schmidt Center Broad Institute of MIT and Harvard Cambridge Spotify London UK Computational Neuroscience Unit University of Bristol Bristol UK Centre Inria de l'Université Grenoble Alpes Grenoble France Department of Statistical Science Duke University Statistics Program KAUST Saudi Arabia Helmholtz AI Munich Germany and Department of Computer Science Technical University of Munich Munich Germany and Munich Center for Machine Learning Munich Germany Tübingen AI Center University of Tübingen Tübingen Germany Department of Engineering University of Cambridge Cambridge UK Department of Mathematics University of Oslo Oslo Norway and Bioinformatics and Applied Statistics Norwegian University of Life Sciences Ås Norway Department of Computer Science ETH Zurich Switzerland Chan Zuckerberg Initiative California Center for Advanced Intelligence Project RIKEN Tokyo Japan Vector Institute Toronto Canada Department of Computing Imperial College London London UK Department of Computer Science UC Irvine Irvine Department of Mathematics and Statistics Lancaster University Lancaster UK Department of Engineering Science University of Oxford Oxford UK Center for Data Science New York University New York Munich Center for Machine Learning Munich Germany and Department of Statistics LMU Munich Munich Germany DeepMind London UK and Department of Statistics University of Oxford Oxford UK Informatics Institute University of Amsterdam Amsterdam Netherlands Courant Institute of Mathematical Sciences and Center for Data Science Computer Science Department New York University New York Department of Computer Science Purdue University West Lafayette

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential.

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DeePMD-kit v2: A software package for Deep Potential models

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arXiv 2023年

作者： Zeng, Jinzhe Zhang, Duo Lu, Denghui Mo, Pinghui Li, Zeyu Chen, Yixiao Rynik, Marián Huang, Li'ang Li, Ziyao Shi, Shaochen Wang, Yingze Ye, Haotian Tuo, Ping Yang, Jiabin Ding, Ye Li, Yifan Tisi, Davide Zeng, Qiyu Bao, Han Xia, Yu Huang, Jiameng Muraoka, Koki Wang, Yibo Chang, Junhan Yuan, Fengbo Bore, Sigbjørn Løland Cai, Chun Lin, Yinnian Wang, Bo Xu, Jiayan Zhu, Jia-Xin Luo, Chenxing Zhang, Yuzhi Goodall, Rhys E.A. Liang, Wenshuo Singh, Anurag Kumar Yao, Sikai Zhang, Jingchao Wentzcovitch, Renata Han, Jiequn Liu, Jie Jia, Weile York, Darrin M. Weinan, E. Car, Roberto Zhang, Linfeng Wang, Han Laboratory for Biomolecular Simulation Research Institute for Quantitative Biomedicine Department of Chemistry and Chemical Biology Rutgers University PiscatawayNJ08854 United States AI for Science Institute Beijing100080 China DP Technology Beijing100080 China Academy for Advanced Interdisciplinary Studies Peking University Beijing100871 China HEDPS CAPT College of Engineering Peking University Beijing100871 China College of Electrical and Information Engineering Hunan University Changsha China Yuanpei College Peking University Beijing100871 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States Department of Experimental Physics Comenius University Mlynská Dolina F2 Bratislava842 48 Slovakia Center for Quantum Information Institute for Interdisciplinary Information Sciences Tsinghua University Beijing100084 China Center for Data Science Peking University Beijing100871 China ByteDance Research Zhonghang Plaza No. 43 North 3rd Ring West Road Haidian District Beijing China College of Chemistry and Molecular Engineering Peking University Beijing100871 China Baidu Inc. Beijing China Key Laboratory of Structural Biology of Zhejiang Province School of Life Sciences Westlake University Zhejiang Hangzhou China Westlake AI Therapeutics Lab Westlake Laboratory of Life Sciences and Biomedicine Zhejiang Hangzhou China Department of Chemistry Princeton University PrincetonNJ08544 United States SISSA Scuola Internazionale Superiore di Studi Avanzati Trieste34136 Italy Laboratory of Computational Science and Modeling Institute of Materials École Polytechnique Fédérale de Lausanne Lausanne1015 Switzerland Department of Physics National University of Defense Technology Hunan Changsha410073 China State Key Lab of Processors Institute of Computing Technology Chinese Academy of Sciences Beijing China University of Chinese Academy of Sciences Beijing China School of Electronics Engineerin

DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials (MLP) known as Deep Potential (DP) models. This package, which was released in 2017, has been widely used in the fields of physics, chemistry, biology, and material science for studying atomistic systems. The current version of DeePMD-kit offers numerous advanced features such as DeepPot-SE, attention-based and hybrid descriptors, the ability to fit tensile properties, type embedding, model deviation, Deep Potential - Range Correction (DPRc), Deep Potential Long Range (DPLR), GPU support for customized operators, model compression, non-von Neumann molecular dynamics (NVNMD), and improved usability, including documentation, compiled binary packages, graphical user interfaces (GUI), and application programming interfaces (API). This article presents an overview of the current major version of the DeePMD-kit package, highlighting its features and technical details. Additionally, the article benchmarks the accuracy and efficiency of different models and discusses ongoing developments. © 2023, CC BY-NC-ND.

关键词： Molecular dynamics

Multiscale Modelling of the Antiferromagnet Mn2Au: From ab-initio to Micromagnetics

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arXiv 2022年

作者： Hirst, Joel Atxitia, Unai Ruta, Sergiu Jackson, Jerome Petit, Leon Ostler, Thomas Materials & Engineering Research Institute Sheffield Hallam University Howard Street SheffieldS1 1WB United Kingdom Dahlem Center for Complex Quantum Systems and Fachbereich Physik Freie Universitat Berlin Berlin14195 Germany Instituto de Ciencia de Materiales de Madrid CSIC Cantoblanco Madrid28049 Spain Scientific Computing Department STFC Daresbury Laboratory Warrington WA4 4AD United Kingdom Department of Physics & Mathematics University of Hull HullHU6 7RX United Kingdom Department of Engineering and Mathematics Sheffield Hallam University Howard Street SheffieldS1 1WB United Kingdom

Antiferromagnets (AFMs) are strong candidates for the future spintronic and memory applications largely because of their inherently fast dynamics and lack of stray fields, with Mn2Au being one of the most promising. For the numerical modelling of magnetic material properties, it is common to use ab-initio methods, atomistic models and micromagnetics. However, each method alone describes the physics within certain limits. Multiscale methods bridging the gap between these three approaches have been already proposed for ferromagnetic materials. Here, we present a complete multiscale model of the AFM Mn2Au as an exemplar material, starting with results from ab-initio methods going via atomistic spin dynamics (ASD) to an AFM Landau-Lifshitz-Bloch (AFM-LLB) model. Firstly, bulk Mn2Au is modelled using a classical spin Hamiltonian constructed based on earlier first-principles calculations. Secondly, this spin model is used in the stochastic Landau-Lifshitz-Gilbert (LLG) to calculate temperature-dependent equilibrium properties, such as magnetization and magnetic susceptibilities. Thirdly, the temperature dependent micromagnetic parameters are used in the AFM-LLB. We validate our approach by comparing the ASD and AFM-LLB models for three paradigmatic cases;(i) Damped magnetic oscillations, (ii) magnetization dynamics following a heat pulse resembling pump-probe experiments, (iii) magnetic domain wall motion under thermal gradients. © 2022, CC BY.

关键词： Magnetization