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arXiv 2022年

作者： Hong, Jialin Jin, Diancong Sheng, Derui LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

This paper presents the convergence analysis of the spatial finite difference method (FDM) for the stochastic Cahn–Hilliard equation with Lipschitz nonlinearity and multiplicative noise. Based on fine estimates of the discrete Green function, we prove that both the spatial semi-discrete numerical solution and its Malliavin derivative have strong convergence order 1. Further, by showing the negative moment estimates of the exact solution, we obtain that the density of the spatial semi-discrete numerical solution converges in L1(R) to the exact one. Finally, we apply an exponential Euler method to discretize the spatial semi-discrete numerical solution in time and show that the temporal strong convergence order is nearly 83, where a difficulty we overcome is to derive the optimal Hölder continuity of the spatial semi-discrete numerical solution. Copyright © 2022, The Authors. All rights reserved.

关键词： Stochastic systems

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DENSITY CONVERGENCE OF A FULLY DISCRETE FINITE DIFFERENCE METHOD FOR STOCHASTIC CAHN-HILLIARD EQUATION

arXiv

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arXiv 2022年

This paper focuses on investigating the density convergence of a fully discrete finite difference method when applied to numerically solve the stochastic Cahn-Hilliard equation driven by multiplicative space-time white noises. The main difficulty lies in the control of the drift coefficient that is neither globally Lipschitz nor one-sided Lipschitz. To handle this difficulty, we propose a novel localization argument and derive the strong convergence rate of the numerical solution to estimate the total variation distance between the exact and numerical solutions. This along with the existence of the density of the numerical solution finally yields the convergence of density in L1() of the numerical solution. Our results partially answer positively to the open problem emerged in [J. Cui and J. Hong, J. Differential Equations (2020)] on computing the density of the exact solution numerically. Copyright © 2022, The Authors. All rights reserved.

关键词： Finite difference method

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Static hand gesture segmentation: Comparison and selection of existing methods

Static hand gesture segmentation: Comparison and selection o...

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Youth Academic Annual Conference of Chinese Association of Automation (YAC)

作者： Yajie Liao Gongfa Li Ying Sun Guozhang Jiang Jianyi Kong Du Jiang Zhaojie Ju Ministry of Education Wuhan University of Science and Technology China Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering Wuhan University of Science and Technology Wuhan China School of Computing University of Portsmouth Portsmouth UK

ISBN: (纸本)9781538629024

This paper focuses on the introduction and summary of static hand gesture segmentation methods. Starting with the research on image segmentation methods and the development of hand gesture recognition, we illustrate the most popular methods in static hand gesture segmentation and their advantages and applicable scope in each image processing steps, by comparing different processing methods used in different stages of static hand gesture segmentation, for example calibrating image color, choosing color space, choosing a certain skin color model and using different post-processing scheme. Finally, the static gesture segmentation methods are summarized and prospected, The conclusion provided researchers with certain theoretical basis for choosing static hand gestures segmentation method, in turn lay a good foundation for subsequent gesture recognition works.

关键词： Image color analysis Image segmentation Skin Object segmentation Gesture recognition Mathematical model Electronic mail

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Data-driven method to learn the most probable transition pathway and stochastic differential equations

arXiv

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arXiv 2021年

作者： Chen, Xiaoli Duan, Jinqiao Hu, Jianyu Li, Dongfang School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Department of Mathematics National University of Singapore 119077 Singapore Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Department of Applied Mathematics College of Computing Illinois Institute of Technology ChicagoIL60616 United States

Transition phenomena between metastable states play an important role in complex systems due to noisy fluctuations. We introduce the Onsager-Machlup theory and the Freidlin-Wentzell theory to quantify rare events in stochastic differential equations. By the variational principle, the most probable transition pathway is the minimizer of the action functional, which is governed by the Euler-Lagrange equation. In this paper, the physics-informed neural networks (PINNs) are presented to compute the most probable transition pathway through computing the Euler-Lagrange equation. The convergence result for the empirical loss is obtained for the forward problem. Then we investigate the inverse problem to extract the stochastic differential equation from the most probable transition pathway data. Finally, several numerical experiments are presented to verify the effectiveness of our methods. Copyright © 2021, The Authors. All rights reserved.

关键词： Inverse problems

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Image Denoising Method Based on Channel Compression and Split-Attention Mechanism

Image Denoising Method Based on Channel Compression and Spli...

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Computer engineering and Intelligent Control (ICCEIC) International Conference on

作者： Hao Sun Xiaoyan Qiao Yantai Key Laboratory of Big Data Modeling and Intelligent Computing Immersion School of Computer Science and Technology Shandong Technology and Business University Technology and Evaluation Shandong Engineering Research Center Yantai Shandong

ISBN: (数字)9798331507992

ISBN: (纸本)9798331508005

In the image restoration task, how to make full use of spatial and channel feature information to improve the reconstruction quality of the model without significantly increasing the computational complexity is an important research issue. To address this challenge, this paper proposes a CS module (Channel Compression and Split-Attention) specifically for optimizing image denoising tasks. The module first compresses the features through a preliminary convolution operation, then introduces the split attention convolution mechanism to split the features by channel and dynamically weight them, thereby enhancing the model's adaptive attention to different feature channels and improving feature expression capabilities. Through experiments on multiple image denoising datasets, the results show that the CS module significantly improves the image reconstruction quality, especially in terms of peak signal-to-noise ratio (PSNR). At the same time, the introduction of the CS module does not lead to a significant increase in computational complexity, maintaining a high computational efficiency, which verifies the practicality and superiority of the module in image denoising tasks.

关键词： Image coding PSNR Convolution Computational modeling Refining Image restoration Computational efficiency Computational complexity Image reconstruction Image denoising

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Effective Concurrency Testing for Go via Directional Primitive-Constrained Interleaving Exploration

Effective Concurrency Testing for Go via Directional Primiti...

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IEEE International Conference on Automated Software engineering (ASE)

作者： Zongze Jiang Ming Wen Yixin Yang Chao Peng Ping Yang Hai Jin School of Cyber Science and Engineering Huazhong University of Science and Technology China Hubei Key Laboratory of Distributed System Security Services Computing Technology and System Lab Cluster and Grid Computing Lab Hubei Engineering Research Center on Big Data Security National Engineering Research Center for Big Data Technology and System ByteDance Beijing China School of Computer Science and Technology Huazhong University of Science and Technology China

The Go language (Go/Golang) has been attracting increasing attention from the industry over recent years due to its strong concurrency support and ease of deployment. This programming language encourages developers to use channel-based concurrency, which simplifies the development of concurrent programs. Unfortunately, it also introduces new concurrency problems that differ from those caused by the mechanism of shared memory concurrency. However, there are only few works that aim to detect such Go-specific concurrency issues. Even state-of-the-art testing tools will miss critical concurrent bugs that require fine-grained and effective interleaving exploration. This paper presents GoPie, a novel testing approach for detecting Go concurrency bugs through primitive-constrained interleaving exploration. GoPie utilizes execution histories to identify new interleavings instead of relying on exhaustive exploration or random scheduling. To evaluate its performance, we applied GoPie to existing benchmarks and large-scale open-source projects. Results show that GoPie can effectively explore concurrent interleavings and detect significantly more bugs in the benchmark. Furthermore, it uncovered 11 unique previously unknown concurrent bugs, and 9 of which have been confirmed.

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AOCC-FL: Federated Learning with Aligned Overlapping via Calibrated Compensation

AOCC-FL: Federated Learning with Aligned Overlapping via Cal...

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IEEE Annual Joint Conference: INFOCOM, IEEE Computer and Communications Societies

作者： Haozhao Wang Wenchao Xu Yunfeng Fan Ruixuan Li Pan Zhou School of Computer Science and Technology Huazhong University of Science and Technology Wuhan China Department of Computing The Hong Kong Polytechnic University Hong Kong Hubei Key Laboratory of Distributed System Security Hubei Engineering Research Center on Big Data Security School of Cyber Science and Engineering Huazhong University of Science and Technology Wuhan China

Federated Learning enables collaboratively model training among a number of distributed devices with the coordination of a centralized server, where each device alternatively performs local gradient computation and communication to the server. FL suffers from significant performance degradation due to the excessive communication delay between the server and devices, especially when the network bandwidth of these devices is limited, which is common in edge environments. Existing methods overlap the gradient computation and communication to hide the communication latency to accelerate the FL training. However, the overlapping can also lead to an inevitable gap between the local model in each device and the global model in the server that seriously restricts the convergence rate of learning process. To address this problem, we propose a new overlapping method for FL, AOCC-FL, which aligns the local model with the global model via calibrated compensation such that the communication delay can be hidden without deteriorating the convergence performance. Theoretically, we prove that AOCC-FL admits the same convergence rate as the non-overlapping method. On both simulated and testbed experiments, we show that AOCC-FL achieves a comparable convergence rate relative to the non-overlapping method while outperforming the state-of-the-art overlapping methods.

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A lattice Boltzmann model for two-phase flow in porous media

arXiv

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arXiv 2018年

作者： Chai, Zhenhua Liang, Hong Du, Rui Shi, Baochang School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China State Key Laboratory of Coal Combustion Huazhong University of Science and Technology Wuhan430074 China Department of Physics Hangzhou Dianzi University Hangzhou310018 China School of Mathematics Southeast University Nanjing210096 China

In this paper, a lattice Boltzmann (LB) model with double distribution functions is proposed for two-phase flow in porous media where one distribution function is used for pressure governed by the Poisson equation, and the other is applied for saturation evolution described by the convection-diffusion equation with a source term. We first performed a Chapman-Enskog analysis, and show that the macroscopic nonlinear equations for pressure and saturation can be recovered correctly from present LB model. Then in the framework of LB method, we develop a local scheme for pressure gradient or equivalently velocity, which may be more efficient than the nonlocal second-order finite-difference schemes. We also perform some numerical simulations, and the results show that the developed LB model and local scheme for velocity are accurate and also have a second-order convergence rate in space. Finally, compared to the available pore-scale LB models for two-phase flow in porous media, the present LB model has more potential in the study of the large-scale problems. Copyright © 2018, The Authors. All rights reserved.

关键词： Two phase flow

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Shape correspondence using anisotropic Chebyshev spectral CNNs

Shape correspondence using anisotropic Chebyshev spectral CN...

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Conference on Computer Vision and Pattern Recognition (CVPR)

作者： Qinsong Li Shengjun Liu Ling Hu Xinru Liu Institute of Engineering Modeling and Scientific Computing Central South University State Key Laboratory of High Performance Manufacturing Complex Central South University School of Mathematics and Computational Science Hunan First Normal University

ISBN: (数字)9781728171685

ISBN: (纸本)9781728171692

Establishing correspondence between shapes is a very important and active research topic in many domains. Due to the powerful ability of deep learning on geometric data, lots of attractive results have been achieved by convolutional neural networks (CNNs). In this paper, we propose a novel architecture for shape correspondence, termed Anisotropic Chebyshev spectral CNNs (ACSCNNs), based on a new extension of the manifold convolution operator. The extended convolution operators aggregate the local features of signals by a set of oriented kernels around each point, which allows to much more comprehensively capture the intrinsic signal information. Rather than using fixed oriented kernels in the spatial domain in previous CNNs, in our framework, the kernels are learned by spectral filtering, based on the eigen-decompositions of multiple Anisotropic Laplace-Beltrami Operators. To reduce the computational complexity, we employ an explicit expansion of the Chebyshev polynomial basis to represent the spectral filters whose expansion coefficients are trainable. Through the benchmark experiments of shape correspondence, our architecture is demonstrated to be efficient and be able to provide better than the state-of-the-art results in several datasets even if using constant functions as inputs.

关键词： Shape Manifolds Convolution Kernel Machine learning Eigenvalues and eigenfunctions Chebyshev approximation

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Intersecting-boundary-sensitive fingerprinting for tampering detection of DNN models 24

Intersecting-boundary-sensitive fingerprinting for tampering...

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Proceedings of the 41st International Conference on Machine Learning

作者： Xiaofan Bai Chaoxiang He Xiaojing Ma Bin Benjamin Zhu Hai Jin School of Cyber Science and Engineering Huazhong University of Science and Technology National Engineering Research Center for Big Data Technology and System and Services Computing Technology and System Lab and Hubei Engineering Research Center on Big Data Security and Hubei Key Laboratory of Distributed System Security Microsoft School of Computer Science and Technology Huazhong University of Science and Technology and National Engineering Research Center for Big Data Technology and System and Services Computing Technology and System Lab and Cluster and Grid Computing Lab.

Cloud-based AI services offer numerous benefits but also introduce vulnerabilities, allowing for tampering with deployed DNN models, ranging from injecting malicious behaviors to reducing computing resources. Fingerprint samples are generated to query models to detect such tampering. In this paper, we present Intersecting-Boundary-Sensitive Fingerprinting (IBSF), a novel method for black-box integrity verification of DNN models using only top-1 labels. Recognizing that tampering with a model alters its decision boundary, IBSF crafts fingerprint samples from normal samples by maximizing the partial Shannon entropy of a selected subset of categories to position the fingerprint samples near decision boundaries where the categories in the subset intersect. These fingerprint samples are almost indistinguishable from their source samples. We theoretically establish and confirm experimentally that these fingerprint samples' expected sensitivity to tampering increases with the cardinality of the subset. Extensive evaluation demonstrates that IBSF surpasses existing state-of-the-art fingerprinting methods, particularly with larger subset cardinality, establishing its state-of-the-art performance in black-box tampering detection using only top-1 labels. The IBSF code is available at: https://***/CGCL-codes/IBSF.

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