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2023 International Conference on Evolutionary Algorithms and Soft computing Techniques, EASCT 2023

作者： Pasha, Syed Nawaz Anitha, D. Anbunathan, R. Gobinath, C. Madhura, G.K. Sr University School of Computer Science & Artificial Intelligence Warangal India School of Computing Srm Institute of Science and Technology Department of Computational Intelligence Kattankulathur India Sa Engineering College Department of Mathematics Chennai India Reva University School of Computing and Information Technology Bangalore India Nitte Meenakshi Institute of Technology Department of Ai and Ml Bengaluru India

ISBN: (纸本)9798350313413

Iris recognition stands out as one of the most stable and accurate biometric identification systems such as facial, voice, fingerprint, handwriting, and iris recognition itself. Deep Learning (DL) plays a pivotal role in enhancing security by leveraging Convolutional Neural Networks (CNNs) for iris recognition. The acquisition of iris images and real-time processing have become focal points demanding heightened attention in the realm of DL. Iris recognition is prized for its high level of protection, making it challenging to reconstruct iris data easily from the database. The CASIA-Iris Dataset serves as a benchmark to verify the uniqueness of iris patterns and evaluate the performance of iris recognition. However, due to limitations in iris image access, the application of CNNs in the segmentation approach remains critical for iris localization and pupil boundary identification, ensuring both efficiency and specificity in iris images. The results obtained from this study reveal that the proposed CNN, utilizing DL models, achieves an impressive accuracy of 99.89% on the CASIA-Iris dataset, better performance of other existing models, such as U-Net and VGG-Net, and ensuring accurate classification. © 2023 IEEE.

关键词： Contrast-Limited Adaptive Histogram Equalization Convolution Neural Network Deep Learning Iris Recognition and Support Vector Machine

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A Symplectic Discretization Based Proximal Point Algorithm for Convex Minimization

arXiv

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arXiv 2024年

作者： Yuan, Ya-Xiang Zhang, Yi Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China

The proximal point algorithm plays a central role in non-smooth convex programming. The Augmented Lagrangian Method, one of the most famous optimization algorithms, has been found to be closely related to the proximal point algorithm. Due to its importance, accelerated variants of the proximal point algorithm have received considerable attention. In this paper, we first study an Ordinary Differential Equation (ODE) system, which provides valuable insights into proving the convergence rate of the desired algorithm. Using the Lyapunov function technique, we establish the convergence rate of the ODE system. Next, we apply the Symplectic Euler Method to discretize the ODE system to derive a new proximal point algorithm, called the Symplectic Proximal Point Algorithm (SPPA). By utilizing the proof techniques developed for the ODE system, we demonstrate the convergence rate of the SPPA. Additionally, it is shown that existing accelerated proximal point algorithm can be considered a special case of the SPPA in a specific manner. Furthermore, under several additional assumptions, we prove that the SPPA exhibits a finer convergence *** Codes 49J52, 65B99, 65K10, 65K15, 68Q25, 90C25, 90C26 © 2024, CC BY.

关键词： Lyapunov functions

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SYMPLECTIC EXTRA-GRADIENT TYPE METHOD FOR SOLVING GENERAL NON-MONOTONE INCLUSION PROBLEM

arXiv

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arXiv 2024年

In recent years, accelerated extra-gradient methods have attracted much attention by researchers, for solving monotone inclusion problems. A limitation of most current accelerated extra-gradient methods lies in their direct utilization of the initial point, which can potentially decelerate numerical convergence rate. In this work, we present a new accelerated extra-gradient method, by utilizing the symplectic acceleration technique. We establish the inverse of quadratic convergence rate by employing the Lyapunov function technique. Also, we demonstrate a faster inverse of quadratic convergence rate alongside its weak convergence property under stronger assumptions. To improve practical efficiency, we introduce a line search technique for our symplectic extra-gradient method. Theoretically, we prove the convergence of the symplectic extra-gradient method with line search. Numerical tests show that this adaptation exhibits faster convergence rates in practice compared to several existing extra-gradient type *** Codes 47J20, 47H05, 65K10, 65K15, 65Y20, 90C30, 90C52 © 2024, CC BY.

关键词： Lyapunov functions

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SOC-MARTNET: A MARTINGALE NEURAL NETWORK FOR THE HAMILTON-JACOBI-BELLMAN EQUATION WITHOUT EXPLICIT infU∈U H IN STOCHASTIC OPTIMAL CONTROLS

arXiv

引用

arXiv 2024年

作者： Cai, Wei Fang, Shuixin Zhou, Tao Department of Mathematics Southern Methodist University DallasTX75275 United States Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

In this paper, we propose a martingale-based neural network, SOC-MartNet, for solving high-dimensional Hamilton-Jacobi-Bellman (HJB) equations where no explicit expression is needed for the infimum of the Hamiltonian, infu∈U H(t, x, u, z, p), and stochastic optimal control problems (SOCPs) with controls on both drift and volatility. We reformulate the HJB equations for the value function by training two neural networks, one for the value function and one for the optimal control with the help of two stochastic processes - a Hamiltonian process and a cost process. The control and value networks are trained such that the associated Hamiltonian process is minimized to satisfy the minimum principle of a feedback SOCP, and the cost process becomes a martingale, thus, ensuring the value function network as the solution to the corresponding HJB equation. Moreover, to enforce the martingale property for the cost process, we employ an adversarial network and construct a loss function characterizing the projection property of the conditional expectation condition of the martingale. Numerical results show that the proposed SOC-MartNet is effective and efficient for solving HJB-type equations and SOCPs with a dimension up to 10, 000 in a small number of iteration steps (less than 6000) of training. © 2024, CC BY.

关键词： Hamiltonians

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αSetup-PCTL:An Adaptive Setup-Based Two-Level Preconditioner for Sequence of Linear Systems of Three-Temperature Energy Equations

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Communications in computational Physics 2022年第10期32卷 1287-1309页

作者： Silu Huang Xiaoqiang Yue Xiaowen Xu Laboratory of Computational Physics Institute of Applied Physics and ComputationalMathematicsBeijing 100088China National Center for Applied Mathematics in Hunan Key Laboratory of Intelligent Computing and Information Processing of Ministry of EducationHunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtan 411105China

The iterative solution of the sequence of linear systems arising from threetemperature(3-T)energy equations is an essential component in the numerical simulation of radiative hydrodynamic(RHD)***,due to the complicated application features of the RHD problems,solving 3-T linear systems with classical preconditioned iterative techniques is *** address this difficulty,a physicalvariable based coarsening two-level(PCTL)preconditioner has been proposed by dividing the fully coupled system into four individual easier-to-solve *** its nearly optimal complexity and robustness,the PCTL algorithm suffers from poor efficiency because of the overhead associatedwith the construction of setup phase and the solution of ***,the PCTL algorithm employs a fixed strategy for solving the sequence of 3-T linear systems,which completely ignores the dynamically and slowly changing features of these linear *** address these problems and to efficiently solve the sequence of 3-T linear systems,we propose an adaptive two-level preconditioner based on the PCTL algorithm,referred to as α*** adaptive strategies of the αSetup-PCTL algorithm are inspired by those of αSetup-AMG algorithm,which is an adaptive-setup-based AMG solver for sequence of sparse linear *** proposed αSetup-PCTL algorithm could adaptively employ the appropriate strategies for each linear system,and thus increase the overall *** results demonstrate that,for 36 linear systems,the αSetup-PCTL algorithm achieves an average speedup of 2.2,and a maximum speedup of 4.2 when compared to the PCTL algorithm.

关键词： Sequence of linear systems sparse linear solver preconditioning methods radiation hydrodynamics simulation

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A Natural Deep Ritz Method for Essential Boundary Value Problems

arXiv

引用

arXiv 2024年

作者： Yu, Haijun Zhang, Shuo LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China

Deep neural network approaches show promise in solving partial differential equations. However, unlike traditional numerical methods, they face challenges in enforcing essential boundary conditions. The widely adopted penalty-type methods, for example, offer a straightforward implementation but introduces additional complexity due to the need for hyper-parameter tuning;moreover, the use of a large penalty parameter can lead to artificial extra stiffness, complicating the optimization process. In this paper, we propose a novel, intrinsic approach to impose essential boundary conditions through a framework inspired by intrinsic structures. We demonstrate the effectiveness of this approach using the deep Ritz method applied to Poisson problems, with the potential for extension to more general equations and other deep learning techniques. Numerical results are provided to substantiate the efficiency and robustness of the proposed method. Copyright © 2024, The Authors. All rights reserved.

关键词： Numerical methods

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A New Multi-point Stepsize Gradient Method for Optimization 5th

A New Multi-point Stepsize Gradient Method for Optimization

引用

5th International Conference on Numerical Analysis and Optimization: Theory, Methods, Applications and Technology Transfer, NAOV 2020

作者： Huang, Yakui Dai, Yu-Hong Liu, Xin-Wei Institute of Mathematics Hebei University of Technology Tianjin300401 China 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

ISBN: (纸本)9783030720391

The Barzilai-Borwein (BB) gradient method, which employs two-point stepsizes computed by the information of two consecutive iterations, is efficient in solving large-scale unconstrained optimization. In this paper, motivated by the success of BB method and the multi-point stepsize proposed by Dai and Fletcher (Mathematical Programming, 2006, 106: 403–421), we develop a new efficient gradient method, called MPSG, which adaptively uses the Dai-Fletcher long stepsize and Dai-Fletcher short stepsize. The R-linear convergence of MPSG for general n-dimensional strictly convex quadratic functions is established. By making use of two modified multi-point stepsizes and nonmonotone line searches, MPSG is extended to solve general unconstrained optimization. Moreover, the proposed MPSG method is further generalized for solving extreme eigenvalue problems. Numerical experiments on quadratic optimization, general unconstrained optimization and extreme eigenvalue problems demonstrate the efficiency of our method. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Gradient methods

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FINITE ELEMENT SPACES BY WHITNEY k-FORMS ON CUBICAL MESHES

arXiv

引用

arXiv 2024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 University of Chinese Academy of Sciences Beijing100049 China

Finite element spaces by Whitney k-forms on cubical meshes in Rn are presented. Based on the spaces, compatible discretizations to HΛk problems are provided, and discrete de Rham complexes and commutative diagrams ar... 详细信息

关键词： Mesh generation

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Martingale deep learning for very high dimensional quasi-linear partial differential equations and stochastic optimal controls

arXiv

引用

arXiv 2024年

作者： Cai, Wei Fang, Shuixin Zhang, Wenzhong Zhou, Tao Department of Mathematics Southern Methodist University United States Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences China Suzhou Institute for Advanced Research University of Science and Technology of China China

In this paper, a highly parallel and derivative-free martingale neural network learning method is proposed to solve Hamilton-Jacobi-Bellman (HJB) equations arising from stochastic optimal control problems (SOCPs), as well as general quasilinear parabolic partial differential equations (PDEs). In both cases, the PDEs are reformulated into a martingale formulation such that loss functions will not require the computation of the gradient or Hessian matrix of the PDE solution, while its implementation can be parallelized in both time and spatial domains. Moreover, the martingale conditions for the PDEs are enforced using a Galerkin method in conjunction with adversarial learning techniques, eliminating the need for direct computation of the conditional expectations associated with the martingale property. For SOCPs, a derivative-free implementation of the maximum principle for optimal controls is also introduced. The numerical results demonstrate the effectiveness and efficiency of the proposed method, which is capable of solving HJB and quasilinear parabolic PDEs accurately in dimensions as high as 10,000. © 2024, CC BY.

关键词： Galerkin methods

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

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

引用

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

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