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arXiv 2025年

作者： Zhan, Yongtao Ding, Zhiyan Huhn, Jakob Gray, Johnnie Preskill, John Chan, Garnet Kin-Lic Lin, Lin Institute for Quantum Information and Matter California Institute of Technology United States Division of Physics Mathematics and Astronomy California Institute of Technology United States Department of Mathematics University of California Berkeley United States Department of Physics Arnold Sommerfeld Center for Theoretical Physics Ludwig-Maximilians-Universität München Germany Division of Chemistry and Chemical Engineering California Institute of Technology United States Department of Physics California Institute of Technology United States AWS Center for Quantum Computing Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory United States

Inspired by natural cooling processes, dissipation has become a promising approach for preparing low-energy states of quantum systems. However, the potential of dissipative protocols remains unclear beyond certain commuting Hamiltonians. This work provides significant analytical and numerical insights into the power of dissipation for preparing the ground state of non-commuting Hamiltonians. For quasi-free dissipative dynamics, including certain 1D spin systems with boundary dissipation, our results reveal a new connection between the mixing time in trace distance and the spectral properties of a non-Hermitian Hamiltonian, leading to an explicit and sharp bound on the mixing time that scales polynomially with system size. For more general spin systems, we develop a tensor network-based algorithm for constructing the Lindblad jump operator and for simulating the dynamics. Using this algorithm, we demonstrate numerically that dissipative ground state preparation protocols can achieve rapid mixing for certain 1D local Hamiltonians under bulk dissipation, with a mixing time that scales logarithmically with the system size. We then prove the rapid mixing result for certain weakly interacting spin and fermionic systems in arbitrary dimensions, extending recent results for high-temperature quantum Gibbs samplers to the zero-temperature regime. Our theoretical approaches are applicable to systems with singular stationary states, and are thus expected to have applications beyond the specific systems considered in this study. © 2025, CC BY.

关键词： Dynamics

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Improved time integration for phase-field crystal models of solidification

arXiv

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arXiv 2022年

作者： Punke, Maik Wise, Steven M. Voigt, Axel Salvalaglio, Marco Institute of Scientific Computing TU Dresden Dresden01062 Germany Department of Mathematics The University of Tennessee KnoxvilleTN37996 United States Dresden Center for Computational Materials Science TU Dresden Dresden01062 Germany

We optimize a numerical time-stabilization routine for the phase-field crystal (PFC) models of solidification. By numerical experiments, we showcase that our approach can improve the accuracy of underlying time integration schemes by a few orders of magnitude. We investigate different time integration schemes. Moreover, as a prototypical example for applications, we extend our numerical approach to a PFC model of solidification with an explicit temperature coupling. Copyright © 2022, The Authors. All rights reserved.

关键词： Solidification

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Explicit temperature coupling in phase-field crystal models of solidification

arXiv

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arXiv 2022年

We present a phase-field crystal (PFC) model for solidification that accounts for thermal transport and a temperature-dependent lattice parameter. Elasticity effects are characterized through the continuous elastic field computed from the microscopic density field. We showcase the model capabilities via selected numerical investigations which focus on the prototypical growth of two-dimensional crystals from the melt, resulting in faceted shapes and dendrites. This work sets the grounds for a comprehensive mesoscale model of solidification including thermal expansion. Copyright © 2022, The Authors. All rights reserved.

关键词： Heat flux

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DPA-2:a large atomic model as a multitask learner

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npj computational Materials 2024年第1期10卷 185-199页

作者： Duo Zhang Xinzijian Liu Xiangyu Zhang Chengqian Zhang Chun Cai Hangrui Bi Yiming Du Xuejian Qin Anyang Peng Jiameng Huang Bowen Li Yifan Shan Jinzhe Zeng Yuzhi Zhang Siyuan Liu Yifan Li Junhan Chang Xinyan Wang Shuo Zhou Jianchuan Liu Xiaoshan Luo Zhenyu Wang Wanrun Jiang Jing Wu Yudi Yang Jiyuan Yang Manyi Yang Fu-Qiang Gong Linshuang Zhang Mengchao Shi Fu-Zhi Dai Darrin M.York Shi Liu Tong Zhu Zhicheng Zhong Jian Lv Jun Cheng Weile Jia Mohan Chen Guolin Ke Weinan E Linfeng Zhang Han Wang AI for Science Institute BeijingP.R.China DP Technology BeijingP.R.China Academy for Advanced Interdisciplinary Studies Peking UniversityBeijingP.R.China State Key Lab of Processors Institute of Computing TechnologyChinese Academy of SciencesBeijingP.R.China University of Chinese Academy of Sciences BeijingP.R.China HEDPS CAPTCollege of EngineeringPeking UniversityBeijingP.R.China Ningbo Institute of Materials Technology and Engineering Chinese Academy of SciencesNingboP.R.China CAS Key Laboratory of Magnetic Materials and Devices and Zhejiang Province Key Laboratory of Magnetic Materials and Application Technology Chinese Academy of SciencesNingboP.R.China School of Electronics Engineering and Computer Science Peking UniversityBeijingP.R.China Shanghai Engineering Research Center of Molecular Therapeutics&New Drug Development School of Chemistry and Molecular EngineeringEast China Normal UniversityShanghaiP.R.China Laboratory for Biomolecular Simulation Research Institute for Quantitative Biomedicine and Department of Chemistry and Chemical BiologyRutgers UniversityPiscatawayNJUSA Department of Chemistry Princeton UniversityPrincetonNJUSA College of Chemistry and Molecular Engineering Peking UniversityBeijingP.R.China Yuanpei College Peking UniversityBeijingP.R.China School of Electrical Engineering and Electronic Information Xihua UniversityChengduP.R.China State Key Laboratory of Superhard Materials College of PhysicsJilin UniversityChangchunP.R.China Key Laboratory of Material Simulation Methods&Software of Ministry of Education College of PhysicsJilin UniversityChangchunP.R.China International Center of Future Science Jilin UniversityChangchunP.R.China Key Laboratory for Quantum Materialsof Zhejiang Province Department of PhysicsSchool of ScienceWestlake UniversityHangzhouP.R.China Atomistic Simulations Italian Institute of TechnologyGenovaItaly State Key Laboratory of Physical Chemistry of Solid Surface iChEMCollege of Chemistry and Chemical EngineeringXiame

The rapid advancements in artificial intelligence(AI)are catalyzing transformative changes in atomic modeling,simulation,and ***-driven potential energy models havedemonstrated the capability to conduct large-scale,long-duration simulations with the accuracy of ab initio electronic structure ***,the model generation process remains a bottleneck for large-scale *** propose a shift towards a model-centric ecosystem,wherein a large atomic model(LAM),pretrained across multiple disciplines,can be efficiently fine-tuned and distilled for various downstream tasks,thereby establishing a new framework for molecular *** this study,we introduce the DPA-2 architecture as a prototype for ***-trained on a diverse array of chemical and materials systemsusing a multi-task approach,DPA-2demonstrates superior generalization capabilities across multiple downstream tasks compared to the traditional single-task pre-training and fine-tuning *** approach sets the stage for the development and broad application of LAMs in molecular and materials simulation research.

关键词： DPA establishing thereby

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Boundary layer challenges: A comparative analysis of two efficient meshless approaches

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Partial Differential Equations in Applied mathematics 2024年 10卷

作者： Alshammari, Abdulrahman Obaid Khan, Muhammad Nawaz Ahmad, Imtiaz Department of Mathematics College of Science Jouf University Sakaka 72388 Saudi Arabia Mathematics in Applied Sciences and Engineering Research Group Scientific Research Center Al-Ayen University Nasiriyah 64001 Iraq Institute of Informatics and Computing in Energy (IICE) Universiti Tenaga Nasional Kajang Selangor Malaysia

This article presents two meshless computational techniques: the radial basis function (RBF) method and the polynomial method, for numerically analyzing boundary layer problems, with a specific focus on singularly perturbed two-point boundary value problems. Both of these suggested meshless methods offer an advantage over globally supported meshless techniques, as they involve approximating derivatives by employing a constrained set of nodes located in the neighborhood of each collocation node. As a result, they demand significantly reduced computational effort compared to the globally supported collocation method. To assess the accuracy of these methods, we employ the maximum error norm, and the results are presented in the form of tables and graphs. The simulation results demonstrate that both approaches exhibit robust performance in addressing the investigated boundary layer problems. © 2024 The Author(s)

关键词： Boundary layer problems Meshless computational techniques Polynomial method Radial basis function method

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A highly accurate perfectly-matched-layer boundary integral equation solver for acoustic layered-medium problems

arXiv

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arXiv 2022年

作者： Lu, Wangtao Xu, Liwei Yin, Tao Zhang, Lu School of Mathematical Sciences Zhejiang University Zhejiang Hangzhou310027 China School of Mathematical Sciences University of Electronic Science and Technology of China Sichuan Chengdu611731 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

Based on the perfectly matched layer (PML) technique, this paper develops a high-accuracy boundary integral equation (BIE) solver for acoustic scattering problems in locally defected layered media in both two and three dimensions. The original scattering problem is truncated onto a bounded domain by the PML. Assuming the vanishing of the scattered field on the PML boundary, we derive BIEs on local defects only in terms of using PML-transformed free-space Green’s function, and the four standard integral operators: single-layer, double-layer, transpose of double-layer, and hypersingular boundary integral operators. The hyper-singular integral operator is transformed into a combination of weakly-singular integral operators and tangential derivatives. We develop a high-order Chebyshev-based rectangular-polar singular-integration solver to discretize all weakly-singular integrals. Numerical experiments for both two- and three-dimensional problems are carried out to demonstrate the accuracy and efficiency of the proposed solver. Copyright © 2022, The Authors. All rights reserved.

关键词： Boundary integral equations

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A monotone finite volume method for time fractional Fokker-Planck equations

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Science China mathematics 2019年第4期62卷 783-794页

作者： Yingjun Jiang Xuejun Xu School of Mathematics and Statistics Changsha University of Science and Technology Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematical Sciences Tongji University

We develop a monotone finite volume method for the time fractional Fokker-Planck equations and theoretically prove its unconditional stability. We show that the convergence rate of this method is of order 1 in the space and if the space grid becomes sufficiently fine, the convergence rate can be improved to order *** results are given to support our theoretical findings. One characteristic of our method is that it has monotone property such that it keeps the nonnegativity of some physical variables such as density, concentration,etc.

关键词： time fractional Fokker-Planck equations finite volume methods monotone convergence

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A Unified Framework for Exploratory Learning-Aided Community Detection Under Topological Uncertainty

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IEEE Transactions on Network Science and engineering 2025年

作者： Hou, Yu Tran, Cong Li, Ming Shin, Won-Yong Yonsei University School of Mathematics and Computing Computational Science and Engineering Seoul03722 Korea Republic of Posts and Telecommunications Institute of Technology Faculty of Information Technology Hanoi100000 Viet Nam Zhejiang Institute of Optoelectronics Jinhua321004 China Zhejiang Normal University Zhejiang Key Laboratory of Intelligent Education Technology and Application Jinhua321004 China Graduate School of Artificial Intelligence Pohang37673 Korea Republic of

In social networks, the discovery of community structures has received considerable attention as a fundamental problem in various network analysis tasks. However, due to privacy concerns or access restrictions, the network structure is often uncertain, thereby rendering established community detection approaches ineffective without costly network topology acquisition. To tackle this challenge, we present META-CODE, a unified framework for detecting overlapping communities via exploratory learning aided by easy-to-collect node metadata when networks are topologically unknown (or only partially known). Specifically, META-CODE consists of three iterative steps in addition to the initial network inference step: 1) node-level community-affiliation embeddings based on graph neural networks (GNNs) trained by our new reconstruction loss, 2) network exploration via community-affiliation-based node queries, and 3) network inference using an edge connectivity-based Siamese neural network model from the explored network. Through extensive experiments on three real-world datasets including two large networks, we demonstrate: (a) the superiority of META-CODE over benchmark community detection methods, achieving remarkable gains up to 65.55% on the Facebook dataset over the best competitor among our selected competitive methods in terms of normalized mutual information (NMI), (b) the impact of each module in META-CODE, (c) the effectiveness of node queries in META-CODE based on empirical evaluations and theoretical findings, and (d) the convergence of the inferred network. © 2013 IEEE.

关键词： Structured Query Language

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Improved accuracy of continuum surface flux models for metal additive manufacturing melt pool simulations

arXiv

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arXiv 2024年

作者： Much, Nils Schreter-Fleischhacker, Magdalena Munch, Peter Kronbichler, Martin Wall, Wolfgang A. Meier, Christoph Institute for Computational Mechanics Technical University of Munich Boltzmannstrasse 15 Garching85748 Germany Department of Information Technology Uppsala University Box 337 Uppsala75105 Sweden Institute for High-Performance Scientific Computing University of Augsburg Universitätsstraße 12a Augsburg86159 Germany Faculty of Mathematics Ruhr University Bochum Universitätsstraße 150 Bochum44780 Germany

computational modeling of the melt pool dynamics in laser-based powder bed fusion metal additive manufacturing (PBF-LB/M) promises to shed light on fundamental mechanisms of defect generation. These processes are accompanied by rapid evaporation so that the evaporation-induced recoil pressure and cooling arise as major driving forces for fluid dynamics and temperature evolution. The magnitude of these interface fluxes depends exponentially on the melt pool surface temperature, which, therefore, has to be predicted with high accuracy. The present work utilizes a diffuse interface finite element model based on a continuum surface flux (CSF) description of interface fluxes to study dimensionally reduced thermal two-phase problems representative for PBF-LB/M in a finite element framework. It is demonstrated that the extreme temperature gradients combined with the high ratios of material properties between metal and ambient gas lead to significant errors in the interface temperatures and fluxes when classical CSF approaches, along with typical interface thicknesses and discretizations, are applied. It is expected that this finding is also relevant for other types of diffuse interface PBF-LB/M melt pool models. A novel parameter-scaled CSF approach is proposed, which is constructed to yield a smoother temperature field in the diffuse interface region, significantly increasing the solution accuracy. The interface thickness required to predict the temperature field with a given level of accuracy is less restrictive by at least one order of magnitude for the proposed parameter-scaled approach compared to classical CSF, drastically reducing computational costs. Finally, we showcase the general applicability of the parameter-scaled CSF to a 3D simulation of stationary laser melting of PBF-LB/M considering the fully coupled thermo-hydrodynamic multi-phase problem, including phase change. Copyright © 2024, The Authors. All rights reserved.

关键词： Hydrodynamics

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A FOURTH-ORDER UNFITTED CHARACTERISTIC FINITE ELEMENT METHOD FOR SOLVING THE ADVECTION-DIFFUSION EQUATION ON TIME-VARYING DOMAINS

arXiv

引用

arXiv 2021年

作者： Ma, Chuwen Zhang, Qinghai Zheng, Weiying School of Mathematical Science University of Chinese Academy of Sciences China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences Zhejiang University 38 Zheda Road Zhejiang Province Hangzhou310027 China LSEC NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

We propose a fourth-order unfitted characteristic finite element method to solve the advection-diffusion equation on time-varying domains. Based on a characteristic-Galerkin formulation, our method combines the cubic MARS method for interface tracking, the fourth-order backward differentiation formula for temporal integration, and an unfitted finite element method for spatial discretization. Our convergence analysis includes errors of discretely representing the moving boundary, tracing boundary markers, and the spatial discretization and the temporal integration of the governing equation. Numerical experiments are performed on a rotating domain and a severely deformed domain to verify our theoretical results and to demonstrate the optimal convergence of the proposed method. Copyright © 2021, The Authors. All rights reserved.

关键词： Finite element method

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