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GLOBAL WELL-POSEDNESS FOR THE LANDAU-LIFSHITZ-BARYAKHTAR EQUATION IN 3

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arXiv 2024年

作者： Xu, Fan Liu, Bin School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China

This paper establishes the global well-posedness of the Landau-Lifshitz-Baryakhtar (LLBar) equation in the whole space 3. The study first demonstrates the existence and uniqueness of global strong solutions using the weak compactness approach. Furthermore, the existence and uniqueness of classical solutions, as well as arbitrary smooth solutions, are derived through a bootstrap argument. The proofs for the existence of these three types of global solutions are based on Friedrichs mollifier approximation and energy estimates, with the structure of the LLBar equation playing a crucial role in the derivation of the results. Copyright © 2024, The Authors. All rights reserved.

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A CHEMOTAXIS-FLUID MODEL DRIVEN BY LÉVY NOISE IN R2

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arXiv 2024年

In this paper, we investigate the existence and uniqueness of global solutions to the Cauchy problem for a coupled stochastic chemotaxis-Navier-Stokes system with multiplicative Lévy noises in R2. The existence of global martingale solutions is proved under a framework that is based on the Faedo-Galerkin approximation scheme and stochastic compactness method, where the verification of tightness depends crucially on a novel stochastic version of Lyapunov functional inequality and proper compactness criteria in Fréchet spaces. A pathwise uniqueness result is also established with suitable assumption on the jump noises, which indicates that the considered system admits a unique global strong solution. Copyright © 2024, The Authors. All rights reserved.

关键词： Lyapunov functions

WELL-POSEDNESS AND INVARIANT MEASURES FOR THE STOCHASTICALLY PERTURBED LANDAU-LIFSHITZ-BARYAKHTAR EQUATION

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arXiv 2024年

In this paper, we study the initial-boundary value problem for the stochastic Landau-Lifshitz-Baryakhtar (SLLBar) equation with Stratonovich-type noise in bounded domains O ⊂ Rd, d = 1, 2, 3. Our main results can be briefly described as follows: (1) for d = 1, 2, 3 and any u0 ∈ H1, the SLLBar equation admits a unique local-in-time pathwise weak solution;(2) for d = 1 and small-data u0 ∈ H1, the SLLBar equation has a unique global-in-time pathwise weak solution and at least one invariant measure;(3) for d = 1, 2 and small-data u0 ∈ L2, the SLLBar equation possesses a unique global-in-time pathwise very weak solution and at least one invariant measure, while for d = 3 only the existence of martingale solution is obtained due to the loss of pathwise uniqueness. Copyright © 2024, The Authors. All rights reserved.

关键词： Stochastic systems

WELL-POSEDNESS AND LARGE DEVIATIONS OF LÉVY-DRIVEN MARCUS STOCHASTIC LANDAU-LIFSHITZ-BARYAKHTAR EQUATION

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arXiv 2024年

作者： Xu, Fan Liu, Bin Zhang, Lei School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China

This paper considers the stochastic Landau-Lifshitz-Baryakhtar (SLLBar) equation with pure jump noise in Marcus canonical form, which describes the dynamics of magnetic spin field in a ferromagnet at elevated temperatures with the effective field Heff influenced by external random noise. Under the natural assumption that the magnetic body O ⊂ Rd (d = 1, 2, 3) is bounded with smooth boundary, we shall prove that the initial-boundary value problem of SLLBar equation possesses a unique global probabilistically strong and analytically weak solution with initial data in the energy space H1(O). Then by employing the weak convergence method, we proceed to establish a Freidlin-Wentzell type large deviation principle for pathwise solutions to the SLLBar equation. Copyright © 2024, The Authors. All rights reserved.

关键词： Stochastic systems

Task Separation and Knowledge Sharing for Class Incremental Learning 5

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Task Separation and Knowledge Sharing for Class Incremental ...

5th International Conference on Intelligent computing and Human-Computer Interaction, ICHCI 2024

作者： Zhang, Jiali Qiao, Xiaoyan School of Computer Science and Technology Shandong Technology and Business University Yantai Key Laboratory of Big Data Modeling and Intelligent Computing Immersion Technology and Evaluation Shandong Engineering Research Center Shandong Yantai China School of Mathematics and Information Science Shandong Technology and Business University Yantai Key Laboratory of Big Data Modeling and Intelligent Computing Immersion Technology and Evaluation Shandong Engineering Research Center Shandong Yantai China

ISBN: (纸本)9798350368284

Methods based on dynamically expanding architectures can effectively mitigate catastrophic forgetting in class incremental learning (CIL), but they often overlook information sharing and integration between subnetworks, leading to performance degradation and increased parameter count and memory consumption as the network expands. To address these complex issues, we introduce a new method called Task Separation and Knowledge Sharing (TSKS), which transfers knowledge at both the logical and feature levels through Hybrid Knowledge Distillation (HKD). In logical distillation, we combine Global Knowledge Distillation (GKD) and Task Knowledge Distillation (TKD) to establish connections between tasks. To prevent the model from favoring new classes, we design an Attention- Based Feature Fusion (ABFF) mechanism to capture important features. Additionally, we introduce a Soft-Margin Auxiliary Loss (SMAL) to help the model learn new concepts. Extensive experiments show that TSKS outperforms existing models on CIFAR100 and ImageNet100, regardless of whether memory samples are used. Notably, TSKS demonstrates superior performance in memory-free settings, indicating a reduced reliance on rehearsal memory. © 2024 IEEE.

关键词： Adversarial machine learning

BOUNDARY VALUE METHODS FOR CA PUTO FR ACTIONAL DIFFERENTIAL EQUATIONS

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Journal of Computational Mathematics 2021年第1期39卷 108-129页

作者： Yongtao Zhou Chengiian Zhang Huiru Wang School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China

This paper deals with the numerical computation and analysis for Caputo fractional differential equations(CFDEs).By combining the p-order boundary value methods(B-VMs)and the m-th Lagrange interpolation,a type of exte... 详细信息

关键词： Fractional differential equations Caputo derivatives Boundary value methods Local stability Unique solvability Convergence.

Improving Adversarial Transferability with Ghost Samples 26

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Improving Adversarial Transferability with Ghost Samples

26th European Conference on Artificial Intelligence, ECAI 2023

作者： Zhao, Yi Mou, Ningping Ge, Yunjie Wang, Qian The Key Laboratory of Aerospace Information Security and Trusted Computing Ministry of Education School of Cyber Science and Engineering Wuhan University Hubei Wuhan430072 China

ISBN: (纸本)9781643684369

Adversarial transferability presents an intriguing phenomenon, where adversarial examples designed for one model can effectively deceive other models. By exploiting this property, various transfer-based methods are proposed to conduct adversarial attacks without knowledge of target models, posing significant threats to practical black-box applications. However, these methods either have limited transferability or require high resource consumption. To bridge the gap, we investigate adversarial transferability from the optimization perspective and propose the ghost sample attack (GSA). GSA improves adversarial transferability by alleviating the overfitting issue of adversarial examples on the surrogate model. Based on the insight that a slight shift of the adversarial example is similar to a minor change in the decision boundary, we aggregate gradients of perturbed adversarial copies (named ghost samples) to efficiently achieve a similar effect to calculating gradients of multiple ensemble surrogate models. Extensive experiments demonstrate that GSA achieves state-of-the-art adversarial transferability with restricted resources. On average, GSA improves the attack success rate by 4.8% on normally trained models compared to state-of-the-art attacks. Additionally, GSA reduces the computational cost by 62% compared with TAIG-R. When combined with other methods, GSA further improves transferability to 96.9% on normally trained models and 82.7% on robust models. © 2023 The Authors.

关键词： Machine learning

MODERATE DEVIATION PRINCIPLES FOR A REACTION DIFFUSION MODEL IN NON-EQUILIBRIUM

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arXiv 2024年

作者： Zhao, Linjie School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

We study moderate deviations from hydrodynamic limits of a reaction diffusion model. The process is defined as the superposition of the symmetric exclusion process with a Glauber dynamics. When the process starts from a product measure with a constant density, which is a non-equilibrium measure for the process, we prove that the re-scaled density fluctuation field satisfies the moderate deviation principle. Our proof relies on the so-called main lemma developed by Jara and Menezes [5, 6]. © 2024, CC BY.

关键词： Equilibrium constants

Image Denoising Method Based on Channel Compression and Split-Attention Mechanism 5

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

5th International Conference on Computer engineering and Intelligent Control, ICCEIC 2024

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

ISBN: (纸本)9798331507992

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. © 2024 IEEE.

关键词： Restoration