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arXiv 2024年

作者： Zheng, Nanyi Cai, Xiaofeng Qiu, Jing-Mei Qiu, Jianxian Department of Mathematical Sciences University of Delaware NewarkDE19716 United States Research Center for Mathematics Advanced Institute of Natural Sciences Beijing Normal University Zhuhai519087 China Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science BNU-HKBU United International College Zhuhai519087 China School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University Fujian Xiamen361005 China

In this paper, we develop high-order, conservative, non-splitting Eulerian-Lagrangian (EL) Runge-Kutta (RK) finite volume (FV) weighted essentially non-oscillatory (WENO) schemes for convection-diffusion equations. The proposed EL-RK-FV-WENO scheme defines modified characteristic lines and evolves the solution along them, significantly relaxing the time-step constraint for the convection term. The main algorithm design challenge arises from the complexity of constructing accurate and robust reconstructions on dynamically varying Lagrangian meshes. This reconstruction process is needed for flux evaluations on time-dependent upstream quadrilaterals and time integrations along moving characteristics. To address this, we propose a strategy that utilizes a WENO reconstruction on a fixed Eulerian mesh for spatial reconstruction, and updates intermediate solutions on the Eulerian background mesh for implicit-explicit RK temporal integration. This strategy leverages efficient reconstruction and remapping algorithms to manage the complexities of polynomial reconstructions on time-dependent quadrilaterals, while ensuring local mass conservation. The proposed scheme ensures mass conservation due to the flux-form semi-discretization and the mass-conservative reconstruction on both background and upstream cells. Extensive numerical tests have been performed to verify the effectiveness of the proposed scheme. © 2024, CC BY.

关键词： Mesh generation

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First-principles determination of the phonon-point defect scattering and thermal transport due to fission products in ThO2

arXiv

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arXiv 2023年

作者： Malakkal, Linu Katre, Ankita Zhou, Shuxiang Jiang, Chao Hurley, David H. Marianetti, Chris A. Khafizov, Marat Computational Mechanics and Materials Department Idaho National Laboratory Idaho FallsID83415 United States Department of Scientific Computing Modeling and Simulation SP Pune University Pune411007 India Idaho National Laboratory Idaho FallsID83415 United States Department of Applied Physics and Applied Mathematics Columbia University 500 West 120th Street New YorkNY10027 United States Department of Mechanical and Aerospace Engineering The Ohio State University 201 West 19th Ave ColumbusOH43210 United States

This work presents the first-principles calculations of the lattice thermal conductivity degradation due to point defects in thorium dioxide using an iterative solution of the Peirels-Boltzmann transport equation. We have used the non-perturbative Green's function methodology to compute the phononpoint defect scattering rates that consider the local distortion around the point defect, including the mass difference changes, interatomic force constants, and structural relaxation near the point defects. The point defects considered in this work include the vacancy of thorium (VTh) and oxygen (VO), substitutions of helium (HeTh), krypton (KrTh), zirconium (ZrTh), iodine (ITh) and xenon (XeTh) in the thorium site, and the three different configurations of the Schottky defects. The results of the phonon-defect scattering rate reveal that, among all the considered intrinsic defects, the thorium vacancy and helium substitution in the thorium site scatter the phonon most due to the substantial changes in the force constant and structural distortions. The scattering of phonons due to the substitutional defects unveils that the zirconium atom scatters phonons the least, followed by xenon, iodine, krypton, and helium. This is contrary to the intuition that the scattering strength follows HeTh > KrTh > ZrTh > ITh > XeTh based on the mass difference. This striking difference in the zirconium phonon scattering is due to the local chemical environment changes. Zirconium is an electropositive element with valency similar to thorium and, therefore, can bond with the oxygen atoms, thus creating less force constant variance compared to iodine, an electronegative element, and the noble gases helium, xenon, and krypton. These results can serve as a benchmark for analytical models and help the engineering-scale modeling effort for nuclear design. © 2023, CC BY.

关键词： Boltzmann equation

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A Hybrid Deep Neural Operator/Finite Element Method for Ice-Sheet modeling

arXiv

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arXiv 2023年

作者： He, QiZhi Perego, Mauro Howard, Amanda A. Karniadakis, George Em Stinis, Panos Department of Civil Environmental and Geo- Engineering University of Minnesota 500 Pillsbury Drive S.E. MinneapolisMN55455 United States Center for Computing Research Sandia National Laboratories P.O. Box 5800 AlbuquerqueNM87185 United States Advanced Computing Mathematics and Data Division Pacific Northwest National Laboratory RichlandWA99352 United States Division of Applied Mathematics School of Engineering Brown University 182 George Street ProvidenceRI02912 United States

One of the most challenging and consequential problems in climate modeling is to provide probabilistic projections of sea level rise. A large part of the uncertainty of sea level projections is due to uncertainty in ice sheet dynamics. At the moment, accurate quantification of the uncertainty is hindered by the cost of ice sheet computational models. In this work, we develop a hybrid approach to approximate existing ice sheet computational models at a fraction of their cost. Our approach consists of replacing the finite element model for the momentum equations for the ice velocity, the most expensive part of an ice sheet model, with a Deep Operator Network, while retaining a classic finite element discretization for the evolution of the ice thickness. We show that the resulting hybrid model is very accurate and it is an order of magnitude faster than the traditional finite element model. Further, a distinctive feature of the proposed model compared to other neural network approaches, is that it can handle high-dimensional parameter spaces (parameter fields) such as the basal friction at the bed of the glacier, and can therefore be used for generating samples for uncertainty quantification. We study the impact of hyper-parameters, number of unknowns and correlation length of the parameter distribution on the training and accuracy of the Deep Operator Network on a synthetic ice sheet model. We then target the evolution of the Humboldt glacier in Greenland and show that our hybrid model can provide accurate statistics of the glacier mass loss and can be effectively used to accelerate the quantification of uncertainty. © 2023, CC BY.

关键词： Finite element method

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Direct determination of optimal real-space orbitals for correlated electronic structure of molecules

arXiv

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arXiv 2022年

作者： Valeev, Edward F. Harrison, Robert J. Holmes, Adam A. Peterson, Charles C. Penchoff, Deborah A. Department of Chemistry Virginia Tech BlacksburgVA24061 United States Department of Applied Mathematics & Statistics Stony Brook University Stony BrookNY11794 United States Office of Advanced Research Computing University of California Los AngelesCA90095 United States UT Innovative Computing Laboratory University of Tennessee KnoxvilleTN37996 United States

We demonstrate how to determine numerically nearly exact orthonormal orbitals that are optimal for evaluation of the energy of arbitrary (correlated) states of atoms and molecules by minimization of the energy Lagrangian. Orbitals are expressed in real space using a multiresolution spectral element basis that is refined adaptively to achieve the user-specified target precision while avoiding the ill-conditioning issues that plague AO basis set expansions traditionally used for correlated models of molecular electronic structure. For light atoms, the orbital solver, in conjunction with a variational electronic structure model [selected Configuration Interaction(CI)] provides energies of comparable precision to a state-of-the-art atomic CI solver. The computed electronic energies of atoms and molecules are significantly more accurate than the counterparts obtained with the Gaussian AO bases of the same rank, and can be determined even when linear dependence issues preclude the use of the AO bases. It is feasible to optimize more than 100 fully-correlated numerical orbitals on a single computer node, and significant room exists for additional improvement. These findings suggest that the real-space orbital representations might be the preferred alternative to AO representations for high-end models of correlated electronic states of molecules and materials. Copyright © 2022, The Authors. All rights reserved.

关键词： Electronic structure

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Transformative effects of ChatGPT on modern education: Emerging Era of AI Chatbots

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Internet of Things and Cyber-Physical Systems 2024年第1期4卷 19-23页

作者： Gill, Sukhpal Singh Xu, Minxian Patros, Panos Wu, Huaming Kaur, Rupinder Kaur, Kamalpreet Fuller, Stephanie Singh, Manmeet Arora, Priyansh Parlikad, Ajith Kumar Stankovski, Vlado Abraham, Ajith Ghosh, Soumya K. Lutfiyya, Hanan Kanhere, Salil S. Bahsoon, Rami Rana, Omer Dustdar, Schahram Sakellariou, Rizos Uhlig, Steve Buyya, Rajkumar School of Electronic Engineering and Computer Science Queen Mary University of London London United Kingdom Shenzhen Institute of Advanced Technology Chinese Academy of Sciences Shenzhen China Raygun Performance Monitoring Wellington New Zealand Center for Applied Mathematics Tianjin University Tianjin China Department of Science Kings Education London United Kingdom Cymax Group Technologies BC Canada QM Academy Queen Mary University of London London United Kingdom Jackson School of Geosciences University of Texas at Austin AustinTX United States Centre for Climate Change Research Indian Institute of Tropical Meteorology Pune India Microsoft Hyderabad India Institute for Manufacturing Department of Engineering University of Cambridge Cambridge United Kingdom Faculty of Computer and Information Science University of Ljubljana Ljubljana Slovenia Machine Intelligence Research Labs AuburnWA United States Faculty of Computing and Data Science FLAME University Maharashtra Pune India Department of Computer Science and Engineering Indian Institute of Technology Kharagpur India Department of Computer Science University of Western Ontario London Canada Sydney Australia School of Computer Science University of Birmingham United Kingdom School of Computer Science and Informatics Cardiff University Cardiff United Kingdom Distributed Systems Group Vienna University of Technology Vienna Austria Department of Computer Science University of Manchester Oxford Road Manchester United Kingdom Laboratory School of Computing and Information Systems The University of Melbourne Australia

ChatGPT, an AI-based chatbot, offers coherent and useful replies based on analysis of large volumes of data. In this article, leading academics, scientists, distinguish researchers and engineers discuss the transformative effects of ChatGPT on modern education. This research discusses ChatGPT capabilities and its use in the education sector, identifies potential concerns and challenges. Our preliminary evaluation shows that ChatGPT perform differently in different subject areas including finance, coding, maths, and general public queries. While ChatGPT has the ability to help educators by creating instructional content, offering suggestions and acting as an online educator to learners by answering questions, transforming education through smartphones and IoT gadgets, and promoting group work, there are clear drawbacks in its use, such as the possibility of producing inaccurate or false data and circumventing duplicate content (plagiarism) detectors where originality is essential. The often reported "hallucinations" within GenerativeAI in general, and also relevant for ChatGPT, can render its use of limited benefit where accuracy is essential. What ChatGPT lacks is a stochastic measure to help provide sincere and sensitive communication with its users. Academic regulations and evaluation practices used in educational institutions need to be updated, should ChatGPT be used as a tool in education. To address the transformative effects of ChatGPT on the learning environment, educating teachers and students alike about its capabilities and limitations will be crucial. © 2023 The Authors

关键词： Machine learning

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

引用

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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Global-aware beam search for neural abstractive summarization 21

Global-aware beam search for neural abstractive summarizatio...

引用

Proceedings of the 35th International Conference on Neural Information Processing Systems

作者： Ye Ma Zixun Lan Lu Zong Kaizhu Huang Department of Financial and Actuarial Mathematics School of Science and Laboratory for Intelligent Computing and Financial Technology Xi'an Jiaotong-Liverpool University SIP Suzhou China Department of Applied Mathematics School of Science and Laboratory for Intelligent Computing and Financial Technology Xi'an Jiaotong-Liverpool University SIP Suzhou China Department of Intelligent Science School of Advanced Technology

ISBN: (纸本)9781713845393

This study develops a calibrated beam-based algorithm with awareness of the global attention distribution for neural abstractive summarization, aiming to improve the local optimality problem of the original beam search in a rigorous way. Specifically, a novel global protocol is proposed based on the attention distribution to stipulate how a global optimal hypothesis should attend to the source. A global scoring mechanism is then developed to regulate beam search to generate summaries in a near-global optimal fashion. This novel design enjoys a distinctive property, i.e., the global attention distribution could be predicted before inference, enabling step-wise improvements on the beam search through the global scoring mechanism. Extensive experiments on nine datasets show that the global (attention)-aware inference significantly improves state-of-the-art summarization models even using empirical hyper-parameters. The algorithm is also proven robust as it remains to generate meaningful texts with corrupted attention distributions. The codes and a comprehensive set of examples are available.

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A Phase-Field-Based Multiple-Relaxation-Time Lattice Boltzmann Method for Incompressible Multiphase Flows with Density and Viscosity Contrasts

SSRN

引用

SSRN 2022年

作者： Yuan, Xiaolei Wu, Yao Zhang, Chunhua Chai, Zhenhua Shi, Baochang College of Mathematics and Information Science Hebei University Baoding071002 China Institute of Interdisciplinary Research for Mathematics and Applied Science School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Department of Mechanics and Aerospace Engineering Southern University of Science and Technology Guangdong Shenzhen518055 China

In this work, we present a unified framework of phase-field-based multiple-relaxation-time lattice Boltzmann (MRT-LB) method for incompressible multiphase flows with density and viscosity contrasts where a block-lower-triangular relaxation matrix is introduced. The present framework includes the classic MRT-LB model and central-moments-based LB model (CLBM, a particular version of the MRT-LB model). The governing equations of incompressible multiphase flows can be reproduced precisely through the direct Taylor expansion method at the second-order of expansion parameters. In this work, the pressure $p$ is re-estimated, and we prove that the present pressure expression is suitable for classic MRT model, CLBM and various lattice structures. In addition, theoretical analysis and modeling are both carried out in the velocity space. As a result, the present model has a similar structure to the traditional Bhatnagar-Gross-Krook (BGK) model and is very easy to analyze and implement. We then test the present model (mainly CLBM) by five classic physical problems. The results show that the present model is found to be accurate and has better numerical stability over the BGK model, and has the ability to simulate multiphase flow problems with large density ratio ($1000$). © 2022, The Authors. All rights reserved.

关键词： Multiphase flow

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Vibrational Levels of a Generalized Morse Potential

arXiv

引用

arXiv 2022年

作者： Qadeer, Saad Santis, Garrett D. Stinis, Panos Xantheas, Sotiris S. Advanced Computing Mathematics and Data Division Pacific Northwest National Laboratory 902 Battelle Boulevard P.O. Box 999 MS K1-83 RichlandWA99352 United States Department of Chemistry University of Washington SeattleWA98195 United States Department of Applied Mathematics University of Washington SeattleWA98195 United States

A Generalized Morse Potential (GMP) is an extension of the Morse Potential (MP) with an additional exponential term and an additional parameter that compensate for MP's erroneous behavior in the long range part of the interaction potential. Because of the additional term and parameter, the vibrational levels of the GMP cannot be solved analytically, unlike the case for the MP. We present several numerical approaches for solving the vibrational problem of the GMP based on Galerkin methods, namely the Laguerre Polynomial Method (LPM), the Symmetrized Laguerre Polynomial Method (SLPM) and the Polynomial Expansion method (PEM) and apply them to the vibrational levels of the homonuclear diatomic molecules B2, O2 and F2, for which high level theoretical Full CI potential energy surfaces and experimentally measured vibrational levels have been reported. Overall the LPM produces vibrational states for the GMP that are converged to within spectroscopic accuracy of 0.01 cm−1 in between 1 and 2 orders of magnitude faster and with much fewer basis functions/grid points than the Colbert-Miller Discrete Variable Representation (CM-DVR) method for the three homonuclear diatomic molecules examined in this study. A python library that fits and solves the GMP and similar potentials can be downloaded from https://***/gds001uw/*** Codes 65L15 Copyright © 2022, The Authors. All rights reserved.

关键词： Morse potential

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Data-driven method to learn the most probable transition pathway and stochastic differential equations

arXiv

引用

arXiv 2021年

作者： Chen, Xiaoli Duan, Jinqiao Hu, Jianyu Li, Dongfang School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Department of Mathematics National University of Singapore 119077 Singapore Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Department of Applied Mathematics College of Computing Illinois Institute of Technology ChicagoIL60616 United States

Transition phenomena between metastable states play an important role in complex systems due to noisy fluctuations. We introduce the Onsager-Machlup theory and the Freidlin-Wentzell theory to quantify rare events in stochastic differential equations. By the variational principle, the most probable transition pathway is the minimizer of the action functional, which is governed by the Euler-Lagrange equation. In this paper, the physics-informed neural networks (PINNs) are presented to compute the most probable transition pathway through computing the Euler-Lagrange equation. The convergence result for the empirical loss is obtained for the forward problem. Then we investigate the inverse problem to extract the stochastic differential equation from the most probable transition pathway data. Finally, several numerical experiments are presented to verify the effectiveness of our methods. Copyright © 2021, The Authors. All rights reserved.

关键词： Inverse problems

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