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High-Order Discontinuous Galerkin Schemes for Radiation Hydrodynamics Equations in the Equilibrium-Diffusion Limit

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SSRN

SSRN 2023年

作者： Peng, Gang Luo, Dongmi Qiu, Jianxian Chen, Yibing Command and Control Engineering College Army Engineering University of PLA Nanjing210007 China Institute of Applied Physics and Computational Mathematics National Key Laboratory of Computational Physics Beijing100088 China School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University Fujian Xiamen361005 China

In this paper, the high-order discontinuous Galerkin (DG) schemes are presented for radiation hydrodynamics equations in the equilibrium-diffusion limit. The governor equations contain two parts, one part is a hyperbolic system of conservation laws and another part is a radiative heat transfer term. The discrete schemes are constructed in three parts and possess characteristics of the high-order, oscillation-free and efficient. Firstly, the DG method and local DG (LDG) method are respectively used to discretize the hyperbolic system and radiative heat transfer term to achieve high-order spatial accuracy. Secondly, the combination of the KXRCF shock detector, Hermite WENO limiter, and positivity-preserving limiter is utilized to enhance the robustness of the discretization schemes. Finally, the implicit-explicit schemes are employed for time discretization to enable the schemes suitable for larger time steps. Numerical experiments have verified that the new schemes are high-order accuracy, oscillation-free and efficiency. © 2023, The Authors. All rights reserved.

关键词： Hydrodynamics

ON SCHRÖDINGERIZATION BASED QUANTUM ALGORITHMS FOR LINEAR DYNAMICAL SYSTEMS WITH INHOMOGENEOUS TERMS

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arXiv 2024年

作者： Jin, Shi Liu, Nana Ma, Chuwen School of Mathematical Sciences Shanghai Jiao Tong University Institute of Natural Sciences Shanghai Jiao Tong University Ministry of Education Key Laboratory in Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China Institute of Natural Sciences Shanghai Jiao Tong University Ministry of Education Key Laboratory in Scientific and Engineering Computing Shanghai Jiao Tong University University of Michigan Shanghai Jiao Tong University Joint Institute Shanghai200240 China School of Mathematical Sciences Shanghai Jiao Tong University Institute of Natural Sciences Shanghai Jiao Tong University Shanghai200240 China

We analyze the Schrödingerization method for quantum simulation of a general class of non-unitary dynamics with inhomogeneous source terms. The Schrödingerization technique, introduced in [S. Jin, N. Liu and Y. Yu, Phys. Rev. Lett., 133 (2024), 230602], transforms any linear ordinary and partial differential equations with non-unitary dynamics into a system under unitary dynamics via a warped phase transition that maps the equations into a higher dimension, making them suitable for quantum simulation. This technique can also be applied to these equations with inhomogeneous terms modeling source or forcing terms, or boundary and interface conditions, and discrete dynamical systems such as iterative methods in numerical linear algebra, through extra equations in the system. Difficulty arises with the presence of inhomogeneous terms since they can change the stability of the original system. In this paper, we systematically study—both theoretically and numerically—the important issue of recovering the original variables from the Schrödingerized equations, even when the evolution operator contains unstable modes. We show that, even with unstable modes, one can still construct a stable scheme;however, to recover the original variable, one needs to use suitable data in the extended space. We analyze and compare both the discrete and continuous Fourier transforms used in the extended dimension and derive corresponding error estimates, which allow one to use the more appropriate transform for specific equations. We also provide a smoother initialization for the Schrödingerized system to gain higher-order accuracy in the extended space. We homogenize the inhomogeneous terms with a stretch transformation, making it easier to recover the original variable. Our recovery technique also provides a simple and generic framework to solve general ill-posed problems in a computationally stable way. Copyright © 2024, The Authors. All rights reserved.

关键词： Iterative methods

Convergence analysis of Hermite approximations for analytic functions

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arXiv 2023年

作者： Wang, Haiyong Zhang, Lun 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 School of Mathematical Sciences Shanghai Key Laboratory for Contemporary Applied Mathematics Fudan University Shanghai200433 China

In this paper, we present a rigorous analysis of root-exponential convergence of Hermite approximations, including projection and interpolation methods, for functions that are analytic in an infinite strip containing the real axis and satisfy certain restrictions on the asymptotic behavior at infinity within this strip. Asymptotically sharp error bounds in the weighted and maximum norms are derived. The key ingredients of our analysis are some remarkable contour integral representations for the Hermite coefficients and the remainder of Hermite spectral interpolations. Further extensions to Gauss-Hermite quadrature, Hermite spectral differentiations, generalized Hermite spectral approximations and the scaling factor of Hermite approximation are also discussed. Numerical experiments confirm our theoretical *** Codes 41A25, 41A10 Copyright © 2023, The Authors. All rights reserved.

关键词： Interpolation

Fluorescence interference structured illumination microscopy for 3D morphology imaging with high axial resolution

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Advanced Photonics 2023年第5期5卷 96-105页

作者： Yile Sun Hongfei Zhu Lu Yin Hanmeng Wu Mingxuan Cai Weiyun Sun Yueshu Xu Xinxun Yang Jiaxiao Han Wenjie Liu Yubing Han Xiang Hao Renjie Zhou Cuifang Kuang Xu Liu Zhejiang University College of Optical Science and EngineeringState Key Laboratory of Extreme Photonics and InstrumentationHangzhouChina The Chinese University of Hong Kong Department of Biomedical EngineeringHong KongChina China Jiliang University College of Optical and Electronic TechnologyHangzhouChina Zhejiang University of Technology Institute of PharmacologyCollege of Pharmaceutical SciencesHangzhouChina ZJU-Hangzhou Global Scientific and Technological Innovation Center HangzhouChina Huazhong University of Science and Technology Britton Chance Center for Biomedical Photonics-MoE Key Laboratory for Biomedical PhotonicsAdvanced Biomedical Imaging Facility-Wuhan National Laboratory for OptoelectronicsWuhanChina Shanxi University Collaborative Innovation Center of Extreme OpticsTaiyuanChina

Imaging three-dimensional,subcellular structures with high axial resolution has always been the core purpose of fluorescence ***,trade-offs exist between axial resolution and other important technical indicators,such as temporal resolution,optical power density,and imaging process *** report a new imaging modality,fluorescence interference structured illumination microscopy(FI-SIM),which is based on three-dimensional structured illumination microscopy for wide-field lateral imaging and fluorescence interference for axial ***-SIM can acquire images quickly within the order of hundreds of milliseconds and exhibit even 30 nm axial resolution in half the wavelength depth range without z-axis ***,the relatively low laser power density relaxes the requirements for dyes and enables a wide range of applications for observing fixed and live subcellular structures.

关键词： optical imaging super-resolution microscopy fluorescence interference structured illumination microscopy

ANALYSIS AND APPROXIMATION TO PARABOLIC OPTIMAL CONTROL PROBLEMS WITH MEASURE-VALUED CONTROLS IN TIME

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arXiv 2024年

作者： Gong, Wei Liang, Dongdong The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics National Center for Mathematics and Interdisciplinary Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The Hong Kong Polytechnic University Shenzhen Research Institute Shenzhen518057 China

In this paper, we investigate an optimal control problem governed by parabolic equations with measure-valued controls over time. We establish the well-posedness of the optimal control problem and derive the first-order optimality condition using Clarke’s subgradients, revealing a sparsity structure in time for the optimal control. Consequently, these optimal control problems represent a generalization of impulse control for evolution equations. To discretize the optimal control problem, we employ the space-time finite element method. Here, the state equation is approximated using piecewise linear and continuous finite elements in space, alongside a Petrov-Galerkin method utilizing piecewise constant trial functions and piecewise linear and continuous test functions in time. The control variable is discretized using the variational discretization concept. For error estimation, we initially derive a priori error estimates and stabilities for the finite element discretizations of the state and adjoint equations. Subsequently, we establish weak-* convergence for the control under the norm M(I¯c;L2(ω)), with a convergence order of O(h 21 + τ 41 ) for the *** Codes 65M06, 68M99, 49M40 © 2024, CC BY-SA.

关键词： Optimal control systems

Green Federated Learning Over Cloud-RAN with Limited Fronthual Capacity and Quantized Neural Networks

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arXiv 2023年

作者： Wang, Jiali Mao, Yijie Wang, Ting Shi, Yuanming MoE Engineering Research Center of Software/Hardware Co-design Technology and Application The Shanghai Key Laboratory of Trustworthy Computing Software Engineering Institute East China Normal University Shanghai200062 China School of Information Science and Technology ShanghaiTech University Shanghai201210 China

In this paper, we propose an energy-efficient federated learning (FL) framework for the energy-constrained devices over cloud radio access network (Cloud-RAN), where each device adopts quantized neural networks (QNNs) to train a local FL model and transmits the quantized model parameter to the remote radio heads (RRHs). Each RRH receives the signals from devices over the wireless link and forwards the signals to the CS via the fronthaul link. We rigorously develop an energy consumption model for the local training at devices through the use of QNNs and communication models over Cloud-RAN. Based on the proposed energy consumption model, we formulate an energy minimization problem that optimizes the fronthaul rate allocation, user transmit power allocation, and QNN precision levels while satisfying the limited fronthaul capacity constraint and ensuring the convergence of the proposed FL model to a target accuracy. To solve this problem, we analyze the convergence rate and propose efficient algorithms based on the alternative optimization technique. Simulation results show that the proposed FL framework can significantly reduce energy consumption compared to other conventional approaches. We draw the conclusion that the proposed framework holds great potential for achieving a sustainable and environmentally-friendly FL in Cloud-RAN. Copyright © 2023, The Authors. All rights reserved.

关键词： Radio access networks

Slowly Expanding Neural Network for Class Incremental Learning

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SSRN

SSRN 2023年

作者： Xu, Zhengjin Li, Xuyang Chang, Xiaobin Zheng, Wei-Shi Wang, Ruixuan School of Computer Science and Engineering Sun Yat-sen University Guangzhou China Department of Network Intelligence Pengcheng Laboratory Shenzhen China Key Laboratory of Machine Intelligence and Advanced Computing MOE Guangzhou China School of Artificial Intelligence Sun Yat-sen University Zhuhai China

Currently deep learning models often rapidly forget the knowledge of old classes when they are continually updated to learn knowledge of new classes. To alleviate such catastrophic forgetting issues, the state-of-the-art approach often freezes the learned feature extractor to preserve the old knowledge and introduces an additional network when learning new knowledge each time. The forgetting issue can be effectively handled by this method at the price of rapid model expansion. In this paper, we propose a novel continual learning framework, called SEIL, with a much Slower model Expansion rate and better Incremental Learning performance than its counterparts. Specifically, instead of introducing an entire feature extractor, the majority of network parameters are shared during continual learning, and only the remaining lightweight modules are expanded for each new task. An outof-the-distribution (OOD) technique is also applied to two auxiliary classifiers for more class-balanced predictions. The proposed method achieves new state-of-theart results on multiple benchmark datasets under the standard continual learning settings. The source code will be released publicly. © 2023, The Authors. All rights reserved.

关键词： Image classification

Mixed Matrix Completion in Complex Survey Sampling under Heterogeneous Missingness

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arXiv 2024年

作者： Mao, Xiaojun Wang, Hengfang Wang, Zhonglei Yang, Shu School of Mathematical Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing Shanghai Jiao Tong University China School of Mathematics and Statistics Fujian Provincial Key Laboratory of Statistics and Artificial Intelligence Fujian Normal University China Wang Yanan Institute for Studies in Economics School of Economics Xiamen University China Department of Statistics North Carolina State University United States

Modern surveys with large sample sizes and growing mixed-type questionnaires require robust and scalable analysis methods. In this work, we consider recovering a mixed dataframe matrix, obtained by complex survey sampling, with entries following different canonical exponential distributions and subject to heterogeneous missingness. To tackle this challenging task, we propose a two-stage procedure: in the first stage, we model the entry-wise missing mechanism by logistic regression, and in the second stage, we complete the target parameter matrix by maximizing a weighted log-likelihood with a low-rank constraint. We propose a fast and scalable estimation algorithm that achieves sublinear convergence, and the upper bound for the estimation error of the proposed method is rigorously derived. Experimental results support our theoretical claims, and the proposed estimator shows its merits compared to other existing methods. The proposed method is applied to analyze the National Health and Nutrition Examination Survey data. Copyright © 2024, The Authors. All rights reserved.

关键词： Machine learning

A semi-adaptive finite difference method for simulating two-sided fractional convection-diffusion quenching problems

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arXiv 2025年

作者： Dong, Rumin Zhu, Lin Sheng, Qin Zhao, Bingxin School of Mathematics and Statistics Ningxia Key Laboratory of Interdisciplinary Mechanics and Scientific Computing Ningxia Basic Science Research Center of Mathematics Ningxia University Yinchuan750021 China Department of Mathematics Center for Astrophysics Space Physics and Engineering Research Baylor University WacoTX76798-7328 United States

This paper investigates quenching solutions of an one-dimensional, two-sided Riemann-Liouville fractional order convection-diffusion problem. Fractional order spatial derivatives are discretized using weighted averaging approximations in conjunction with standard and shifted Grünwald formulas. The advective term is handled utilizing a straightforward Euler formula, resulting in a semi-discretized system of nonlinear ordinary differential equations. The conservativeness of the proposed scheme is rigorously proved and validated through simulation experiments. The study is further advanced to a fully discretized, semi-adaptive finite difference method. Detailed analysis is implemented for the monotonicity, positivity and stability of the scheme. Investigations are carried out to assess the potential impacts of the fractional order on quenching location, quenching time, and critical length. The computational results are thoroughly discussed and analyzed, providing a more comprehensive understanding of the quenching phenomena modeled through two-sided fractional order convection-diffusion problems. Copyright © 2025, The Authors. All rights reserved.

关键词： Ordinary differential equations