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αSetup-PCTL:An Adaptive Setup-Based Two-Level Preconditioner for Sequence of Linear Systems of Three-Temperature Energy Equations

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Communications in Computational Physics 2022年第10期32卷 1287-1309页

作者： Silu Huang Xiaoqiang Yue Xiaowen Xu Laboratory of Computational Physics Institute of Applied Physics and ComputationalMathematicsBeijing 100088China National Center for Applied Mathematics in Hunan Key Laboratory of Intelligent Computing and Information Processing of Ministry of EducationHunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtan 411105China

The iterative solution of the sequence of linear systems arising from threetemperature(3-T)energy equations is an essential component in the numerical simulation of radiative hydrodynamic(RHD)***,due to the complicated application features of the RHD problems,solving 3-T linear systems with classical preconditioned iterative techniques is *** address this difficulty,a physicalvariable based coarsening two-level(PCTL)preconditioner has been proposed by dividing the fully coupled system into four individual easier-to-solve *** its nearly optimal complexity and robustness,the PCTL algorithm suffers from poor efficiency because of the overhead associatedwith the construction of setup phase and the solution of ***,the PCTL algorithm employs a fixed strategy for solving the sequence of 3-T linear systems,which completely ignores the dynamically and slowly changing features of these linear *** address these problems and to efficiently solve the sequence of 3-T linear systems,we propose an adaptive two-level preconditioner based on the PCTL algorithm,referred to as α*** adaptive strategies of the αSetup-PCTL algorithm are inspired by those of αSetup-AMG algorithm,which is an adaptive-setup-based AMG solver for sequence of sparse linear *** proposed αSetup-PCTL algorithm could adaptively employ the appropriate strategies for each linear system,and thus increase the overall *** results demonstrate that,for 36 linear systems,the αSetup-PCTL algorithm achieves an average speedup of 2.2,and a maximum speedup of 4.2 when compared to the PCTL algorithm.

关键词： Sequence of linear systems sparse linear solver preconditioning methods radiation hydrodynamics simulation

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Computer-Assisted Knowledge Points and Question Difficulty Classification Based on BERT

Computer-Assisted Knowledge Points and Question Difficulty C...

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2024 International Conference on Mechatronics and Intelligent Control, ICMIC 2024

作者： Zhu, Jia Jun Yang, Zichuan Hong, Binjie Song, Jiacheng Wang, Jiwei Chen, Tianhao Yang, Shuilan Lan, Zixun Ma, Fei Department of Information and Computing Science Xi'an Jiaotong-Liverpool University Suzhou China School of Engineering Suzhou Centennial College Suzhou China Department of Applied Mathematics Xi'an Jiaotong-Liverpool University Suzhou China GROW Inc. Suzhou China EasyStack Inc. Nanjing China TAL Education Group Beijing China

ISBN: (数字)9781510686847

ISBN: (纸本)9781510686830

In recent years, with the increasing use of educational technology and online learning platforms, there has been a growing interest in developing intelligent systems that can automatically predict the knowledge points associated with educational questions. This paper presents a novel approach for knowledge point prediction in middle school mathematics questions. The dataset used in this study consists of a large collection of 591,379 middle school mathematics questions. To leverage the power of natural language processing techniques, the questions are preprocessed using a tokenizer and encoded into word embeddings using BERT (Bidirectional Encoder Representations from Transformers). Matrix dot production is then employed to calculate the similarity between each test question and the training set, and the top-n most similar vectors are selected for each test question. A voting mechanism is introduced to eliminate duplicate knowledge points and rank them based on their total scores in descending order, resulting in k candidate solutions. The performance of the proposed approach is evaluated using top-k accuracy as the evaluation metric and a lowest common ancestor (LCA) algorithm is used to calculate accuracy at different levels of the knowledge point tree. The results demonstrate the effectiveness of the proposed approach in predicting knowledge points for middle school mathematics questions and its potential for application in intelligent tutoring systems and educational assessment tools. © 2025 SPIE.

关键词： Natural language processing systems

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Graph Coarsening via Supervised Granular-Ball for Scalable Graph Neural Network Training 39

Graph Coarsening via Supervised Granular-Ball for Scalable G...

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39th Annual AAAI Conference on Artificial Intelligence, AAAI 2025

作者： Xia, Shuyin Ma, Xinjun Liu, Zhiyuan Liu, Cheng Zhao, Sen Wang, Guoyin Key Laboratory of Big Data Intelligent Computing China Chongqing Key Laboratory of Computational Intelligence China Chongqing University of Posts and Telecommunications Chongqing China Key Laboratory of Cyberspace Big Data Intelligent Security Ministry of Education China National Center for Applied Mathematics in Chongqing Chongqing Normal University Chongqing401331 China

ISBN: (纸本)157735897X

Graph Neural Networks (GNNs) have demonstrated significant achievements in processing graph data, yet scalability remains a substantial challenge. To address this, numerous graph coarsening methods have been developed. However, most existing coarsening methods are training-dependent, leading to lower efficiency, and they all require a predefined coarsening rate, lacking an adaptive approach. In this paper, we employ granular-ball computing to effectively compress graph data. We construct a coarsened graph network by iteratively splitting the graph into granular-balls based on a purity threshold and using these granular-balls as super vertices. This granulation process significantly reduces the size of the original graph, thereby greatly enhancing the training efficiency and scalability of GNNs. Additionally, our algorithm can adaptively perform splitting without requiring a predefined coarsening rate. Experimental results demonstrate that our method achieves accuracy comparable to training on the original graph. Noise injection experiments further indicate that our method exhibits robust performance. Moreover, our approach can reduce the graph size by up to 20 times without compromising test accuracy, substantially enhancing the scalability of GNNs. Copyright © 2025, Association for the Advancement of Artificial Intelligence (***). All rights reserved.

关键词： Graph neural networks

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Anti-symmetric barron functions and their approximation with sums of determinants

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Journal of Computational Physics 2025年 537卷

作者： Abrahamsen, Nilin Lin, Lin Department of Mathematics University of California BerkeleyCA94720 United States The Simons Institute for the Theory of Computing BerkeleyCA94720 United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States

A fundamental problem in quantum physics is to encode functions that are completely anti-symmetric under permutations of identical particles. The architecture of neural network models for the electron wave function typically comprises an equivariant component followed by a summation of determinants. The recently introduced Generic Antisymmetric (GA) block is designed to enhance the expressivity of such neural wave functions, and it was found that the 2-layer GA block achieved more accurate energies than the corresponding single-determinant FermiNet architecure, suggesting its promise as a way to improve the expressivity of neural wave functions. In this paper we show how the function expressed by the 2-layer GA block can be decomposed into a sum of determinants. We formalize this result by defining the antisymmetric Barron space as a generalized version of the 2-layer GA block and providing an appromation theorem for this function class. This result can be viewed as a negative result showing that the 2-layer GA block is not more expressive than using multiple determinants. © 2025 Elsevier Inc.

关键词： Wave functions

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IoT Aquaculture System for Sea Bass and Giant Freshwater Prawn Farming in Brunei 13

IoT Aquaculture System for Sea Bass and Giant Freshwater Pra...

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13th International Conference on Information Technology in Asia, CITA 2023

作者： Suhaili, Wida Aziz, Musyaffa' Ramlee, Hisyamuddin Patchmuthu, Ravi Shams, Shahriar Mohamad, Ismit Isa, Mohamed Nore, Beston Universiti Teknologi Brunei School of Computing and Informatics Bandar Seri BegawanDarussalam Brunei Universiti Teknologi Brunei Faculty of Engineering Bandar Seri Begawan Brunei Universiti Teknologi Brunei School of Applied Sciences and Mathematics Bandar Seri BegawanDarussalam Brunei

ISBN: (纸本)9798350326208

Aquaculture is one of the emerging industries capable of closing the demand and supply gap for aquatic products. However, the current method of farming is facing sustainability challenges due to its resource-intensive nature, particularly in terms of water and feed usage. Additionally, the rapid growth of the aquaculture sector has led to issues such as overfeeding. The Department of Fisheries Brunei Darussalam has introduced several initiatives to boost the output of aquaculture. With assistance from the Department of Fisheries and Hiseaton Fisheries Ltd, this study aims to implement an IoT-based system to monitor water quality to culture marine species, in particular Sea Bass & Giant Freshwater Prawn, a popular choice for aquaculture in Asia. These species have a high environmental tolerance for thriving in both marine and freshwater. Traditional water monitoring has been a standard way to measure water quality in aquaculture industries in Brunei Darussalam. Water quality is the most important factor that determines the growth rate and health of aquatic creatures. The proposed setup employs a Recirculating Aquaculture System together with the Internet of Things in the rearing of Sea Bass and Giant Freshwater prawns by monitoring the water quality parameters, automating the feeding schedule, and regulating the water quality. © 2023 IEEE.

关键词： Water quality

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Use neural Networks to Recognize Students' Handwritten Letters and Incorrect Symbols

Use neural Networks to Recognize Students' Handwritten Lette...

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2024 International Conference on Mechatronics and Intelligent Control, ICMIC 2024

ISBN: (数字)9781510686847

ISBN: (纸本)9781510686830

Correcting students' multiple-choice answers is a repetitive and mechanical task that can be considered an image multi-classification task. Assuming possible options are 'abcd' and the correct option is one of the four, some students may write incorrect symbols or options that do not exist. In this paper, five classifications were set up - four for possible correct options and one for other incorrect writing. This approach takes into account the possibility of non-standard writing options. © 2025 SPIE.

关键词： Education and training Machine learning Data modeling Neural networks Image classification Visual process modeling Computer vision technology Deep learning Performance modeling Transformers

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Modeling wildfire dynamics through a physics-based approach incorporating fuel moisture and landscape heterogeneity

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Environmental Modelling and Software 2025年 192卷

作者： Navas-Montilla, Adrián Reisch, Cordula Diaz, Pablo Özgen-Xian, Ilhan University of Zaragoza Spain Institute for Partial Differential Equations Technische Universität Braunschweig Germany Department of Mathematics and Scientific Computing University of Graz Austria Department of Applied Mathematics University of Zaragoza Spain Institute of Geoecology Technische Universität Braunschweig Germany

Anthropogenic climate change has increased the probability, severity, and duration of heat waves and droughts, subsequently escalating the risk of wildfires. Mathematical and computational models can enhance our understanding of wildfire propagation dynamics. In this work, we present a simplified Advection–Diffusion–Reaction (ADR) model that accounts for the effect of fuel moisture, and also considers wind, local radiation, natural convection and topography. The model explicitly represents fuel moisture effects by means of the apparent calorific capacity method, distinguishing between live and dead fuel moisture content. Using this model, we conduct exploratory simulations and present theoretical insights into various modeling decisions in the context of ADR-based models. We aim to shed light on the interplay between the different modeled mechanisms in wildfire propagation to identify key factors influencing fire spread and to estimate the model's predictive capacity. © 2025 The Authors

关键词： Radiation damage

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Quasi-Monte Carlo integration for feedback control under uncertainty

arXiv

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arXiv 2024年

作者： Guth, Philipp A. Kritzer, Peter Kunisch, Karl Johann Radon Institute for Computational and Applied Mathematics ÖAW Altenbergerstrasse 69 Linz4040 Austria Institute of Mathematics and Scientific Computing Karl-Franzens University Graz Heinrichstrasse 36 Graz8010 Austria

A control in feedback form is derived for linear quadratic, time-invariant optimal control problems subject to parabolic partial differential equations with coefficients depending on a countably infinite number of uncertain parameters. It is shown that the Riccati-based feedback operator depends analytically on the parameters provided that the system operator depends analytically on the parameters, as is the case, for instance, in diffusion problems when the diffusion coefficient is parameterized by a Karhunen–Loève expansion. These novel parametric regularity results allow the application of quasi-Monte Carlo (QMC) methods to efficiently compute an a-priori chosen feedback law based on the expected value. Moreover, under moderate assumptions on the input random field, QMC methods achieve superior error rates compared to ordinary Monte Carlo methods, independently of the stochastic dimension of the problem. Indeed, our paper for the first time studies Banach-space-valued integration by higher-order QMC *** Codes 35R60, 49N10, 65D30, 65D32, 93B52 © 2024, CC BY.

关键词： Stochastic systems

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Parameter identification in PDEs by the solution of monotone inclusion problems

arXiv

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arXiv 2024年

作者： Gautam, Pankaj Grasmair, Markus Department of Applied Mathematics and Scientific Computing Indian Institute of Technology Roorkee India Department of Mathematical Sciences Norwegian University of Science and Technology Trondheim Norway

In this paper we consider the solution of monotone inverse problems using the particular example of a parameter identification problem for a semilinear parabolic PDE. For the regularized solution of this problem, we introduce a total variation based regularization method requiring the solution of a monotone inclusion problem. We show well-posedness in the sense of inverse problems of the resulting regularization scheme. In addition, we introduce and analyze a numerical algorithm for the solution of this inclusion problem using a nested inertial primal dual method. We demonstrate by means of numerical examples the convergence of both the numerical algorithm and the regularization *** Codes 65J20, 47H05, 47J06, 49J20 © 2024, CC BY.

关键词： Parameter estimation

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Confidential Spatio-Temporal Graph Convolutional Networks with Differential Privacy for Traffic Forecasting

Confidential Spatio-Temporal Graph Convolutional Networks wi...

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Electronic Communication and Artificial Intelligence (IWECAI), International Workshop on

作者： Xiangyang Chen Aiwen Xiao Weiling Pang Xinyi Jiang Zehua Ren Min Tang Key Laboratory of Data Analysis and Computation School of Mathematics and Computing Science Guangxi Colleges and Universities Guilin University of Electronic Technology Guilin China Center for Applied Mathematics of Guangxi (GUET) Guilin China

ISBN: (数字)9798350386943

ISBN: (纸本)9798350386950

Traffic forecasting is essential for urban traffic management in intelligent transportation systems (ITS). However, it involves personal sensitive information, such as user location data. In this paper, we propose an innovative secure protocol for addressing the privacy challenges of traffic prediction in ITS. Our model integrates Spatio-Temporal Graph Convolutional Network (STGCN) and differential privacy (DP) to effectively protect user privacy on the premise of predictive performance. Our experimental results demonstrate that the model maintains a high level of prediction accuracy while offering privacy protection for the user data. On the PeMSD7 dataset, compared to the STGCN benchmark model, our model shows a slight increase of 0.5% in performance metrics (e.g., mean absolute error) while safeguarding the user data. Additionally, the model's average training time increases by roughly 8.4% in the ciphertext domain.

关键词： Training Differential privacy Privacy Protocols Graph convolutional networks Predictive models Data models

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