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arXiv 2023年

作者： Zhang, Xuan Wang, Limei Helwig, Jacob Luo, Youzhi Fu, Cong Xie, Yaochen Liu, Meng Lin, Yuchao Xu, Zhao Yan, Keqiang Adams, Keir Weiler, Maurice Li, Xiner Fu, Tianfan Wang, Yucheng Strasser, Alex Yu, Haiyang Xie, YuQing Fu, Xiang Xu, Shenglong Liu, Yi Du, Yuanqi Saxton, Alexandra Ling, Hongyi Lawrence, Hannah Stärk, Hannes Gui, Shurui Edwards, Carl Gao, Nicholas Ladera, Adriana Wu, Tailin Hofgard, Elyssa F. Tehrani, Aria Mansouri Wang, Rui Daigavane, Ameya Bohde, Montgomery Kurtin, Jerry Huang, Qian Phung, Tuong Xu, Minkai Joshi, Chaitanya K. Mathis, Simon V. Azizzadenesheli, Kamyar Fang, Ada Aspuru-Guzik, Alán Bekkers, Erik Bronstein, Michael Zitnik, Marinka Anandkumar, Anima Ermon, Stefano Liò, Pietro Yu, Rose Günnemann, Stephan Leskovec, Jure Ji, Heng Sun, Jimeng Barzilay, Regina Jaakkola, Tommi Coley, Connor W. Qian, Xiaoning Qian, Xiaofeng Smidt, Tess Ji, Shuiwang Department of Computer Science & Engineering Texas A&M University College StationTX United States Department of Chemical Engineering Massachusetts Institute of Technology Cambridge United Kingdom AMLab University of Amsterdam Amsterdam Netherlands Department of Computer Science University of Illinois Urbana-Champaign UrbanaIL United States Department of Electrical & Computer Engineering Texas A&M University College StationTX United States Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology Cambridge United Kingdom Department of Materials Science & Engineering Texas A&M University College StationTX United States Department of Physics & Astronomy Texas A&M University College StationTX United States Department of Applied Mathematics & Statistics Stony Brook University Stony BrookNY United States Department of Computer Science Stony Brook University Stony BrookNY United States Department of Computer Science Cornell University IthacaNY United States Department of Computer Science Technical University of Munich München Germany Department of Computer Science Stanford University StanfordCA United States Department of Computer Science & Engineering University of California San Diego La Jolla CA United States Department of Computer Science & Technology University of Cambridge Cambridge United Kingdom Nvidia Santa ClaraCA United States Department of Chemistry and Chemical Biology Harvard University Cambridge United Kingdom Department of Chemistry University of Toronto Toronto Canada Department of Computer Science University of Toronto Toronto Canada Department of Computer Science University of Oxford Oxford United Kingdom Department of Biomedical Informatics Harvard University BostonMA United States Department of Computing & Mathematical Sciences California Institute of Technology PasadenaCA United States Computational Science Initiative Brookhaven National Laboratory UptonNY United States

Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural sciences. Today, AI has started to advance natural sciences by improving, accelerating, and enabling our understanding of natural phenomena at a wide range of spatial and temporal scales, giving rise to a new area of research known as AI for science (AI4Science). Being an emerging research paradigm, AI4Science is unique in that it is an enormous and highly interdisciplinary area. Thus, a unified and technical treatment of this field is needed yet challenging. This work aims to provide a technically thorough account of a subarea of AI4Science;namely, AI for quantum, atomistic, and continuum systems. These areas aim at understanding the physical world from the subatomic (wavefunctions and electron density), atomic (molecules, proteins, materials, and interactions), to macro (fluids, climate, and subsurface) scales and form an important subarea of AI4Science. A unique advantage of focusing on these areas is that they largely share a common set of challenges, thereby allowing a unified and foundational treatment. A key common challenge is how to capture physics first principles, especially symmetries, in natural systems by deep learning methods. We provide an in-depth yet intuitive account of techniques to achieve equivariance to symmetry transformations. We also discuss other common technical challenges, including explainability, out-of-distribution generalization, knowledge transfer with foundation and large language models, and uncertainty quantification. To facilitate learning and education, we provide categorized lists of resources that we found to be useful. We strive to be thorough and unified and hope this initial effort may trigger more community interests and efforts to further advance AI4Science. Copyright © 2023, The Authors. All rights reserved.

关键词： Deep learning

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A practical guide to machine learning interatomic potentials – Status and future

arXiv

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arXiv 2025年

作者： Jacobs, Ryan Morgan, Dane Attarian, Siamak Meng, Jun Shen, Chen Wu, Zhenghao Xie, Clare Yijia Yang, Julia H. Artrith, Nongnuch Blaiszik, Ben Ceder, Gerbrand Choudhary, Kamal Csanyi, Gabor Cubuk, Ekin Dogus Deng, Bowen Drautz, Ralf Fu, Xiang Godwin, Jonathan Honavar, Vasant Isayev, Olexandr Johansson, Anders Kozinsky, Boris Martiniani, Stefano Ong, Shyue Ping Poltavsky, Igor Schmidt, K.J. Takamoto, So Thompson, Aidan Westermayr, Julia Wood, Brandon M. Department of Materials Science and Engineering University of Wisconsin-Madison MadisonWI55705 United States Harvard University Center for the Environment Harvard University CambridgeMA02138 United States John A. Paulson School of Engineering and Applied Sciences Harvard University CambridgeMA02138 United States Materials Chemistry and Catalysis Debye Institute for Nanomaterials Science Utrecht University Utrecht3584 CG Netherlands Globus University of Chicago ChicagoIL United States Data Science and Learning Division Argonne National Laboratory LemontIL United States Department of Materials Science and Engineering University of California BerkeleyCA94720 United States Materials Sciences Division Lawrence Berkeley National Laboratory CA94720 United States Material Measurement Laboratory National Institute of Standards and Technology GaithersburgMD20899 United States Department of Engineering University of Cambridge CambridgeCB2 1PZ United Kingdom Google DeepMind Mountain ViewCA United States Ruhr-Universität Bochum Bochum44780 Germany Meta United States Orbital Materials London United Kingdom Department of Computer Science and Engineering The Pennsylvania State University University ParkPA United States College of Information Sciences and Technology The Pennsylvania State University University ParkPA United States Artificial Intelligence Research Laboratory The Pennsylvania State University University ParkPA United States Center for Artificial Intelligence Foundations and Scientific Applications The Pennsylvania State University University ParkPA United States Department of Chemistry Mellon College of Science Carnegie Mellon University PittsburghPA15213 United States Computational Biology Department School of Computer Science Carnegie Mellon University PittsburghPA15213 United States Courant Institute of Mathematical Sciences New York University New YorkNY10003 United States Center for Soft Matter Research Department of P

The rapid development and large body of literature on machine learning interatomic potentials (MLIPs) can make it difficult to know how to proceed for researchers who are not experts but wish to use these tools. The spirit of this review is to help such researchers by serving as a practical, accessible guide to the state-of-the-art in MLIPs. This review paper covers a broad range of topics related to MLIPs, including (i) central aspects of how and why MLIPs are enablers of many exciting advancements in molecular modeling, (ii) the main underpinnings of different types of MLIPs, including their basic structure and formalism, (iii) the potentially transformative impact of universal MLIPs for both organic and inorganic systems, including an overview of the most recent advances, capabilities, downsides, and potential applications of this nascent class of MLIPs, (iv) a practical guide for estimating and understanding the execution speed of MLIPs, including guidance for users based on hardware availability, type of MLIP used, and prospective simulation size and time, (v) a manual for what MLIP a user should choose for a given application by considering hardware resources, speed requirements, energy and force accuracy requirements, as well as guidance for choosing pre-trained potentials or fitting a new potential from scratch, (vi) discussion around MLIP infrastructure, including sources of training data, pre-trained potentials, and hardware resources for training, (vii) summary of some key limitations of present MLIPs and current approaches to mitigate such limitations, including methods of including long-range interactions, handling magnetic systems, and treatment of excited states, and finally (viii) we finish with some more speculative thoughts on what the future holds for the development and application of MLIPs over the next 3-10+ years. © 2025, CC BY.

关键词： Digital storage

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VisGraphNet: A complex network interpretation of convolutional neural features

arXiv

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arXiv 2021年

作者： Florindo, Joao B. Lee, Young-Sup Jun, Kyungkoo Jeon, Gwanggil Albertini, Marcelo K. Institute of Mathematics Statistics and Scientific Computing University of Campinas Rua Sérgio Buarque de Holanda 651 Cidade Universitária"Zeferino Vaz" - Distr. Barão Geraldo SP CampinasCEP 13083-859 Brazil Department of Embedded Systems Engineering Incheon National University 119 Academy-ro Yeonsu-gu Incheon22012 Korea Republic of Department of Computer Science Federal University of Uberlandia Av. Joao Naves de Avila 2121 room Minas Gerais Uberlandia1B150 Brazil

Here we propose and investigate the use of visibility graphs to model the feature map of a neural network. The model, initially devised for studies on complex networks, is employed here for the classification of texture images. The work is motivated by an alternative viewpoint provided by these graphs over the original data. The performance of the proposed method is verified in the classification of four benchmark databases, namely, KTHTIPS-2b, FMD, UIUC, and UMD and in a practical problem, which is the identification of plant species using scanned images of their leaves. Our method was competitive with other state-of-the-art approaches, confirming the potential of techniques used for data analysis in different contexts to give more meaningful interpretation to the use of neural networks in texture classification. © 2021, CC BY.

关键词： Complex networks

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Nektar++: Enhancing the capability and application of high-fidelity spectral/hp element methods

引用

Computer Physics Communications 2020年 249卷

作者： Moxey, David Cantwell, Chris D. Bao, Yan Cassinelli, Andrea Castiglioni, Giacomo Chun, Sehun Juda, Emilia Kazemi, Ehsan Lackhove, Kilian Marcon, Julian Mengaldo, Gianmarco Serson, Douglas Turner, Michael Xu, Hui Peiró, Joaquim Kirby, Robert M. Sherwin, Spencer J. College of Engineering Mathematics and Physical Sciences University of Exeter United Kingdom Department of Aeronautics Imperial College London United Kingdom Department of Civil Engineering Shanghai Jiao Tong University Shanghai China Underwood International College Yonsei University Korea Republic of School of Aeronautics and Astronautics Shanghai Jiao Tong University Shanghai China Department of Energy and Power Plant Technology Technische Universität Darmstadt Germany Division of Engineering and Applied Science. California Institute of Technology United States Scientific Computing and Imaging Institute University of Utah United States

Nektar++ is an open-source framework that provides a flexible, high-performance and scalable platform for the development of solvers for partial differential equations using the high-order spectral/hp element method. In particular, Nektar++ aims to overcome the complex implementation challenges that are often associated with high-order methods, thereby allowing them to be more readily used in a wide range of application areas. In this paper, we present the algorithmic, implementation and application developments associated with our Nektar++ version 5.0 release. We describe some of the key software and performance developments, including our strategies on parallel I/O, on in situ processing, the use of collective operations for exploiting current and emerging hardware, and interfaces to enable multi-solver coupling. Furthermore, we provide details on a newly developed Python interface that enables a more rapid introduction for new users unfamiliar with spectral/hp element methods, C++ and/or Nektar++. This release also incorporates a number of numerical method developments – in particular: the method of moving frames (MMF), which provides an additional approach for the simulation of equations on embedded curvilinear manifolds and domains;a means of handling spatially variable polynomial order;and a novel technique for quasi-3D simulations (which combine a 2D spectral element and 1D Fourier spectral method) to permit spatially-varying perturbations to the geometry in the homogeneous direction. Finally, we demonstrate the new application-level features provided in this release, namely: a facility for generating high-order curvilinear meshes called NekMesh;a novel new AcousticSolver for aeroacoustic problems;our development of a ‘thick’ strip model for the modelling of fluid–structure interaction (FSI) problems in the context of vortex-induced vibrations (VIV). We conclude by commenting on some lessons learned and by discussing some directions for future code developmen

关键词： Numerical methods

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On a nonlocal Cahn-Hilliard model permitting sharp interfaces

arXiv

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arXiv 2020年

作者： Burkovska, Olena Gunzburger, Max Computer Science and Mathematics Division Oak Ridge National Laboratory One Bethel Valley Road TN37831 United States Department of Scientific Computing Florida State University 400 Dirac Science Library TallahasseFL32306-4120 United States The Oden Institute for Computer Engineering and Sciences University of Texas at Austin AustinTX78712 United States

A nonlocal Cahn–Hilliard model with a nonsmooth potential of double-well obstacle type that promotes sharp interfaces in the solution is presented. To capture long-range interactions between particles, a nonlocal Ginzburg-Landau energy functional is defined which recovers the classical (local) model as the extent of nonlocal interactions vanish. In contrast to the local Cahn–Hilliard problem that always leads to diffuse interfaces, the proposed nonlocal model can lead to a strict separation into pure phases of the substance. Here, the lack of smoothness of the potential is essential to guarantee the aforementioned sharp-interface property. Mathematically, this introduces additional inequality constraints that, in a weak formulation, lead to a coupled system of variational inequalities which at each time instance can be restated as a constrained optimization problem. We prove the well posedness and regularity of the semi-discrete and continuous in time weak solutions, and derive the conditions under which pure phases are admitted. Moreover, we develop discretizations of the problem based on finite element methods and implicit-explicit time stepping methods that can be realized efficiently. Finally, we illustrate our theoretical findings through several numerical experiments in one and two spatial dimensions that highlight the differences in features of local and nonlocal solutions and also the sharp interface properties of the nonlocal model. Copyright © 2020, The Authors. All rights reserved.

关键词： Variational techniques

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Uniform structural stability and uniqueness of poiseuille flows in a two dimensional periodic strip

arXiv

引用

arXiv 2020年

作者： Kaijian, S.H.A. Wang, Yun Chunjing, X.I.E. Department of mathematics East China University of Science and Technology Shanghai China School of Mathematical Sciences Center for dynamical systems and differential equations Soochow University Suzhou China School of mathematical Sciences Institute of Natural Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing and SHL-MAC Shanghai Jiao Tong University 800 Dongchuan Road Shanghai China

In this paper, we prove the uniform nonlinear structural stability of Poiseuille flows with arbitrarily large flux for the Navier-Stokes system in a two dimensional periodic strip when the period is not large. The key point is to establish the a priori estimate for the associated linearized problem via the careful analysis for the associated boundary layers. Furthermore, the well-posedness theory for the Navier-Stokes system is also proved even when the external force is large in L2. Finally, if the vertical velocity is suitably small where the smallness is independent of the flux, then Poiseuille flow is the unique solution of the steady Navier-Stokes system in the periodic strip. Copyright © 2020, The Authors. All rights reserved.

关键词： Boundary layers

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A CASCADIC MULTIGRID METHOD FOR EIGENVALUE PROBLEM

引用

Journal of computational mathematics 2017年第1期35卷 74-90页

作者： Xiaole Han Hehu Xie Fei Xu IAPCM Institute of Applied Physics and Computational Mathematics Beijing 100093 China LSEC NCMIS Institute of Computational Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China Beijing Institute for Scientific and Engineering Computing Beijing University of Technology Beijing 100124 China

A cascadic multigrid method is proposed for eigenvalue problems based on the multilevel correction scheme. With this new scheme, an eigenvalue problem on the finest space can be solved by linear smoothing steps on a series of multilevel finite element spaces and nonlinear correcting steps on special coarsest spaces. Once the sequence of finite element spaces and the number of smoothing steps are appropriately chosen, the optimal convergence rate with the optimal computational work can be obtained. Some numerical experiments are presented to validate our theoretical analysis.

关键词： Eigenvalue problem Cascadic multigrid Multilevel correction scheme Finiteelement method.

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On optimal finite element schemes for biharmonic equation

arXiv

引用

arXiv 2018年

作者： Zhang, Shuo LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China

In this paper, two nonconforming finite element schemes that use piecewise cubic and piecewise quartic polynomials respectively are constructed for the planar biharmonic equation with optimal convergence rates on general shape-regular triangulations. Therefore, it is proved that optimal finite element schemes of arbitrary order for planar biharmonic equation can be constructed on general shape-regular triangulations. Copyright © 2018, The Authors. All rights reserved.

关键词： Finite element method

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A First Glance to the Quality Assessment of Dental Photostimulable Phosphor Plates with Deep Learning

A First Glance to the Quality Assessment of Dental Photostim...

引用

International Joint Conference on Neural Networks (IJCNN)

作者： Ariana Bermudez Saul Calderon-Ramirez Trevor Thang Pascal Tyrrell Armaghan Moemeni Shengxiang Yang Jordina Torrents-Barrena School of Computing Costa Rica Institute of Technology Pattern Recognition and Machine Learning Group Costa Rica Centre for Computational Intelligence (CCI) De Montfort University United Kingdom Faculty of Dentistry University of Toronto Canada Department of Medical Imaging University of Toronto Canada University of Nottingham United Kingdom Department of Mathematics and Computer Engineering Universitat Rovira i Virgili Spain

ISBN: (数字)9781728169262

ISBN: (纸本)9781728169279

Photostimulable Phosphor Plates are commonly used in digital X-ray imaging for dentistry. During its usage, these plates get damaged, influencing the diagnosis performance and confidence of the dentistry professional. We propose a deep learning based classifier to discard or extend the use of photostimulable phosphor (PSP) plates based on their physical damage. The system automatically assesses, for the first time in the literature, when dentists should discard their plates. To validate our methodology, an in-house dataset is built on 25 PSP artifact masks (Carestream, CS 7600) digitally superimposed over 100 Complementary Metal-oxide-semiconductor (CMOS) periapical images (Carestream, RVG 6200) with known radiologic interpretations. From these 2500 images, unique subsets of 100 images were evaluated by 25 dentists to find periapical inflammatory lesions on the tooth. Doctors' opinion on whether the plates should be discarded or not was also collected. State-of-the-art deep convolutional networks were tested using fivefold cross validation, yielding classification accuracies from 87% to almost 89%. Specifically, InceptionV3 and Resnet50 obtained the best performances with statistical significance. Qualitative heat-maps showed that such models can identify and employ artifacts to decide on whether to discard the PSP plate or not. This work intends to be the base line for future works related to the automatic PSP plate assessment.

关键词： Dentistry Machine learning Sensitivity Teeth Visualization Quality assessment Diagnostic radiography

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Scalability of high-performance PDE solvers

arXiv

引用

arXiv 2020年

作者： Fischer, Paul Min, Misun Rathnayake, Thilina Dutta, Som Kolev, Tzanio Dobrev, Veselin Camier, Jean-Sylvain Kronbichler, Martin Warburton, Tim Swirydowicz, Kasia Brown, Jed Mathematics and Computer Science Argonne National Laboratory LemontIL60439 Department of Computer Science University of Illinois at Urbana-Champaign UrbanaIL61801 Department of Mechanical Science and Engineering University of Illinois at Urbana-Champaign UrbanaIL61801 Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA94550 Institute for Computational Mechanics Technical University of Munich Garching b. Muenchen85748 Germany Department of Computer Science University of Colorado BoulderCO80309 National Renewable Energy Laboratory LakewoodCO80401 Department of Mathematics Virginia Tech BlacksburgVA24061 Mechanical & Aerospace Engineering Utah State University UT84322

Performance tests and analyses are critical to effective HPC software development and are central components in the design and implementation of computational algorithms for achieving faster simulations on existing and future computing architectures for large-scale application problems. In this paper, we explore performance and space-time trade-offs for important compute-intensive kernels of large-scale numerical solvers for PDEs that govern a wide range of physical applications. We consider a sequence of PDE-motivated bake-off problems designed to establish best practices for efficient high-order simulations across a variety of codes and platforms. We measure peak performance (degrees of freedom per second) on a fixed number of nodes and identify effective code optimization strategies for each architecture. In addition to peak performance, we identify the minimum time to solution at 80% parallel efficiency. The performance analysis is based on spectral and p-type finite elements but is equally applicable to a broad spectrum of numerical PDE discretizations, including finite difference, finite volume, and h-type finite *** Codes 35-04 Copyright © 2020, The Authors. All rights reserved.

关键词： Computer architecture

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