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A NEURAL MULTIGRID SOLVER FOR HELMHOLTZ EQUATIONS WITH HIGH WAVENUMBER AND HETEROGENEOUS MEDIA

SIAM Journal on Scientific computing 2025年第3期47卷 C655-C679页

作者： Cui, Chen Jiang, Kai Shu, Shi Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

In this paper, we propose a deep learning-enhanced multigrid solver for high-frequency and heterogeneous Helmholtz equations. By applying spectral analysis, we categorize the iteration error into characteristic and noncharacteristic components. We eliminate the noncharacteristic components by a multigrid wave cycle, which employs carefully selected smoothers on each grid. We diminish the characteristic components by a learned phase function and the approximate solution of an advection-diffusion-reaction (ADR) equation, which is solved using another multigrid V-cycle on a coarser scale, referred to as the ADR cycle. The resulting solver, termed Wave-ADR-NS, enables the handling of error components with varying frequencies and overcomes constraints on the number of grid points per wavelength on coarse grids. Furthermore, we provide an efficient implementation using differentiable programming, making Wave-ADR-NS an end-to-end Helmholtz solver that incorporates parameters learned through semisupervised training. Wave-ADR-NS demonstrates robust generalization capabilities for both in-distribution and out-of-distribution velocity fields of varying difficulty. Comparative experiments with other multigrid methods validate its superior performance in solving heterogeneous 2D Helmholtz equations with wavenumbers exceeding 2000. © 2025 Society for Industrial and Applied Mathematics Publications. All rights reserved.

关键词： Helmholtz equation

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MFS: A Serverless FaaS Simulator 9

MFS: A Serverless FaaS Simulator

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9th International Conference on Web Research, ICWR 2023

作者： Hanaforoosh, Mahrad Ashtiani, Mehrdad Azgomi, Mohammad Abdollahi Iran University of Science and Technology Trustworthy Computing Laboratory School of Computer Engineering Tehran Iran Iran University of Science and Technology Social Computing Laboratory School of Computer Engineering Tehran Iran

ISBN: (纸本)9798350399691

Serverless computing is one of the concepts that has become a trend these days. Serverless computing facilitates the deployment of software on the cloud, fog, edge, and IoT infrastructures. Serverless computing helps developers implement their codebase without worrying about server management hassles. These are the reasons why the concept of serverless computing is presented in the cloud, the edge, the fog, and the Internet of things. Research on serverless computing, on the other hand, requires extensive hardware equipments. It can also be time consuming. Simulation is needed to overcome these problems. MFS is a simulator based on the Apache Open Whisk architecture that seeks to facilitate the evaluation process of serverless computing researches. Compared to similar researches, this simulator supports more features including containers, heterogeneous processing resources (e.g., CPU, GPU, and TPU), different runtimes, and Apache OpenWhisk architecture. It also calculates and reports metrics such as average response time, utilization of different computing resources, rejection ratio, missed ratio, number of containers used, and costs. The mentioned metrics can be calculated in overall and individually for each physical machine. The status of all functions is also reported at the end of the simulation (e.g., completed, missed, and rejected). © 2023 IEEE.

关键词： Containers

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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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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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Characterization of Exact One-Query Quantum Algorithms for Partial Boolean Functions

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Journal of Computer science & Technology 2023年第6期38卷 1423-1430页

作者：叶泽坤李绿周 Institute of Quantum Computing and Computer Theory School of Computer Science and EngineeringSun Yat-sen UniversityGuangzhou 510006China Ministry of Education Key Laboratory of Machine Intelligence and Advanced Computing Sun Yat-sen UniversityGuangzhou 510006China

The query model(or black-box model)has attracted much attention from the communities of both classical and quantum ***,quantum advantages are revealed by presenting a quantum algorithm that has a better query complexity than its classical *** the history of quantum algorithms,the Deutsch algorithm and the Deutsch-Jozsa algorithm play a fundamental role and both are exact one-query quantum *** leads us to con-sider the problem:what functions can be computed by exact one-query quantum algorithms?This problem has been ad-dressed in the literature for total Boolean functions and symmetric partial Boolean functions,but is still open for general partial Boolean ***,in this paper,we continue to characterize the computational power of exact one-query quantum algorithms for general partial Boolean ***,we present several necessary and sufficient conditions for a partial Boolean function to be computed by exact one-query quantum ***,inspired by these conditions,we discover some new representative functions that can be computed by exact one-query quantum algorithms but have an essential difference from the already known ***,it is worth pointing out that before our work,the known func-tions that can be computed by exact one-query quantum algorithms are all symmetric functions and the quantum algo-rithm used is essentially the Deutsch-Jozsa algorithm,whereas the functions discovered in this paper are generally asym-metric and new algorithms to compute these functions are ***,this expands the class of functions that can be computed by exact one-query quantum algorithms.

关键词： quantum computing quantum query complexity quantum algorithm

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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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Uncertainty-Calibrated Test-Time Model Adaptation without Forgetting

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IEEE Transactions on Pattern Analysis and Machine Intelligence 2025年 PP卷 1-14页

作者： Tan, Mingkui Chen, Guohao Wu, Jiaxiang Zhang, Yifan Chen, Yaofo Zhao, Peilin Niu, Shuaicheng South China University of Technology School of Software Engineering China Pazhou Laboratory Guangzhou China XVERSE China National University of Singapore School of Computing Singapore Tencent AI Lab China Nanyang Technological University College of Computing and Data Science Singapore

Test-time adaptation (TTA) seeks to tackle potential distribution shifts between training and testing data by adapting a given model w.r.t. any testing sample. This task is particularly important when the test environment changes frequently. Although some recent attempts have been made to handle this task, we still face two key challenges: 1) prior methods have to perform backpropagation for each test sample, resulting in unbearable optimization costs to many applications;2) while existing TTA solutions can significantly improve the test performance on out-of-distribution data, they often suffer from severe performance degradation on in-distribution data after TTA (known as catastrophic forgetting). To this end, we have proposed an Efficient Anti-Forgetting Test-Time Adaptation (EATA) method which develops an active sample selection criterion to identify reliable and non-redundant samples for test-time entropy minimization. To alleviate forgetting, EATA introduces a Fisher regularizer estimated from test samples to constrain important model parameters from drastic changes. However, in EATA, the adopted entropy loss consistently assigns higher confidence to predictions even when the samples are underlying uncertain, leading to overconfident predictions that underestimate the data uncertainty. To tackle this, we further propose EATA with Calibration (EATA-C) to separately exploit the reducible model uncertainty and the inherent data uncertainty for calibrated TTA. Specifically, we compare the divergence between predictions from the full network and its sub-networks to measure the reducible model uncertainty, on which we propose a test-time uncertainty reduction strategy with divergence minimization loss to encourage consistent predictions instead of overconfident ones. To further re-calibrate predicting confidence on different samples, we utilize the disagreement among predicted labels as an indicator of the data uncertainty. Based on this, we devise a min-max entropy

关键词： Semantic Segmentation

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SEED-VII: A Multimodal Dataset of Six Basic Emotions with Continuous Labels for Emotion Recognition

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IEEE Transactions on Affective computing 2024年第2期16卷 969-985页

作者： Jiang, Wei-Bang Liu, Xuan-Hao Zheng, Wei-Long Lu, Bao-Liang Shanghai Jiao Tong University Center for Brain-Like Computing and Machine Intelligence Department of Computer Science and Engineering Key Laboratory of Shanghai Education Commission for Intelligent Interaction and Cognitive Engineering Brain Science and Technology Research Center Shanghai200240 China

Recognizing emotions from physiological signals is a topic that has garnered widespread interest, and research continues to develop novel techniques for perceiving emotions. However, the emergence of deep learning has highlighted the need for comprehensive and high-quality emotional datasets that enable the accurate decoding of human emotions. To systematically explore human emotions, we develop a multimodal dataset consisting of six basic (happiness, sadness, fear, disgust, surprise, and anger) emotions and the neutral emotion, named SEED-VII. This multimodal dataset includes electroencephalography (EEG) and eye movement signals. The seven emotions in SEED-VII are elicited by 80 different videos and fully investigated with continuous labels that indicate the intensity levels of the corresponding emotions. Additionally, we propose a novel Multimodal Adaptive Emotion Transformer (MAET), that can flexibly process both unimodal and multimodal inputs. Adversarial training is utilized in the MAET to mitigate subject discrepancies, which enhances domain generalization. Our extensive experiments, encompassing both subject-dependent and cross-subject conditions, demonstrate the superior performance of the MAET in terms of handling various inputs. Continuous labels are used to filter the data with high emotional intensity, and this strategy is proven to be effective for attaining improved emotion recognition performance. Furthermore, complementary properties between the EEG signals and eye movements and stable neural patterns of the seven emotions are observed. © 2010-2012 IEEE.

关键词： Eye movements

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Correcting Pronoun Homophones with Subtle Semantics in Chinese Speech Recognition 30

Correcting Pronoun Homophones with Subtle Semantics in Chine...

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Joint 30th International Conference on Computational Linguistics and 14th International Conference on Language Resources and Evaluation, LREC-COLING 2024

作者： Zhang, Zhaobo Gan, Rui Yuan, Pingpeng Jin, Hai National Engineering Research Center for Big Data Technology and System Service Computing Technology and System Laboratory Cluster and Grid Computing Laboratory Huazhong University of Science and Technology Wuhan China

ISBN: (纸本)9782493814104

Speech recognition is becoming prevalent in daily life. However, due to the similar semantic context of the entities and the overlap of Chinese pronunciation, the pronoun homophone, especially "他/她/它 (he/she/it)", (their pronunciation is "Tā") is usually recognized incorrectly. It poses a challenge to automatically correct them during the post-processing of Chinese speech recognition. In this paper, we propose three models to address the common confusion issues in this domain, tailored to various application scenarios. We implement the language model, the LSTM model with semantic features, and the rule-based assisted Ngram model, enabling our models to adapt to a wide range of requirements, from high-precision to low-resource offline devices. The extensive experiments show that our models achieve the highest recognition rate for "Tā" correction with improvements from 70% in the popular voice input methods up to 90%. Further ablation analysis underscores the effectiveness of our models in enhancing recognition accuracy. Therefore, our models improve the overall experience of Chinese speech recognition of "Tā" and reduce the burden of manual transcription corrections. © 2024 ELRA Language Resource Association: CC BY-NC 4.0.

关键词： Speech recognition

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ONE-PARAMETER FINITE DIFFERENCE METHODS AND THEIR ACCELERATED SCHEMES FOR SPACE-FRACTIONAL SINE-GORDON EQUATIONS WITH DISTRIBUTED DELAY

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Journal of Computational Mathematics 2024年第3期42卷 705-734页

作者： Tao Sun Chengjian Zhang Haiwei Sun 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 Department of Mathematics University of MacaoMacaoChina

This paper deals with numerical methods for solving one-dimensional(1D)and twodimensional(2D)initial-boundary value problems(IBVPs)of space-fractional sine-Gordon equations(SGEs)with distributed *** 1D problems,we construct a kind of oneparameter finite difference(OPFD)*** is shown that,under a suitable condition,the proposed method is convergent with second order accuracy both in time and *** implementation,the preconditioned conjugate gradient(PCG)method with the Strang circulant preconditioner is carried out to improve the computational efficiency of the OPFD *** 2D problems,we develop another kind of OPFD *** such a method,two classes of accelerated schemes are suggested,one is alternative direction implicit(ADI)scheme and the other is ADI-PCG *** particular,we prove that ADI scheme can arrive at second-order accuracy in time and *** some numerical experiments,the computational effectiveness and accuracy of the methods are further ***,for the suggested methods,a numerical comparison in computational efficiency is presented.

关键词： Fractional sine-Gordon equation with distributed delay One-parameter finite difference methods Convergence analysis ADI scheme PCG method

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