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TensorMD: Molecular Dynamics Simulation with Ab Initio Accuracy of 50 Billion Atoms 25

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TensorMD: Molecular Dynamics Simulation with Ab Initio Accur...

Proceedings of the 30th ACM SIGPLAN Annual Symposium on Principles and Practice of Parallel Programming

作者： Yucheng Ouyang Ying Liu Honghui Shang Zhenchuan Chen Jiahao Shan Huimin Cui Xiaobing Feng Xin Chen Xingyu Gao Lifang Wang Haifeng Song Rongfen Lin Fang Li Institute of Computing Technology Chinese Academy of Sciences Beijing China National Research Center of Parallel Computer Engineering and Technology Beijing China Institute of Applied Physics and Computational Mathematics Beijing China

ISBN: (纸本)9798400714436

Molecular dynamics simulation emerges as an important area that HPC+AI helps to investigate the physical properties, with machine-learning interatomic potentials (MLIPs) being used. General-purpose machine-learning (ML) tools have been leveraged in MLIPs, but they are not perfectly matched with each other, since many optimization opportunities in MLIPs have been missed by ML tools. This inefficiency arises from the fact that HPC+AI applications work with far more computational complexity compared with pure AI scenarios. This paper has developed an MLIP, named TensorMD, independently from any ML tool. TensorMD has been evaluated on two supercomputers and scaled to 51.8 billion atoms, i.e., ~ 3× compared with state-of-the-art.

关键词： GPU

A Mathematical Aspect of Bloch's Theorem

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arXiv 2024年

作者： Li, Yan Yang, Bin Zhou, Aihui LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China NCMIS Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

In this paper, by studying a class of 1-D Sturm-Liouville problems with periodic coefficients, we show and classify the solutions of periodic Schrodinger equations in a multidimensional case, which tells that not all the solutions are Bloch solutions. In addition, we also provide several properties of the solutions and quasimomenta and illustrate the relationship between bounded solutions and Bloch solutions. Copyright © 2024, The Authors. All rights reserved.

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On a Robin-type non-singular coupling scheme for solving the wave scattering problems

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arXiv 2023年

作者： Liu, Xiaojuan Li, Maojun Yin, Tao 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

This paper studies a non-singular coupling scheme for solving the acoustic and elastic wave scattering problems and its extension to the problems of Laplace and Lamé equations and the problem with a compactly supported inhomogeneity is also briefly discussed. Relying on the solution representation of the wave scattering problem, a Robin-type artificial boundary condition in terms of layer potentials whose kernels are non-singular, is introduced to obtain a reduced problem on a bounded domain. The wellposedness of the reduced problems and the a priori error estimates of the corresponding finite element discretization are proved. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method. Copyright © 2023, The Authors. All rights reserved.

关键词： Numerical methods

A new framework of high-order unfitted finite element methods using ALE maps for moving-domain problems

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arXiv 2024年

作者： Lu, Wenhao Ma, Chuwen Zheng, Weiying LSEC NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Science University of Chinese Academy of Sciences Beijing100049 China Institute of Natural Sciences Shanghai Jiao Tong University Shanghai200240 China

As a sequel to our previous work [C. Ma, Q. Zhang and W. Zheng, SIAM J. Numer. Anal., 60 (2022)], [C. Ma and W. Zheng, J. Comput. Phys. 469 (2022)], this paper presents a generic framework of arbitrary Lagrangian-Eulerian unfitted finite element (ALE-UFE) methods for partial differential equations (PDEs) on time-varying domains. The ALE-UFE method has a great potential in developing high-order unfitted finite element methods. The usefulness of the method is demonstrated by a variety of moving-domain problems, including a linear problem with explicit velocity of the boundary (or interface), a PDE-domain coupled problem, and a problem whose domain has a topological change. Numerical experiments show that optimal convergence is achieved by both third- and fourth-order methods on domains with smooth boundaries, but is deteriorated to the second order when the domain has topological changes. Copyright © 2024, The Authors. All rights reserved.

关键词： Finite element method

AN END-TO-END DEEP LEARNING METHOD FOR SOLVING NONLOCAL ALLEN-CAHN AND CAHN-HILLIARD PHASE-FIELD MODELS

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arXiv 2024年

作者： Geng, Yuwei Burkovska, Olena Ju, Lili Zhang, Guannan Gunzburger, Max Department of Mathematics University of South Carolina United States Computer Science and Mathematics Division Oak Ridge National Laboratory United States Department of Scientific Computing Florida State University United States Oden Institute for Computational Engineering and Sciences University of Texas at Austin United States

We propose an efficient end-to-end deep learning method for solving nonlocal Allen-Cahn (AC) and Cahn-Hilliard (CH) phase-field models. One motivation for this effort emanates from the fact that discretized partial differential equation-based AC or CH phase-field models result in diffuse interfaces between phases, with the only recourse for remediation is to severely refine the spatial grids in the vicinity of the true moving sharp interface whose width is determined by a grid-independent parameter that is substantially larger than the local grid size. In this work, we introduce non-mass conserving nonlocal AC or CH phase-field models with regular, logarithmic, or obstacle double-well potentials. Because of non-locality, some of these models feature totally sharp interfaces separating phases. The discretization of such models can lead to a transition between phases whose width is only a single grid cell wide. Another motivation is to use deep learning approaches to ameliorate the otherwise high cost of solving discretized nonlocal phase-field models. To this end, loss functions of the customized neural networks are defined using the residual of the fully discrete approximations of the AC or CH models, which results from applying a Fourier collocation method and a temporal semi-implicit approximation. To address the long-range interactions in the models, we tailor the architecture of the neural network by incorporating a nonlocal kernel as an input channel to the neural network model. We then provide the results of extensive computational experiments to illustrate the accuracy, structure-preserving properties, predictive capabilities, and cost reductions of the proposed method. Copyright © 2024, The Authors. All rights reserved.

关键词： Partial differential equations

Securing Neural Network in the Cloud: A Systematic Approach of Cloud Security Based on ANN-SVM Model 4

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Securing Neural Network in the Cloud: A Systematic Approach ...

4th International Conference on Sustainable Expert Systems, ICSES 2024

作者： Arunarani, Ar Vijayagopal, V. Kartheesan, L. Dwivedi, Vijay Kumar Rajesh Kumar, A. Nishant, Neerav School of Computing College of Engineering Srm Institute of Science and Technology Department of Computational Intelligence Tamilnadu Chennai India Dr. M.G.R. Educational and Research Institute Faculty of Computer Applications Tamilnadu Chennai India School of Computing Vel Tech Rangarajan Dr. Sagunthala R&d Institute of Science and Technology Department of Computer Science and Engineering Tamilnadu Chennai India Vishwavidyalaya Engineering College Department of Mathematics Chhattisgarh Surguja India N.S.N. College of Engineering and Technology Department of Computer Science and Engineering Tamilnadu Karur India School of Engineering Babu Banarasi Das University Department of Computer Science and Engineering Lucknow India

ISBN: (纸本)9798331540364

Many services have made the transition to the cloud because of the increased reliability and efficiency of cloud computing. Due to their capacity to ease service access while also securing communications in the public network, the three-factor Mutual Authentication and Key Agreement (MAKA) protocols are seeing increased use in multi-server designs. A lack of formal security proof or high communication and computation costs makes the limited three-factor MAKA protocols that are currently available susceptible to a wide range of attacks. The proposed approach consists of three phases, which are preprocessing, feature selection, and model training. Text scheduling and normalization make up preprocessing. In feature selection, the PSO is an optimization method that uses a population-based approach to find optimal solutions. An ANN-SVM was employed throughout the model's training phase. With an average accuracy of 93.30%, the proposed technique surpasses ANN and SVM. © 2024 IEEE.

关键词： Cloud security

BOUNDED KRNET AND ITS APPLICATIONS TO DENSITY ESTIMATION AND APPROXIMATION

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arXiv 2023年

作者： Zeng, Li Wan, Xiaoliang Zhou, Tao Fuzhou University Fuzhou China Department of Mathematics Center for Computation and Technology Louisiana State University Baton Rouge70803 United States Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

In this paper, we develop an invertible mapping, called B-KRnet, on a bounded domain and apply it to density estimation/approximation for data or the solutions of PDEs such as the Fokker-Planck equation and the Keller-Segel equation. Similar to KRnet, the structure of B-KRnet adapts the pseudo-triangular structure into a normalizing flow model. The main difference between B-KRnet and KRnet is that B-KRnet is defined on a hypercube while KRnet is defined on the whole space, in other words, a new mechanism is introduced in B-KRnet to maintain the exact invertibility. Using B-KRnet as a transport map, we obtain an explicit probability density function (PDF) model that corresponds to the pushforward of a prior (uniform) distribution on the hypercube. It can be directly applied to density estimation when only data are available. By coupling KRnet and B-KRnet, we define a deep generative model on a high-dimensional domain where some dimensions are bounded and other dimensions are unbounded. A typical case is the solution of the stationary kinetic Fokker-Planck equation, which is a PDF of position and momentum. Based on B-KRnet, we develop an adaptive learning approach to approximate partial differential equations whose solutions are PDFs or can be treated as PDFs. A variety of numerical experiments is presented to demonstrate the effectiveness of B-KRnet. Copyright © 2023, The Authors. All rights reserved.

关键词： Fokker Planck equation

Device Activity Detection in mMTC with Low-Resolution ADC: A New Protocol

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arXiv 2023年

作者： Wang, Zhaorui Liu, Ya-Feng Wang, Ziyue Liu, Liang Pan, Haoyuan Cui, Shuguang The Future Network of Intelligence Institute The School of Science and Engineering The Chinese University of Hong Kong Shenzhen518172 China The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The Department of Electronic and Information Engineering The Hong Kong Polytechnic University Hong Kong College of Computer Science and Software Engineering Shenzhen University Shenzhen China

This paper investigates the effect of low-resolution analog-to-digital converters (ADCs) on device activity detection in massive machine-type communications (mMTC). The low-resolution ADCs induce two challenges on the device activity detection compared with the traditional setup with the assumption of infinite ADC resolution. First, the codebook design for signal quantization by the low-resolution ADC is particularly important since a good design of the codebook can lead to small quantization error on the received signal, which in turn has significant influence on the activity detector performance. To this end, prior information about the received signal power is needed, which depends on the number of active devices K. This is sharply different from the activity detection problem in traditional setups, in which the knowledge of K is not required by the BS as a prerequisite. Second, the covariance-based approach achieves good activity detection performance in traditional setups while it is not clear if it can still achieve good performance in this paper. To solve the above challenges, we propose a communication protocol that consists of an estimator for K and a detector for active device identities: 1) For the estimator, the technical difficulty is that the design of the ADC quantizer and the estimation of K are closely intertwined and doing one needs the information/execution from the other. We propose a progressive estimator which iteratively performs the estimation of K and the design of the ADC quantizer;2) For the activity detector, we propose a custom-designed stochastic gradient descent algorithm to estimate the active device identities. Numerical results demonstrate the effectiveness of the communication protocol. © 2023, CC BY.

关键词： Stochastic systems

Secure numerical simulations using fully homomorphic encryption

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arXiv 2024年

作者： Kholod, Arseniy Polyakov, Yuriy Schlottke-Lakemper, Michael High-Performance Scientific Computing Institute of Mathematics University of Augsburg Germany Centre for Advanced Analytics and Predictive Sciences University of Augsburg Germany Applied and Computational Mathematics RWTH Aachen University Germany Duality Technologies Inc. United States

Data privacy is a significant concern when using numerical simulations for sensitive information such as medical, financial, or engineering data. This issue becomes especially relevant in untrusted environments like public cloud infrastructures. Fully homomorphic encryption (FHE) offers a promising solution for achieving data privacy by enabling secure computations directly on encrypted data. In this paper, aimed at computational scientists, we explore the viability of FHE-based, privacy-preserving numerical simulations of partial differential equations. We begin with an overview of the CKKS scheme, a widely used FHE method for computations with real numbers. Next, we introduce our Julia-based packages *** and ***, which wrap the OpenFHE C++ library and provide a convenient interface for secure arithmetic operations. We then evaluate the accuracy and performance of key FHE operations in OpenFHE as a baseline for more complex numerical algorithms. Following that, we demonstrate the application of FHE to scientific computing by implementing two finite difference schemes for the linear advection equation. Finally, we discuss potential challenges and solutions for extending secure numerical simulations to other models and methods. Our results show that cryptographically secure numerical simulations are possible, but that careful consideration must be given to the computational overhead and the numerical errors introduced by using *** Codes 65-04, 65M06, 65Y99 Copyright © 2024, The Authors. All rights reserved.

关键词： Digital elevation model