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Distributed Kernel-Based gradient descent algorithms

CONSTRUCTIVE APPROXIMATION 2018年第2期47卷 249-276页

作者： Lin, Shao-Bo Zhou, Ding-Xuan Wenzhou Univ Coll Math & Informat Sci Wenzhou Peoples R China City Univ Hong Kong Dept Math Kowloon Hong Kong Peoples R China

We study the generalization ability of distributed learning equipped with a divide-and-conquer approach and gradient descent algorithm in a reproducing kernel Hilbert space (RKHS). Using special spectral features of the gradient descent algorithms and a novel integral operator approach, we provide optimal learning rates of distributed gradient descent algorithms in probability and partly conquer the saturation phenomenon in the literature in the sense that the maximum number of local machines to guarantee the optimal learning rates does not vary if the regularity of the regression function goes beyond a certain quantity. We also find that additional unlabeled data can help relax the restriction on the number of local machines in distributed learning.

关键词： Learning theory Distributed learning gradient descent algorithm Integral operator

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Dynamic Event-Triggered Control for a Class of Uncertain Strict-Feedback Systems via an Improved Adaptive Neural Networks Backstepping Approach

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2025年 22卷 2041-2050页

作者： Xu, Ning Liu, Xiang Li, Yulin Zong, Guangdeng Zhao, Xudong Wang, Huanqing Bohai Univ Coll Informat Sci & Technol Jinzhou 121013 Peoples R China Dongguan Univ Technol Inst Sci & Technol Innovat Dongguan 523000 Peoples R China MIIT Talent Big Data Intelligent Anal & Evaluat Key La Beijing 100804 Peoples R China Nankai Univ Coll Artificial Intelligence Tianjin 300381 Peoples R China Tiangong Univ Sch Control Sci & Engn Tianjin 300387 Peoples R China Bohai Univ Coll Control Sci & Engn Jinzhou 121013 Liaoning Peoples R China Bohai Univ Coll Math Sci Jinzhou 121013 Liaoning Peoples R China

This article focuses on a dynamic event-triggered adaptive neural networks backstepping control for a class of uncertain strict-feedback systems with communication constraints. The uncertain terms including external disturbances and unknown nonlinear functions are approximated by radial basis function neural networks, in which the weight update laws are obtained via the gradient descent algorithm, ensuring the local boundedness of the approximation error of neural networks. Then, to enhance the transmission efficiency of control signals, a dynamic event-triggered mechanism is introduced, which enables the dynamic adjustment of threshold parameters in response to the actual tracking performance. It is strictly proved via the Lyapunov stability criterion that the tracking error can converge to a desired small neighborhood of the origin, and all signals in the closed-loop system are bounded. Finally, the validity of the control strategy is demonstrated through a simulation example. Note to Practitioners-In practical network control systems, control signals are typically transmitted continuously or periodically to devices through the communication network in the form of data packets. As communication networks are usually shared by various system nodes, and resources such as communication channel bandwidth and computational capabilities are limited, improving the transmission efficiency of control signals becomes a crucial design problem for controllers in network control systems. Therefore, This study introduces a control method via event-triggered sampling, aiming to enhance sampling efficiency while ensuring the stability and reliability of the system. The proposed control method is suitable for a broad category of strict-feedback nonlinear systems with communication constraints, offering notable advantages such as low-complexity design and straightforward implementation.

关键词： Adaptation models Adaptive backstepping design strict-feedback systems dynamic event-triggered control gradient descent algorithm neural networks

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Tikhonov regularization and gradient descent algorithms for tomography using first-arrival seismic traveltimes

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CHINESE JOURNAL OF GEOPHYSICS-CHINESE EDITION 2015年第4期58卷 1367-1377页

作者： Cui Yan Wang Yan-Fei Chinese Acad Sci Inst Geol & Geophys Key Lab Petr Resources Res Beijing 100029 Peoples R China China Univ Petr Shengli Coll Dongying 257097 Peoples R China Univ Chinese Acad Sci Beijing 100049 Peoples R China

With the development of seismic exploration, inversion and imaging become key issues because of complex structures. It is in urgent need to build accurate near-surface velocity models. Nowadays, three primary numerical methods are developed to acquire the velocity model, i.e., stack velocity analysis, migration velocity analysis and tomography velocity analysis. For the near-surface seismic problem, the first two methods are not suitable because of insufficient fold numbers and reflections. So the tomography method has received much more attention. First-arrival traveltime seismic tomography refers to inversion of medium velocity using first-arrival seismic wave traveltimes and their ray paths. The first task is model parameterization which discretizes the stratigraphic model into many slowness units by gridding. Secondly, based on the slowness units, the ray paths are analyzed by the shortest traveltime ray tracing. Then the traveltime equation is established to solve the velocity model. This is an ill-posed inverse problem. Proper regularization technique and optimization methods are required. Therefore, a Tikhonov regularization model with constraints on feasible set was established, and a gradient descent method with modified step sizes was also developed to obtain an optimized solution. Three different theoretical models were designed to test the new algorithm. The first is a horizontal layered model: there were three horizontal layers with the velocity of 600 m.s(-1), 1200 m.s(-1) and 2000 m.s(-1) top to bottom in the real model. By random disturbance of the model, we got an initial velocity model which was far away from the real model. The inversion result shows that the new algorithm can converge to the true model quickly even with poor initial condition. This shows that the new algorithm is stable and fast in convergence. Comparison with the well-known conjugate gradient (CG) method indicates that this new algorithm requires less memory and has higher conve

关键词： First-arrival traveltime seismic tomography Regularization gradient descent algorithm Ray tracing

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Heat losses in directly buried solar heat collection networks in high-altitude regions

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SOLAR ENERGY 2025年 290卷

作者： Chen, Hongsen Wang, Baichao Song, Cong Wang, Dengjia Liu, Yanfeng Xian Univ Architecture & Technol Sch Bldg Serv Sci & Engn 13Yanta Rd Xian 710055 Peoples R China Xian Univ Architecture & Technol State Key Lab Green Bldg 13Yanta Rd Xian 710055 Peoples R China

Due to the fluctuations in the medium temperature, the solar collector system (SCS) based on temperature difference control currently lacks a medium temperature value for accurately calculating the operational heat loss of directly buried solar heat collection pipelines. This research proposed a method for calculating heat loss utilizing an equivalent medium temperature (EMT). Initially, a computational model is established for assessing the heat loss of directly buried solar collector pipelines in Xizang plateau. Based on the primary factors influencing heat loss, the study investigated the temperature drop and operational heat loss patterns of directly buried solar heat collection pipelines. The ranges of regional equivalent medium temperature (REMT) and condition equivalent medium temperature (CEMT) were optimized using the gradient descent algorithm and heat loss calculation theory. The variations of REMT and CEMT with different regions and key heat loss factors were analyzed, and a CEMT association model was obtained. The EMT is highest in Lhasa and lowest in Gar, related to the ambient temperature for heating design and collector field operation time. For REMT, Lhasa ranges from 50.4 degrees C to 52.8 degrees C, and Gar from 31.1 degrees C to 33.4 degrees C. CEMT decreases with increasing flow rate coefficient and nominal diameter, ranging in Lhasa from 77.1 degrees C to 35.5 degrees C, and in Gar from 54.9 degrees C to 18.5 degrees C. The study aims to provide fundamental data and theoretical support for heat loss calculation and designing the insulation thickness of directly buried solar heat collection pipelines in high-altitude regions.

关键词： Equivalent medium temperature Solar heat collection pipeline Directly buried pipeline gradient descent algorithm Heat loss calculation Altitude

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Neural fractional order differential equations

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 267卷

作者： Sivalingam, S. M. Govindaraj, V. Natl Inst Technol Puducherry Dept Math Karaikal 609609 India

Neural ordinary differential equations are architectures that connect the neural network theory with dynamical system, providing scope for continuous propagation of the layers. Meanwhile, fractional-order differential equations offer an approach to model systems with the scope to retain long-term memory. In this study, we use the idea of fractional derivative in the neural differential equations and develop the fractional version named the neural fractional differential equations. These networks can retain long-term memory and is trained using the ensemble Kalman inversion algorithm. The detailed derivation of the network architecture and the existence of a solution using Schauder's fixed point theorem are given in detail. The forward propagation of the system is executed utilizing the L1 predictor-corrector. The issue in obtaining the gradient is explained in detail. The ensemble Kalman inversion is used to train the network memory efficiently. Numerical results for studying the dynamics of linear and nonlinear systems are provided to demonstrate the effectiveness of the network with the proposed learning method. Also, the model's capacity to fit with real-world data is shown in the HIV, monkey-pox, Delhi temperature, and Netflix stock price datasets. The method has shown excellent performance in fewer iterations compared to neural ordinary differential equations, classical recurrent neural network, gated recurrent unit, long short-term memory networks and Bi-directional long short-term memory neural network.

关键词： Caputo derivative Neural ordinary differential equations gradient descent algorithm Ensemble Kalman inversion

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Reduced-order identification methods: Hierarchical algorithm or variable elimination algorithm

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AUTOMATICA 2025年 172卷

作者： Chen, Jing Mao, Yawen Wang, Dongqing Gan, Min Zhu, Quanmin Liu, Feng Jiangnan Univ Sch Sci Wuxi 214122 Peoples R China Qingdao Univ Coll Elect Engn Qingdao 266071 Peoples R China Qingdao Univ Coll Comp Sci & Technol Qingdao 266071 Peoples R China Univ West England Dept Engn Design & Math Bristol BS16 1QY England Stevens Inst Technol Sch Syst & Enterprises Hoboken NJ 07030 USA

Reduced-order identification algorithms are usually used in machine learning and big data technologies, where the large-scale systems widely exist. For large-scale system identification, traditional least squares algorithm involves high-order matrix inverse calculation, while traditional gradient descent algorithm has slow convergence rates. The reduced-order algorithm proposed in this paper has some advantages over the previous work: (1) via sequential partitioning of the parameter vector, the calculation of the inverse of a high-order matrix can be reduced to low-order matrix inverse calculations;(2) has a better conditioned information matrix than that of the gradient descent algorithm, thus has faster convergence rates;(3) its convergence rates can be increased by using the Aitken acceleration method, therefore the reduced-order based Aitken algorithm is at least quadratic convergent and has no limitation on the step-size. The properties of the reduced-order algorithm are also given. Simulation results demonstrate the effectiveness of the proposed algorithm. (c) 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： Reduced-order algorithm Least square algorithm gradient descent algorithm Condition number Hierarchical identification algorithm Variable elimination algorithm

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gradient descent-Based Parameter Estimation for Ultra Short Baseline

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IEEE ACCESS 2024年 12卷 174713-174722页

作者： Kim, Yongcheol Ko, Haklim Lee, Hojun Inha Univ Dept Elect & Comp Engn Incheon 22212 South Korea Hoseo Univ Dept Informat & Commun Engn Asan 31066 South Korea

This paper proposes a phase-based pseudorange estimation and a gradient descent-based localization algorithm to improve the positioning performance of the ultra short baseline (USBL) system. Traditional USBL systems estimate the pseudorange by cross-correlating the received chirp signal. Still, the limited sampling rate makes it difficult to estimate an accurate pseudorange, resulting in low positioning performance. The proposed method calculates the number of wavelengths of the received chirp signal and detects the initial phase of the signal to estimate a more precise pseudorange than existing methods. Additionally, the localization performance is enhanced using an optimization algorithm based on gradient descent. Through computer simulations and ocean experiments, the proposed method demonstrated up to 29 times better localization performance in computer simulations and up to 107 times better performance in ocean experiments compared to existing methods, verifying that the proposed method outperforms the existing methods.

关键词： gradient descent algorithm pseudorange source localization source localization ultra short baseline (USBL) ultra short baseline (USBL) underwater sensor networks underwater sensor networks underwater sensor networks

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Distributed gradient descent Localization in Wireless Sensor Networks

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ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2015年第3期40卷 893-899页

作者： Alwan, Nuha A. S. Mahmood, Alaa S. Univ Baghdad Coll Engn Dept Comp Engn Baghdad Iraq

We propose a distributed gradient descent (GD) localization algorithm in 3D space for wireless sensor networks that employ the push-sum (PS) gossip algorithm to compute sums. Sums and averages constitute building blocks for various signal processing applications including the one under consideration. Our contribution lies in combining vector PS and GD approaches achieving fast convergence, high accuracy and a remarkable robustness against link failures. Comparisons are presented with the centralized counterpart and with similar recent works.

关键词： Wireless sensor network Distributed node localization gradient descent algorithm Push-sum gossip algorithm

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gradient descent Bit Flipping algorithms for Decoding LDPC Codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2010年第6期58卷 1610-1614页

作者： Wadayama, Tadashi Nakamura, Keisuke Yagita, Masayuki Funahashi, Yuuki Usami, Shogo Takumi, Ichi Nagoya Inst Technol Nagoya Aichi 4668555 Japan Meijo Univ Nagoya Aichi Japan

A novel class of bit-flipping (BF) algorithm for decoding low-density parity-check (LDPC) codes is presented. The proposed algorithms, which are referred to as gradient descent bit flipping (GDBF) algorithms, can be regarded as simplified gradient descent algorithms. The proposed algorithms exhibit better decoding performance than known BF algorithms, such as the weighted BF algorithm or the modified weighted BF algorithm for several LDPC codes.

关键词： LDPC code bit-flipping algorithm gradient descent algorithm

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On the convergence of gradient descent for robust functional linear regression

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JOURNAL OF COMPLEXITY 2024年 84卷

作者： Wang, Cheng Fan, Jun Huizhou Univ Sch Math & Stat Huizhou Peoples R China Hong Kong Baptist Univ Dept Math Kowloon Hong Kong Peoples R China

Functional data analysis offers a set of statistical methods concerned with extracting insights from intrinsically infinitedimensional data and has attracted considerable amount of attentions in the past few decades. In this paper, we study robust functional linear regression model with a scalar response and a functional predictor in the framework of reproducing kernel Hilbert spaces. A gradient descent algorithm with early stopping is introduced to solve the corresponding empirical risk minimization problem associated with robust loss functions. By appropriately selecting the early stopping rule and the scaling parameter of the robust losses, the convergence of the proposed algorithm is established when the response variable is bounded or satisfies a moment condition. Explicit learning rates with respect to both estimation and prediction error are provided in terms of regularity of the regression function and eigenvalue decay rate of the integral operator induced by the reproducing kernel and covariance function. (c) 2024 Elsevier Inc. All rights reserved.

关键词： Learning theory gradient descent algorithm Robust functional linear regression Learning rate Integral operator

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