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A kernel-based method for solving the time-fractional diffusion equation

NUMERICAL methodS FOR PARTIAL DIFFERENTIAL EQUATIONS 2023年第3期39卷 2719-2733页

作者： Fardi, Mojtaba Shahrekord Univ Fac Math Sci Dept Appl Math Shahrekord Iran Shahrekord Univ Fac Math Sci Dept Appl Math POB 115 Shahrekord Iran

In this paper, we focus on the development and study of a numerical method based on the idea of kernel-based approximation and finite difference discretization to obtain the solution for the time-fractional diffusion equation. Using the theory of reproducing kernel, reproducing kernel functions with a polynomial form will be established in polynomial reproducing kernel spaces spanned by the Chebychev basis polynomials. In the numerical method, first the time-fractional derivative term in the aforementioned equation is approximated by using the finite difference scheme. Then, by the help of collocation method based on reproducing kernel approximation, we will illustrate how to derive the numerical solution in polynomial reproducing kernel space. Finally, to support the accuracy and efficiency of the numerical method, we provide several numerical examples. In numerical experiments, the quality of approximation is calculated by absolute error and discrete error norms.

关键词： finite difference kernel-based method reproducing kernel collocation method time-fractional diffusion equation

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Structure-Preserving kernel-based Meshless methods for Solving Dissipative PDEs on Surfaces

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JOURNAL OF SCIENTIFIC COMPUTING 2025年第3期102卷 1-25页

作者： Sun, Zhengjie Ling, Leevan Chen, Meng Nanjing Univ Sci & Technol Sch Math & Stat Nanjing Peoples R China Hong Kong Baptist Univ Dept Math Kowloon Hong Kong Peoples R China Nanchang Univ Inst Math & Interdisciplinary Sci Sch Math & Comp Sci Nanchang Peoples R China

In this paper, we propose a general meshless structure-preserving Galerkin method for solving dissipative PDEs on surfaces. By posing the PDE in the variational formulation and simulating the solution in the finite-dimensional approximation space spanned by (local) Lagrange functions generated with positive definite kernels, we obtain a semi-discrete Galerkin equation that inherits the energy dissipation property. The fully-discrete structure-preserving scheme is derived with the average vector field method. We provide a convergence analysis of the proposed method for the Allen-Cahn equation. The numerical experiments also verify the theoretical analysis including the convergence order and structure-preserving properties. Furthermore, we provide numerical evidence demonstrating that the Lagrange function and the coefficients generated by a restricted kernel decay exponentially, even though a comprehensive theory has not yet been developed.

关键词： kernel-based method Dissipative PDEs Structure-preserving scheme Lagrange functions Surface PDEs

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A methodology for the Multitemporal Analysis of Land Cover Changes and Urban Expansion Using Synthetic Aperture Radar (SAR) Imagery: A Case Study of the Aburrá Valley in Colombia

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REMOTE SENSING 2025年第3期17卷 554-554页

作者： Cardona-Mesa, Ahmed Alejandro Vasquez-Salazar, Ruben Dario Parra, Juan Camilo Olmos-Severiche, Cesar Travieso-Gonzalez, Carlos M. Gomez, Luis Inst Univ Digital Antioquia Fac Sci & Humanities 55th Av42-90 Medellin 050015 Colombia Politecn Colombiano Jaime Isaza Cadavid Fac Engn 48th Av7-151 Medellin 050022 Colombia Univ Las Palmas Gran Canaria Signals & Commun Dept IDeT Las Palmas Gran Canaria 35017 Spain Univ Las Palmas Gran Canaria Elect Engn & Automat Control Dept IUCES Las Palmas Gran Canaria 35017 Spain

The Aburr & aacute;Valley, located in the northwestern region of Colombia, has undergone significant land cover changes and urban expansion in recent decades, driven by rapid population growth and infrastructure development. This region, known for its steep topography and dense urbanization, faces considerable environmental challenges. Monitoring these transformations is essential for informed territorial planning and sustainable development. This study leverages Synthetic Aperture Radar (SAR) imagery from the Sentinel-1 mission, covering 2017-2024, to propose a methodology for the multitemporal analysis of land cover dynamics and urban expansion in the valley. The novel proposed methodology comprises several steps: first, monthly SAR images were acquired for every year under study from 2017 to 2024, ensuring the capture of surface changes. These images were properly calibrated, rescaled, and co-registered. Then, various multitemporal fusions using statistics operations were proposed to detect and find different phenomena related to land cover and urban expansion. The methodology also involved statistical fusion techniques-median, mean, and standard deviation-to capture urbanization dynamics. The kurtosis calculations highlighted areas where infrequent but significant changes occurred, such as large-scale construction projects or sudden shifts in land use, providing a statistical measure of surface variability throughout the study period. An advanced clustering technique segmented images into distinctive classes, utilizing fuzzy logic and a kernel-based method, enhancing the analysis of changes. Additionally, Pearson correlation coefficients were calculated to explore the relationships between identified land cover change classes and their spatial distribution across nine distinct geographic zones in the Aburr & aacute;Valley. The results highlight a marked increase in urbanization, particularly along the valley's periphery, where previously vegetated areas have bee

关键词： Synthetic Aperture Radar (SAR) remote sensing multitemporal analysis land cover change clustering kurtosis fuzzy logic kernel-based method

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An effective implementation for kernel-based positive system identification using Gibbs sampling

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ASIAN JOURNAL OF CONTROL 2025年

作者： Qiu, Chen Zheng, Man Song, Jun Anhui Univ Sch Artificial Intelligence 111 Jiulong Rd Hefei Anhui Peoples R China

Recently, the kernel-based method has been applied for the positive system identification where the hyperparameter estimation is a crucial and critical part. The regularized identification problem for the positive system is first formulated. Due to the nonnegative constraint of the positive system, the Bayesian interpretation chooses the truncated Gaussian distribution as the prior of the system parameter. The hyperparameters estimation is cast as a marginal likelihood optimization. A Bayesian network for the positive system is established to construct a probabilistic framework for handling the hyperparameter estimation. based on the derived conditional distributions, this paper develops a Markov chain Monte Carlo method to sample according to the likelihood function, where the Gibbs sampling is available to improve the sampling efficiency. The proposed sampling-based algorithm facilitates searching for hyperparameters globally. The simulation results demonstrate that the proposed algorithm provides more precise and efficient identification compared to the conventional method.

关键词： Bayesian network Gibbs sampling hyperparameter estimation kernel-based method positive system identification

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kernel Regularization based Volterra Series Identification method for Time-delayed Nonlinear Systems with Unknown Structure

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INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS 2023年第5期21卷 1465-1474页

作者： Zhang, Yanxin Zhang, Zili Chen, Jing Hu, Manfeng Jiangnan Univ Sch Sci Wuxi 214122 Peoples R China

This paper develops a kernel regularization based Adam algorithm for nonlinear systems with unknown structure and time-delay by using self-organized maps. based on the redundant rule method, a model pool constituted of several Volterra series is constructed which contains the true time-delayed model. Then, the Adam algorithm combining a self-organized maps technique is applied to iteratively estimate the time-delay and parameters. Furthermore, a kernel regularization method is introduced to deal with the curse of dimensionality, and by which a more simple Volterra model can be obtained. Experimental results show the effectiveness of proposed algorithm in estimating time-delay and parameters.

关键词： Adam optimization kernel-based method nonlinear system self-organized maps time-delay Volterra series

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A simple and novel coupling method for CFD-DEM modeling with uniform kernel-based approximation

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COMPUTATIONAL PARTICLE MECHANICS 2024年第6期11卷 2381-2397页

作者： Zhang, Yan Ren, Wanlong Li, Peng Zhang, Xuhui Lu, Xiaobing Chinese Acad Sci Inst Mech Beijing 100190 Peoples R China Univ Chinese Acad Sci Sch Engn Sci Beijing 100049 Peoples R China

The Eulerian-Lagrangian approach is commonly employed in particulate flows, which can be classified into two subcategories: unresolved computational fluid dynamics-discrete element method (CFD-DEM) and resolved CFD-DEM. When the particle sizes are comparable to the cell sizes, the interphase coupling is not straightforward anymore and both the conventional unresolved CFD-DEM and resolved CFD-DEM are not applicable. In this paper, we propose a simple and novel coupling method for projecting and reconstructing the particle and interphase quantities, which is also called semi-resolved CFD-DEM. The particle quantities are uniformly distributed to the surrounding cells by expanding the fluid domain. The fluid phase quantities at the particle location are also reconstructed from the surrounding cells. Then, the relative velocity and the local void fraction for calculating the drag force are corrected. The expanding factor for the fluid domain is determined by comparing the drag force of the semi-resolved CFD-DEM with the resolved CFD-DEM results. It is found that the expanding factor increases linearly with the autocorrelation length. The developed method is validated by the simulation of a particle sedimentation and a sediment transport process, which proves that the present semi-resolved CFD-DEM fills the gap between the resolved and unresolved CFD-DEM. The difference between the implicit and explicit treatment of momentum exchange term is also discussed, and the explicit treatment shows better performance for large particles.

关键词： CFD-DEM Multiphase flow Momentum exchange kernel-based method

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EFFICIENT REDUCTION OF SUPPORT VECTORS IN kernel-based methodS

EFFICIENT REDUCTION OF SUPPORT VECTORS IN KERNEL-BASED METHO...

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16th IEEE International Conference on Image Processing

作者： Kobayashi, Takumi Otsu, Nobuyuki Natl Inst Adv Ind Sci & Technol Tsukuba Ibaraki Japan

ISBN: (纸本)9781424456536

kernel-based methods, e.g., support vector machine (SVM), produce high classification performances. However, the computation becomes time-consuming as the number of the vectors supporting the classifier increases. In this paper, we propose a method for reducing the computational cost of classification by kernel-based methods while retaining the high performance. By using linear algebra of a kernel Gram matrix of the support vectors (SVs) at low computational cost, the method efficiently prunes the redundant SVs which are unnecessary for constructing the classifier. The pruning is based on the evaluation of the performance of the classifier formed by the reduced SVs in SVM. In the experiment of classification using SVM for various datasets, the feasibility of the evaluation criterion and the effectiveness of the proposed method are demonstrated.

关键词： Reduction of support vectors kernel-based method Support vector machine

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method for classification of PQ events based on discrete Gabor transform with FIR window and T2FK-based SVM and its experimental verification

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IET GENERATION TRANSMISSION & DISTRIBUTION 2017年第1期11卷 133-141页

作者： Naderian, Sobhan Salemnia, Ahmad Shahid Beheshti Univ Abbaspour Sch Engn Tehran Iran

This paper aims to develop a new method for identification of Power Quality (PQ) events based on Discrete Gabor Transform (DGT) with a Finite Impulse Response Window (FIR-DGT) and Type-2 Fuzzy kernel-based Support Vector Machine (T2FK-SVM). The FIR-DGT extracted features from the input signals and the T2FK-SVM classified them. Using proper window function for DGT is essential. Iterated sine window was used as window function to extract the events' features. The iterated sine window's function is four times faster than the default window function of DGT. kernel design is a main part of many kernel-based methods such as SVM, so by using T2FK, the total accuracy of classification is enhanced. In the present work, use of this hybrid approach decreased the extracted features size, so the execution time and total required memory were optimized for the classification section. The simulation results revealed accurate classification and execution in the detection and classification of nine types of PQ events. The overall accuracy of the proposed method was comparable to other methods and the accuracy evaluated under noisy conditions. Hardware platform was developed for evaluating the proposed method based on ARM LPC 1768 microcontroller to assess accuracy of the method in real conditions.

关键词： power engineering computing iterative methods feature extraction fuzzy reasoning power supply quality discrete transforms support vector machines PQ event detection kernel-based method ARMLPC1768 microcontroller feature size extraction kernel-based methods iterated sine window type-2 fuzzy kernel-based support vector machine power quality even identification FIR-DGT finite impulse response window T2FK-based SVM FIR window discrete Gabor transform PQ event classification

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FORECASTING CHINA'S FOREIGN TRADE VOLUME WITH A kernel-based HYBRID ECONOMETRIC-AI ENSEMBLE LEARNING APPROACH

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Journal of Systems Science & Complexity 2008年第1期21卷 1-19页

作者： Lean YU Shouyang WANG Kin Keung LAI Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China. Department of Management Sciences City University of Hong Kong Tat Chee Avenue Kowloon Hong Kong China.

Due to the complexity of economic system and the interactive effects between all kinds of economic variables and foreign trade, it is not easy to predict foreign trade volume. However, the difficulty in predicting foreign trade volume is usually attributed to the limitation of many conventional forecasting models. To improve the prediction performance, the study proposes a novel kernel-based ensemble learning approach hybridizing econometric models and artificial intelligence (AI) models to predict China's foreign trade volume. In the proposed approach, an important econometric model, the co-integration-based error correction vector auto-regression (EC-VAR) model is first used to capture the impacts of all kinds of economic variables on Chinese foreign trade from a multivariate linear anal- ysis perspective. Then an artificial neural network (ANN) based EC-VAR model is used to capture the nonlinear effects of economic variables on foreign trade from the nonlinear viewpoint. Subsequently, for incorporating the effects of irregular events on foreign trade, the text mining and expert's judgmental adjustments are also integrated into the nonlinear ANN-based EC-VAR model. Finally, all kinds of economic variables, the outputs of linear and nonlinear EC-VAR models and judgmental adjustment model are used as input variables of a typical kernel-based support vector regression (SVR) for en- semble prediction purpose. For illustration, the proposed kernel-based ensemble learning methodology hybridizing econometric techniques and AI methods is applied to China's foreign trade volume predic- tion problem. Experimental results reveal that the hybrid econometric-AI ensemble learning approach can significantly improve the prediction performance over other linear and nonlinear models listed in this study.

关键词： Artificial neural networks error-correction vector auto-regression foreign trade prediction hybrid ensemble learning kernel-based method support vector regression.

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A novel multiple Nystrom-approximating kernel discriminant analysis

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NEUROCOMPUTING 2013年 119卷 385-398页

作者： Wang, Zhe Jie, Wenbo Gao, Daqi E China Univ Sci & Technol Dept Comp Sci & Engn Shanghai 200237 Peoples R China

Multiple kernel Discriminant Analysis (MKDA) adopts an ensemble of multiple kernel matrices K(i)s and is supposed to be more flexible and effective than the original kernel Discriminant Analysis (KDA). However, with n training samples and p kernel matrices K(i)s, MKDA employs pn(2) space units for all the K(i)s in the optimizing process and simultaneously depends on its solving techniques to handle the optimization problem, which would cause a large space and computational complexity and limit the efficiency and applicability. In order to mitigate this problem, this manuscript adopts the Nystrom method approximating K-i and therefore develops a novel Multiple Nystrom-Approximating kernel Discriminant Analysis (MNKDA). In practice, the proposed MNKDA first adopts m (m << n) samples to generate an approximating kernel matrix (K-i) over tilde for each K-i and forms an ensemble matrix G = Sigma(p)(t=1)mu(t)(K-i) over tilde. Then, MNKDA directly applies the eigenvalue decomposition onto the Nystrom-based ensemble matrix G and reformulates the proposed discriminant analysis as an eigenvalue problem. The experimental results show that the proposed method can achieve an effective and efficient performance than the classical MKDA. The advantages of the proposed MNKDA are (1) expressing the formulation as an eigenvalue problem resolution instead of using commercial softwares;(2) decreasing the space complexity from O(pn(2)) to O(n(2)) and mitigating the computational complexity from O(n(3)) to O(pmn(2));and (3) providing an alternative multiple kernel learning technique and inheriting the advantage of multiple kernel learning. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Multiple kernel discriminant analysis Nystrom approximation Eigenvalue decomposition Feature extraction kernel-based method Pattern recognition

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