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arXiv 2025年

作者： Gao, Yuan Wu, Hao Shu, Ruiqi Dong, Huanshuo Xu, Fan Chen, Rui Yan, Yibo Wen, Qingsong Hu, Xuming Wang, Kun Wu, Jiahao Li, Qing Xiong, Hui Huang, Xiaomeng Department of Earth System Science Ministry of Education Key Laboratory for Earth System Modeling Institute for Global Change Studies Tsinghua University China TEG Tencent China Department and Computer and Science University of Science and Technology of China China Institute for Interdisciplinary Information Sciences Tsinghua University China Department of Computer Science and Engineering The HongKong University of Science and Technology Hong Kong AI Thrust The Hong Kong University of Science and Technology Guangzhou China Squirrel Ai Learning China School of Computer Science and Engineering Nanyang Technological University Singapore Department of Computing The Hong Kong Polytechnic University Hong Kong

Accurate weather forecasts are important for disaster prevention, agricultural planning, and water resource management. Traditional numerical weather prediction (NWP) methods offer physically interpretable high-accuracy predictions but are computationally expensive and fail to fully leverage rapidly growing historical data. In recent years, deep learning methods have made significant progress in weather forecasting, but challenges remain, such as balancing global and regional high-resolution forecasts, excessive smoothing in extreme event predictions, and insufficient dynamic system modeling. To address these issues, this paper proposes a global-regional nested weather forecasting framework based on graph neural networks (GNNs). By combining a dynamic system perspective with multi-grid theory, we construct a multi-scale graph structure and densify the target region to capture local high-frequency features. We introduce an adaptive information propagation mechanism, using dynamic gating units to deeply integrate node and edge features for more accurate extreme event forecasting. For high-resolution regional forecasts, we propose a neural nested grid method to mitigate boundary information loss. Experimental results show that the proposed method performs excellently across global to regional scales and short-term to long-term forecasts, especially in extreme event predictions (e.g., typhoons), significantly improving forecast accuracy. Our codes are available at https://***/YuanGao-YG/OneForecast. Copyright © 2025, The Authors. All rights reserved.

关键词： Weather forecasting

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ASYMPTOTICAL STABILITY OF NEUTRAL REACTION-DIFFUSION EQUATIONS WITH PCAS AND THEIR FINITE ELEMENT METHODS

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Acta Mathematica Scientia 2023年第4期43卷 1865-1880页

作者：韩豪张诚坚 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 focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous ***,for the analytical solutions of the equations,we derive their expressions and asymptotical stability ***,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically ***,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.

关键词： neutral reaction-diffusion equations piecewise continuous arguments asymptotical stability finite element methods numerical experiment

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Cherenkov Radiation:A Stochastic Differential Model Driven by Brownian Motions

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Computer modeling in engineering & sciences 2023年第4期135卷 155-168页

作者： Qingqing Li Zhiwen Duan Dandan Yang School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan430074China

With the development of molecular imaging,Cherenkov optical imaging technology has been widely *** studies regard the partial boundary flux as a stochastic variable and reconstruct images based on the steadystate diffusion *** this paper,time-variable will be considered and the Cherenkov radiation emission process will be regarded as a stochastic *** on the original steady-state diffusion equation,we first propose a stochastic partial differential *** numerical solution to the stochastic partial differential model is carried out by using the finite element *** the time resolution is high enough,the numerical solution of the stochastic diffusion equation is better than the numerical solution of the steady-state diffusion equation,which may provide a new way to alleviate the problem of Cherenkov luminescent imaging *** addition,the process of generating Cerenkov and penetrating in vitro imaging of 18 F radionuclide inmuscle tissue are also first proposed by GEANT4Monte *** result of the GEANT4 simulation is compared with the numerical solution of the corresponding stochastic partial differential equations,which shows that the stochastic partial differential equation can simulate the corresponding process.

关键词： Cherenkov radiation stochastic partial differential equations numerical approximation and analysis GEANT4 Monte Carlo simulation

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Spontaneous Infection and Periodic Evolving of Domain in a Diffusive SIS Epidemic Model

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 164-191页

作者： Qiang Wen Guo-qiang Ren Bin Liu School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan430074China

In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the uniform boundedness of solution is established. In addition, the spatial-temporal risk index R0(ρ) depending on the domain evolution rate ρ(t) as well as its analytical properties are discussed. The monotonicity of R0(ρ)with respect to the diffusion coefficients of the infected dI, the spontaneous infection rate η(ρ(t)y) and interval length L is investigated under appropriate conditions. Further, the existence and asymptotic behavior of periodic endemic equilibria are explored by upper and lower solution method. Finally, some numerical simulations are presented to illustrate our analytical results. Our results provide valuable information for disease control and prevention.

关键词： diffusive SIS model spontaneous infection periodically evolving domain periodic endemic equilibrium

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DYNAMIC ANALYSIS AND OPTIMAL CONTROL OF A FRACTIONAL ORDER SINGULAR LESLIE-GOWER PREY-PREDATOR MODEL

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Acta Mathematica Scientia 2020年第5期40卷 1525-1552页

作者： Linjie MA Bin LIU 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

In this article,we investigate a fractional-order singular Leslie-Gower prey-predator bioeconomic model,which describes the interaction bet ween populations of prey and predator,and takes into account the economic *** firstly obtain the solvability condition and the st ability of the model sys tem,and discuss the singularity induced bifurcation ***,we introduce a st ate feedback controller to elimina te the singularity induced bifurcation phenomenon,and discuss the optimal control ***,numerical solutions and their simulations are considered in order to illustrate the theoretical results and reveal the more complex dynamical behavior.

关键词： fractional order system differential-algebraic system prey-predator bioeconomic model singularity induced bifurcation optimal control

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Cole-Hopf Transformation Based Lattice Boltzmann Model for One-dimensional Burgers' Equation

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Communications in Theoretical Physics 2018年第3期69卷 329-335页

作者： Xiao-Tong Qi Bao-Chang Shi Zhen-Hua Chai 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

In this paper,we present a Cole-Hopf transformation based lattice Boltzmann(LB)model for solving one-dimensional Burgers'equation,and compared to available LB models,the effect of nonlinear convection term can be *** Chapman-Enskog analysis,it can be found that the converted diffusion equation based on the Cole-Hopf transformation can be recovered correctly from present LB *** numerical tests are also performed to validate the present LB model,and the numerical results show that,similar to previous LB models,the present model also has a second-order convergence rate in space,but it is more accurate than the previous ones.

关键词： Burgers'equation Cole-Hopf transformation lattice Boltzmann model

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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.

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Linearized Transformed L1 Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schr¨odinger Equations

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Numerical Mathematics(Theory,Methods and Applications) 2023年第2期16卷 348-369页

作者： Wanqiu Yuan Dongfang Li Chengjian Zhang 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

A linearized transformed L1 Galerkin finite element method(FEM)is presented for numerically solving the multi-dimensional time fractional Schr¨odinger *** optimal error estimates of the fully-discrete scheme are *** error estimates are obtained by combining a new discrete fractional Gr¨onwall inequality,the corresponding Sobolev embedding theorems and some inverse *** the previous unconditional convergence results are usually obtained by using the temporal-spatial error spitting *** examples are presented to confirm the theoretical results.

关键词： Optimal error estimates time fractional Schr¨odinger equations transformed L1 scheme discrete fractional Gr¨onwall inequality

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LMP-GAN: Out-Of-Distribution Detection For Non-Control Data Malware Attacks

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IEEE Transactions on Pattern Analysis and Machine Intelligence 2025年 PP卷 PP页

作者： Wood, David Kapp, David Kebede, Temesgen Hirakawa, Keigo Wuhan University School of Computer Science China Wuhan University National Engineering Research Center for Multimedia Software Hubei Key Laboratory of Multimedia and Network Communication Engineering China Zhongguancun Academy China Wuhan University State Key Laboratory of Information Engineering in Surveying Mapping and Remote Sensing China Sun Yat-sen University School of Geography and Planning China Mohamed bin Zayed University of Artificial Intelligence United Arab Emirates Chongqing University College of Computer Science China The University of Tokyo Japan RIKEN Center for Advanced Intelligence Project Japan Intelligent Science & Technology Academy Limited CASIC China iFlytek Company Ltd. National Engineering Research Center of Speech and Language Information Processing China Nanyang Technological University College of Computing & Data Science Singapore Henan Academy of Sciences Aerospace Information Research Institute China

Anomaly detection is a common application of machine learning. Out-of-distribution (OOD) detection in particular is a semi-supervised anomaly detection technique where the detection method is trained only on the inlier (in-distribution) samples - unlike the fully supervised variant, the distribution of the outlier samples are never explicitly modeled in OOD detection tasks. In this work, we design a novel GAN-based OOD detection network specifically designed to protect a cyber-physical signal systems from novel Trojan malware called non-control data (NCD) attack that evades conventional malware detection techniques. Inspired in part by the classical locally most powerful (LMP) test in statistical inferences, the proposed LMP-GAN trains the OOD detector (discriminator) by generating OOD samples that are aimed at making maximal alteration to the inlier samples while evading detection. We experimentally compare the results to the state-of-the-art anomaly detection methods to demonstrate the benefits and the appropriateness of the LMP-GAN OOD detector. © 2025 IEEE.

关键词： Malware

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A GENERAL CLASS OF ONE-STEP APPROXIMATION FOR INDEX-1 STOCHASTIC DELAY-DIFFERENTIAL-ALGEBRAIC *EQUATIONS

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Journal of Computational Mathematics 2019年第2期37卷 151-169页

作者： Tingting Qin Chengjian Zhang School of Mathematics and Statistics Huazhong University of Science and Technology. Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China

This paper develops a class of general one-step discretization methods for solving the index-1 stochastic delay differential-algebraic equations. The existence and uniqueness theorem of strong solutions of index-1 equations is given. A strong convergence criterion of the methods is derived, which is applicable to a series of one-step stochastic numerical methods. Some specific numerical methods, such as the Euler-Maruyama method, stochastic ^-methods, split-step ^-methods are proposed, and their strong convergence results are given. Numerical experiments further illustrate the theoretical results.

关键词： Stochastic delay differential-algebraic equations One-step discretization schemes Strong convergence

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