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arXiv 2024年

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

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. © 2024, CC BY-NC-ND.

关键词： Large datasets

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Benchmark computations for the polarization tensor characterization of small conducting objects

arXiv

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arXiv 2021年

作者： Amad, A.A.S. Ledger, Paul D. Betcke, T. Praetorius, D. Zienkiewicz Centre for Computational Engineering College of Engineering Swansea University Bay Campus Fabian Way SwanseaSA1 8EN United Kingdom School of Computing & Mathematics Keele University Newcastle under Lyme StaffordshireST5 5BG United Kingdom Centre for Inverse Problems University College London Gower Street LondonWC1E 6BT United Kingdom TU Wien Institute for Analysis and Scientific Computing Wiedner Hauptstr. 8-10 / E101 / 4 Wien1040 Austria

The characterisation of small low conducting inclusions in an otherwise uniform background from low-frequency electrical field measurements has important applications in medical imaging using electrical impedance tomography as well as in geological imaging using electrical resistivity tomography. It is known that such objects can be characterised by a Póyla-Szegö (polarizability) tensor. Such characterisations have attracted interest as they can provide object features in a machine learning classification algorithm and provide an alternative imaging solution. However, to be able train machine learning algorithms, large dictionaries are required and it is essential that the characterisations are accurate. In this work, we obtain accurate numerical approximations to the tensor coefficients, by applying an adaptive boundary element method. The goal being to provide a sequence of benchmark computations for the tensor coefficients to allow other software developers check the accuracy of their *** Codes 65N30, 35R30, 35B30 © 2021, CC BY.

关键词： Boundary element method

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DPA-2: a large atomic model as a multi-task learner

arXiv

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arXiv 2023年

作者： Zhang, Duo Liu, Xinzijian Zhang, Xiangyu Zhang, Chengqian Cai, Chun Bi, Hangrui Du, Yiming Qin, Xuejian Peng, Anyang Huang, Jiameng Li, Bowen Shan, Yifan Zeng, Jinzhe Zhang, Yuzhi Liu, Siyuan Li, Yifan Chang, Junhan Wang, Xinyan Zhou, Shuo Liu, Jianchuan Luo, Xiaoshan Wang, Zhenyu Jiang, Wanrun Wu, Jing Yang, Yudi Yang, Jiyuan Yang, Manyi Gong, Fu-Qiang Zhang, Linshuang Shi, Mengchao Dai, Fu-Zhi York, Darrin M. Liu, Shi Zhu, Tong Zhong, Zhicheng Lv, Jian Cheng, Jun Jia, Weile Chen, Mohan Ke, Guolin Weinan, E. Zhang, Linfeng Wang, Han AI for Science Institute Beijing100080 China DP Technology Beijing100080 China Academy for Advanced Interdisciplinary Studies Peking University Beijing100871 China State Key Lab of Processors Institute of Computing Technology Chinese Academy of Sciences Beijing100871 China University of Chinese Academy of Sciences Beijing100871 China HEDPS CAPT College of Engineering Peking University Beijing100871 China Ningbo Institute of Materials Technology and Engineering Chinese Academy of Sciences Ningbo315201 China CAS Key Laboratory of Magnetic Materials and Devices Zhejiang Province Key Laboratory of Magnetic Materials and Application Technology Chinese Academy of Sciences Ningbo315201 China School of Electronics Engineering and Computer Science Peking University Beijing100871 China Shanghai Engineering Research Center of Molecular Therapeutics & New Drug Development School of Chemistry and Molecular Engineering East China Normal University Shanghai200062 China Laboratory for Biomolecular Simulation Research Institute for Quantitative Biomedicine Department of Chemistry and Chemical Biology Rutgers University PiscatawayNJ08854 United States Department of Chemistry Princeton University PrincetonNJ08540 United States College of Chemistry and Molecular Engineering Peking University Beijing100871 China Yuanpei College Peking University Beijing100871 China School of Electrical Engineering and Electronic Information Xihua University Chengdu610039 China State Key Laboratory of Superhard Materials College of Physics Jilin University Changchun130012 China Key Laboratory of Material Simulation Methods & Software of Ministry of Education College of Physics Jilin University Changchun130012 China International Center of Future Science Jilin University Changchun130012 China Key Laboratory for Quantum Materials of Zhejiang Province Department of Physics School of Science Westlake University Zhejiang Hangzhou310030 China Atomistic Simulations Italia

The rapid advancements in artificial intelligence (AI) are catalyzing transformative changes in atomic modeling, simulation, and design. AI-driven potential energy models have demonstrated the capability to conduct large-scale, long-duration simulations with the accuracy of ab initio electronic structure methods. However, the model generation process remains a bottleneck for large-scale applications. We propose a shift towards a model-centric ecosystem, wherein a large atomic model (LAM), pre-trained across multiple disciplines, can be efficiently fine-tuned and distilled for various downstream tasks, thereby establishing a new framework for molecular modeling. In this study, we introduce the DPA-2 architecture as a prototype for LAMs. Pre-trained on a diverse array of chemical and materials systems using a multi-task approach, DPA-2 demonstrates superior generalization capabilities across multiple downstream tasks compared to the traditional single-task pre-training and fine-tuning methodologies. Our approach sets the stage for the development and broad application of LAMs in molecular and materials simulation research. Copyright © 2023, The Authors. All rights reserved.

关键词： Multi-task learning

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Energy-preserving exponential integrable numerical method for stochastic cubic wave equation with additive noise

arXiv

引用

arXiv 2019年

作者： Cui, Jianbo Hong, Jialin Ji, Lihai Sun, Liying School of Mathematics Georgia Institute of Technology AtlantaGA30332 United States Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Institute of Applied Physics and Computational Mathematics Beijing100094 China

In this paper, we present an energy-preserving exponentially integrable numerical method for stochastic wave equation with cubic nonlinearity and additive noise. We first apply the spectral Galerkin method to discretizing the original equation and show that this spatial discretization possesses an energy evolution law and certain exponential integrability property. Then the exponential integrability property of the exact solution is deduced by proving the strong convergence of the semi-discretization. To propose a full discrete numerical method which could inherit both the energy evolution law and the exponential integrability, we use the splitting technique and averaged vector field method in the temporal direction. Combining these structure-preserving properties with regularity estimates of the exact and the numerical solutions, we obtain the strong convergence rate of the numerical method. Numerical experiments coincide with these theoretical results. Copyright © 2019, The Authors. All rights reserved.

关键词： Stochastic systems

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Stochastic Trust-Region Methods with Trust-Region Radius Depending on Probabilistic Models

arXiv

引用

arXiv 2019年

作者： Wang, Xiaoyu Yuan, Ya-Xiang Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Zhong Guan Cun Donglu 55 Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

We present a stochastic trust-region model-based framework in which its radius is related to the probabilistic models. Especially, we propose a specific algorithm, termed STRME, in which the trust-region radius depends linearly on the latest model gradient. The complexity of STRME method in non-convex, convex and strongly convex settings has all been analyzed, which matches the existing algorithms based on probabilistic properties. In addition, several numerical experiments are carried out to reveal the benefits of the proposed methods compared to the existing stochastic trust-region methods and other relevant stochastic gradient *** Codes 65K05, 65K10, 90C60 Copyright © 2019, The Authors. All rights reserved.

关键词： Gradient methods

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Sp(2N) Yang-Mills theories on the lattice: Scale setting and topology

引用

Physical Review D 2022年第9期106卷 094503-094503页

作者： Ed Bennett Deog Ki Hong Jong-Wan Lee C.-J. David Lin Biagio Lucini Maurizio Piai Davide Vadacchino Swansea Academy of Advanced Computing Swansea University Fabian Way SA1 8EN Swansea Wales United Kingdom Department of Physics Pusan National University Busan 46241 Republic of Korea Institute for Extreme Physics Pusan National University Busan 46241 Republic of Korea Institute of Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu 30010 Taiwan Center for High Energy Physics Chung-Yuan Christian University Chung-Li 32023 Taiwan Centre for Theoretical and Computational Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu 30010 Taiwan Physics Division National Centre for Theoretical Sciences Taipei 10617 Taiwan Department of Mathematics Faculty of Science and Engineering Swansea University Fabian Way SA1 8EN Swansea Wales United Kingdom Department of Physics Faculty of Science and Engineering Swansea University Singleton Park SA2 8PP Swansea Wales United Kingdom School of Mathematics and Hamilton Mathematics Institute Trinity College Dublin 2 Ireland Centre for Mathematical Sciences University of Plymouth PL4 8AA Plymouth United Kingdom

We study Yang-Mills lattice theories with Sp(Nc) gauge group, with Nc=2N, for N=1,…,4. We show that if we divide the renormalized couplings appearing in the Wilson flow by the quadratic Casimir C2(F) of the Sp(Nc) group, then the resulting quantities display a good agreement among all values of Nc considered, over a finite interval in flow time. We use this scaled version of the Wilson flow as a scale-setting procedure, compute the topological susceptibility of the Sp(Nc) theories, and extrapolate the results to the continuum limit for each Nc.

关键词： Large-N expansion in field theory Lattice field theory Nonperturbative effects in field theory Quantum field theory Strong interaction Topology

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On the mixing between flavor singlets in lattice gauge theories coupled to matter fields in multiple representations

arXiv

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arXiv 2024年

作者： Bennett, Ed Forzano, Niccolò Hong, Deog Ki Hsiao, Ho Lee, Jong-Wan Lin, C.-J. David Lucini, Biagio Piai, Maurizio Vadacchino, Davide Zierler, Fabian Swansea Academy of Advanced Computing Swansea University Bay Campus Fabian Way Wales SwanseaSA1 8EN United Kingdom Department of Physics Faculty of Science and Engineering Swansea University Singleton Park Wales SwanseaSA2 8PP United Kingdom Department of Physics Pusan National University Busan46241 Korea Republic of Extreme Physics Institute Pusan National University Busan46241 Korea Republic of Institute of Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu30010 Taiwan Daejeon34126 Korea Republic of Centre for Theoretical and Computational Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu30010 Taiwan Centre for High Energy Physics Chung-Yuan Christian University Chung-Li32023 Taiwan Department of Mathematics Faculty of Science and Engineering Swansea University Bay Campus Fabian Way Wales SwanseaSA1 8EN United Kingdom Centre for Mathematical Sciences University of Plymouth PlymouthPL4 8AA United Kingdom

We provide the first extensive, numerical study of the non-trivial problem of mixing between flavor-singlet composite states emerging in strongly coupled lattice field theories with matter field content consisting of fermions transforming in different representations of the gauge group. The theory of interest is the minimal candidate for a composite Higgs model that also accommodates a mechanism for top partial compositeness: the Sp(4) gauge theory coupled to two (Dirac) fermions transforming as the fundamental and three as the two-index antisymmetric representation of the gauge group, respectively. We apply an admixture of APE and Wuppertal smearings, as well as the generalized eigenvalue problem approach, to two-point functions involving flavor-singlet mesons, for ensembles having time extent longer than the space extent. We demonstrate that, in the region of lattice parameter space accessible to this study, both masses and mixing angles can be measured effectively, despite the presence of (numerically noisy) contributions from disconnected diagrams. © 2024, CC BY.

关键词： Fermions

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Analysis of the second order bdf scheme with variable steps for the molecular beam epitaxial model without slope selection

arXiv

引用

arXiv 2020年

作者： Liao, Hong-Lin Song, Xuehua Tang, Tao Zhou, Tao Department of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing211106 China Department of Mathematics Nanjing University of Aeronautics and Astronautics 211101 China Department of Mathematics and International Center for Mathematics Southern University of Science and Technology ShenzhenGuangdong China Division of Science and Technology BNU-HKBU United International College ZhuhaiGuangdong China NCMIS & LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

In this work, we are concerned with the stability and convergence analysis of the second order BDF (BDF2) scheme with variable steps for the molecular beam epitaxial model without slope selection. We first show that the variable-step BDF2 scheme is convex and uniquely solvable under a weak time-step constraint. Then we show that it preserves an energy dissipation law if the adjacent time-step ratios rk := τk/τk−1 2 norm stability and rigorous error estimates are established, under the same step-ratios constraint that ensuring the energy stability., i.e., 0 k MSC Codes 65M06, 65M12 Copyright © 2020, The Authors. All rights reserved.

关键词： Number theory

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An improved gradient method with approximately optimal stepsize based on conic model for unconstrained optimization

arXiv

引用

arXiv 2019年

作者： Liu, Zexian Liu, Hongwei State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering computing AMSS Chinese Academy of Sciences Beijing1000190 China School of Mathematics and Statistics Xidian University Xi’an710126 China

A new type of stepsize, which was recently introduced by Liu and Liu (Optimization, 67(3), 427-440, 2018), is called approximately optimal stepsize and is quit efficient for gradient method. Interestingly, all gradient methods can be regarded as gradient methods with approximately optimal stepsizes. In this paper, based on the work (Numer. Algorithms 78(1), 21-39, 2018), we present an improved gradient method with approximately optimal stepsize based on conic model for unconstrained optimization. If the objective function f is not close to a quadratic on the line segment between the current and latest iterates, we construct a conic model to generate approximately optimal stepsize for gradient method if the conic model can be used;otherwise, we construct some quadratic models to generate approximately optimal stepsizes for gradient method. The convergence of the proposed method is analyzed under suitable conditions. Numerical comparisons with some well-known conjugate gradient software packages such as CG_DESCENT (SIAM J. Optim. 16(1), 170-192, 2005) and CGOPT (SIAM J. Optim. 23(1), 296-320, 2013) indicate the proposed method is very promising. Copyright © 2019, The Authors. All rights reserved.

关键词： Gradient methods

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A PLANE WAVE DISCONTINUOUS GALERKIN METHOD FOR THE HELMHOLTZ EQUATION AND MAXWELL EQUATIONS IN ANISOTROPIC MEDIA ∗

arXiv

引用

arXiv 2019年

作者： Yuan, Long Qiya, H.U. College of Mathematics and Systems Science Shandong University of Science and Technology Qingdao266590 China 1. LSEC Institute of Computational Mathematics and Scientic/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China 2. School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In this paper we are concerned with plane wave discontinuous Galerkin (PWDG) methods for Helmholtz equation and time-harmonic Maxwell equations in three-dimensional anisotropic media, for which the coefficients of the equations are matrices instead of numbers. We first define novel plane wave basis functions based on rigorous choices of scaling transformations and coordinate transformations. Then we derive the error estimates of the resulting approximate solutions with respect to the condition number of the coefficient matrices, under a new assumption on the shape regularity of polyhedral meshes. Numerical results verify the validity of the theoretical results, and indicate that the approximate solutions generated by the proposed PWDG method possess high accuracies.65N30, 65N55 Copyright © 2019, The Authors. All rights reserved.

关键词： Galerkin methods

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