检索结果-内蒙古大学图书馆

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

学校读者我要写书评

暂无评论

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

Detecting and Exploiting Unit Commitment Structures in MIPs

学校读者我要写书评

暂无评论

Detecting and Exploiting Unit Commitment Structures in MIPs

International Conference on Power and Energy Technology (ICPET)

作者： Zhao-Gang Su Sheng-Jie Chen Yu-Fei Li Liang Chen Caixia Kou Zhi Cai Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China College of Sciences Beijing University of Posts and Telecommunications Beijing China Beijing Key Laboratory of Research and System Evaluation of Power Dispatching Automation Technology China Electric Power Research Institute Beijing China

ISBN: (数字)9798350375855

ISBN: (纸本)9798350375862

The unit commitment (UC) problem has been extensively researched in the literature, which is typically formulated as a mixed integer programming (MIP) problem. However, current studies lack effective methods to identify potential UC problem structures within a general MIP problem, making it challenging to leverage well-established valid inequalities for UC problems to accelerate the solution process. In this paper, we present a novel detection method that automatically identifies UC structures within an MIP problem by analyzing the relationships between variables and constraints. Moreover, we enhance the MIP formulation by incorporating three well-studied classes of valid inequalities as cutting planes, based on the identified UC structures. Our experiments demonstrate that our proposed UC detection method greatly improves computational efficacy of a standard MIP solver compared to the default setting.

关键词： Integer programming Production Generators Time factors Standards

Semi-implicit energy-preserving numerical schemes for stochastic wave equation via SAV approach

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Cui, Jianbo Hong, Jialin Sun, Liying Department of Applied Mathematics The Hong Kong Polytechnic University Hung Hom Hong Kong 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 propose and analyze semi-implicit numerical schemes for the stochastic wave equation (SWE) with general nonlinearity and multiplicative noise. These numerical schemes, called stochastic scalar auxiliary variable (SAV) schemes, are constructed by transforming the considered SWE into a higher dimensional stochastic system with a stochastic SAV. We prove that they can be solved explicitly and preserve the modified energy evolution law and the regularity structure of the original system. These structure-preserving properties are the keys to overcoming the mutual effect of the noise and nonlinearity. By proving new regularity estimates of the introduced SAV, we establish the strong convergence rate of stochastic SAV schemes and the further fully-discrete schemes with the finite element method in spatial direction. To the best of our knowledge, this is the first result on the construction and strong convergence of semi-implicit energy-preserving schemes for nonlinear SWE. © 2022, CC BY.

关键词： Stochastic systems

Energy based diffusion generator for efficient sampling of Boltzmann distributions

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Wang, Yan L., Guo H., Wu T., Zhou School of Mathematical Sciences Tongji University Shanghai China Department of Mathematics Shanghai Normal University Shanghai China School of Mathematical Sciences Institute of Natural Sciences MOE-LSC Shanghai Jiao Tong University Shanghai China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing China

Sampling from Boltzmann distributions, particularly those tied to high-dimensional and complex energy functions, poses a significant challenge in many fields. In this work, we present the Energy-Based Diffusion Generator (EDG), a novel approach that integrates ideas from variational autoencoders and diffusion models. EDG leverages a decoder to transform latent variables from a simple distribution into samples approximating the target Boltzmann distribution, while the diffusion-based encoder provides an accurate estimate of the Kullback-Leibler divergence during training. Notably, EDG is simulationfree, eliminating the need to solve ordinary or stochastic differential equations during training. Furthermore, by removing constraints such as bijectivity in the decoder, EDG allows for flexible network design. Through empirical evaluation, we demonstrate the superior performance of EDG across a variety of complex distribution tasks, outperforming existing methods. Copyright © 2024, The Authors. All rights reserved.

关键词： Decoding

A predictor-corrector deep learning algorithm for high dimensional stochastic partial differential equations

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Zhang, He Zhang, Ran Zhou, Tao School of Mathematics Jilin University Jilin Changchun130012 China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

In this paper, we present a deep learning-based numerical method for approximating high dimensional stochastic partial differential equations (SPDEs). At each time step, our method relies on a predictor-corrector procedure. More precisely, we decompose the original SPDE into a degenerate SPDE and a deterministic PDE. Then in the prediction step, we solve the degenerate SPDE with the Euler scheme, while in the correction step we solve the second-order deterministic PDE by deep neural networks via its equivalent backward stochastic differential equation (BSDE). Under standard assumptions, error estimates and the rate of convergence of the proposed algorithm are presented. The efficiency and accuracy of the proposed algorithm are illustrated by numerical examples. Copyright © 2022, The Authors. All rights reserved.

关键词： Numerical methods

A BROKEN HARDY INEQUALITY ON FINITE ELEMENT SPACE AND APPLICATION TO STRAIN GRADIENT ELASTICITY

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Liao, Yulei Ming, Pingbing Department of Mathematics Faculty of Science National University of Singapore 10 Lower Kent Ridge Road Singapore119076 Singapore LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

We illustrate a broken Hardy inequality on discontinuous finite element spaces, blowing up with a logarithmic factor with respect to the meshes size. This is motivated by numerical analysis for the strain gradient elasticity with natural boundary conditions. A mixed finite element pair is employed to solve this model with nearly incompressible materials. This pair is quasi-stable with a logarithmic factor, which is not significant in the approximation error, and converges robustly in the incompressible limit and uniformly in the microscopic material parameter. Numerical results back up that the theoretical predictions are nearly optimal. Moreover, the regularity estimates for the model over a smooth domain have been proved with the aid of the Agmon-Douglis-Nirenberg theory. Copyright © 2025, The Authors. All rights reserved.

关键词： Set theory

Blood Cancer Detection and Classification using Auto Encoder and Regularized Extreme Learning Machine 8

学校读者我要写书评

暂无评论

Blood Cancer Detection and Classification using Auto Encoder...

8th International Conference on Communication and Electronics Systems, ICCES 2023

作者： Kanimozhi, N. Nayak, Swikruti Keshav Kumar, K. Manjramkar, Vinda Kumar, Ranjeet Suganthi, D. Srm Institute of Science and Technology School of Computing Department of Computational Intelligence Chennai Tamilnadu Kattankulathur India Jecrc University Department of Computer Science and Engineering Rajasthan Jaipur India Department of Humanities and Mathematics Shaikpet Telangana Hyderabad India Zoology Maharashtra Thane India University College of Engineering & Technology Vinoba Bhave University Department of Electronics & Communication Jharkhand Hazaribagh India Saveetha Institute of Medical and Technical Sciences Saveetha College of Liberal Arts and Sciences Department of Computer Science Thandalam Chennai India

ISBN: (纸本)9798350396638

Leukaemia is considered as the most common type of blood cancer. The length of time one requires to recover from this disease is determined by how quickly it is recognized and treated. Leukaemia develops when the bone marrow generates an abnormally large amount of white blood cells. Since images of human blood samples are studied under the microscope, haematologists employ techniques such as microscopic colour imaging, image segmentation, grouping, and classification to diagnose patients as fast as possible. Microscopy may identify blood cancer in visible and immature white blood cells in a variety of methods. Early and accurate diagnosis of leukaemia is critical for clinicians to properly treat patients. After the input image is provided, the gaussian filter is used to perform image enhancement, and the Wiener filter is used in image Deblurring, Adaptive K-Means clustering technique, Colour feature, Texture feature, GLCM and Hausdroff are also used, and lastly the Model is trained using AE and RELM. The proposed system outperforms conventional models such as RELM and ELM, which generates an accuracy of 98.45%. © 2023 IEEE.

关键词： Image enhancement

DEEPSPOC: A DEEP LEARNING-BASED PDE SOLVER GOVERNED BY SEQUENTIAL PROPAGATION OF CHAOS

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Du, Kai Xie, Yongle Zhou, Tao Zhou, Yuancheng Shanghai Center for Mathematical Sciences Fudan University Shanghai200438 China Shanghai Center for Mathematical Sciences Fudan University Shanghai200433 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing China

Sequential propagation of chaos (SPoC) is a recently developed tool to solve mean-field stochastic differential equations and their related nonlinear Fokker-Planck equations. Based on the theory of SPoC, we present a new method (deepSPoC) that combines the interacting particle system of SPoC and deep learning. Under the framework of deepSPoC, two classes of frequently used deep models include fully connected neural networks and normalizing flows are considered. For high-dimensional problems, spatial adaptive method are designed to further improve the accuracy and efficiency of deepSPoC. We analysis the convergence of the framework of deepSPoC under some simplified conditions and also provide a posterior error estimation for the algorithm. Finally, we test our methods on a wide range of different types of mean-field equations. Copyright © 2024, The Authors. All rights reserved.

关键词： Stochastic systems

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

学校读者我要写书评

暂无评论

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