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GDGen: A gradient descent-based methodology for the generation of optimized spatial configurations of customized clusters in computational simulations

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COMPUTER PHYSICS COMMUNICATIONS 2025年 310卷

作者： Wang, Ning Peking Univ Sch Adv Mat Shenzhen Grad Sch Lishui Rd Shenzhen 518055 Guangdong Peoples R China

In this study, gradient descent Generation (GDGen) is presented, an innovative methodological framework that utilizes gradient descent algorithms to create dense, non-overlapping configurations of multiple, user- customized clusters and shapes. This technique is crucial for the accuracy and efficacy of molecular dynamics (MD) simulations, finite element analyses, and a multitude of scientific applications where precise spatial arrangement is paramount. GDGen intricately minimizes a loss function tailored to assess spatial overlaps and guide the arrangement process. The implementation of GDGen is encapsulated in Pygdgen, a Python package developed to generate intricate atomic configurations, particularly excelling in scenarios involving dense clustering and unconventional geometries. Pygdgen ensures efficient arrangement processes through its optimized coding structure and GPU acceleration capabilities. Its adaptability is evidenced by its application in various fields, from material science and chemistry to urban planning and mechanical design, for arranging complex structures within constrained spaces.

关键词： Configuration optimization gradient descent algorithms Molecular dynamics simulation Spatial arrangement Non-overlapping clusters Customized cluster geometries GDGen methodology Pygdgen software

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Designing Quantum gradient descent Algorithm for MIMO NOMA Rate Maximization With STAR-RIS

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IEEE WIRELESS COMMUNICATIONS LETTERS 2025年第4期14卷 959-963页

作者： Paul, Anal Singh, Keshav Li, Chih-Peng Mumtaz, Shahid Natl Sun Yat sen Univ Inst Commun Engn Kaohsiung 80424 Taiwan Nottingham Trent Univ Dept Engn Nottingham NG1 4FQ England

We introduce, for the first time in wireless communication networks, a quantum gradient descent (QGD) algorithm to maximize sum data rates in non-orthogonal multiple access (NOMA)-based simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-assisted multiple-input and multiple-output systems. The QGD algorithm utilizes the principles of quantum parallelism and superposition to efficiently solve the high-dimensional optimization challenges inherent in configuring transmit and receive beamformers and STAR-RIS elements. Extensive simulations demonstrate that the QGD algorithm significantly outperforms classical optimization methods, achieving up to 49.50% and 44.88% higher data rates compared to classical gradient descent algorithms for configurations with 256 STAR-RIS elements. Furthermore, the NOMA model shows substantial improvements in sum data rate performance, with gains of 179.65% and 145.61% over space division multiple access schemes under similar frameworks.

关键词： Optimization NOMA Reflection Reconfigurable intelligent surfaces Downlink Vectors Signal to noise ratio Array signal processing Parallel processing Linear programming Quantum computing search space-time complexity gradient descent algorithms quantum gradient descent

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A normalized gradient descent algorithm for nonlinear adaptive filters using a gradient adaptive step size

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IEEE SIGNAL PROCESSING LETTERS 2001年第11期8卷 295-297页

作者： Mandic, DP Hanna, AI Razaz, M Univ E Anglia Sch Informat Syst Norwich NR4 7TJ Norfolk England

A fully adaptive normalized nonlinear gradient descent (FANNGD) algorithm for online adaptation of nonlinear neural filters is proposed. An adaptive stepsize that minimizes the instantaneous output error of the filter is derived using a linearization performed by a Taylor series expansion of the output error. For rigor, the remainder of the truncated Taylor series expansion within the expression for the adaptive learning rate is made adaptive and is updated using gradient descent. The FANNGD algorithm is shown to converge faster than previously introduced algorithms of this kind.

关键词： adaptive step size gradient descent algorithms neural networks nonlinear adaptive prediction

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A Limitation of gradient descent Learning

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2020年第6期31卷 2227-2232页

作者： Sum, John Leung, Chi-Sing Ho, Kevin Natl Chung Hsing Univ Inst Technol Management Taichung 40227 Taiwan City Univ Hong Kong Dept Elect Engn Hong Kong Peoples R China Providence Univ Dept Comp Sci & Commun Engn Taichung 43301 Taiwan

Over decades, gradient descent has been applied to develop learning algorithm to train a neural network (NN). In this brief, a limitation of applying such algorithm to train an NN with persistent weight noise is revealed. Let V(w) be the performance measure of an ideal NN. V(w) is applied to develop the gradient descent learning (GDL). With weight noise, the desired performance measure (denoted as J(w)) is E[ V(w)|w], where w is the noisy weight vector. Applying GDL to train an NN with weight noise, the actual learning objective is clearly not V(w) but another scalar function L(w). For decades, there is a misconception that L(w) = J(w), and hence, the actual model attained by the GDL is the desired model. However, we show that it might not: 1) with persistent additive weight noise, the actual model attained is the desired model as L(w) = J(w);and 2) with persistent multiplicative weight noise, the actual model attained is unlikely the desired model as L(w) = J(w). Accordingly, the properties of the models attained as compared with the desired models are analyzed and the learning curves are sketched. Simulation results on 1) a simple regression problem and 2) the MNIST handwritten digit recognition are presented to support our claims.

关键词： Additive weight noise gradient descent algorithms MNIST multiplicative weight noise

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Hardness Prediction of 7003 Aluminum Alloy by gradient descent Algorithm in BP Artificial Neural Networks

Hardness Prediction of 7003 Aluminum Alloy by Gradient Desce...

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1st International Conference on High Performance Structures and Materials Engineering

作者： Ren, J. P. Song, R. G. Changzhou Univ Sch Mat Sci & Engn Changzhou 213164 Peoples R China

ISBN: (纸本)9783037850756

In order to shorten the fussy experimental process in heat treatment of 7003 aluminum alloy, back-propagation (BP) artificial neural network control of scheme has been proposed. The network of arithmetic has been deduced by using gradient descent algorithms A BP neural network has been established between the heat treatment technique and the hardness. The results indicated that the predicted results are closed to the test results. The weakness that the nonlinear and time variation relationship between heat treatment and the hardness could be approached more accurately, effectively by using single-factor-experiment method has been overcome. Hence providing a effective, economical,rapid way for the heat treatment optimization of nonferrous metals and ferrous metal.

关键词： Artificial neural networks gradient descent algorithms 7003 aluminum ally Heat treatment

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Self-adaptive algorithms for quasiconvex programming and applications to machine learning

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COMPUTATIONAL & APPLIED MATHEMATICS 2024年第4期43卷 1-16页

作者： Thang, Tran Ngoc Hai, Trinh Ngoc Hanoi Univ Sci & Technol Sch Appl Math & Informat Hanoi Vietnam

For solving a broad class of nonconvex programming problems on an unbounded constraint set, we provide a self-adaptive step-size strategy that does not include line-search techniques and establishes the convergence of a generic approach under mild assumptions. Specifically, the objective function may not satisfy the convexity condition. Unlike descent line-search algorithms, it does not need a known Lipschitz constant to figure out how big the first step should be. The crucial feature of this process is the steady reduction of the step size until a certain condition is fulfilled. In particular, it can provide a new gradient projection approach to optimization problems with an unbounded constrained set. To demonstrate the effectiveness of the proposed technique for large-scale problems, we apply it to some experiments on machine learning, such as supervised feature selection, multi-variable logistic regressions and neural networks for classification.

关键词： Nonconvex programming gradient descent algorithms Quasiconvex functions Pseudoconvex functions Self-adaptive step-sizes

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Learning techniques to train neural networks as a state selector for inverter-fed induction machines using direct torque control

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IEEE TRANSACTIONS ON POWER ELECTRONICS 1997年第5期12卷 788-799页

作者： Cabrera, LA Elbuluk, ME Zinger, DS NO ILLINOIS UNIV DEPT ELECT ENGNDE KALBIL 60115

Neural networks are receiving attention as controllers for many industrial applications. Although these networks eliminate the need for mathematical models, they require a lot of training to understand the model of a plant or a process. Issues such as learning speed, stability, and weight convergence remain as areas of research and comparison of many training algorithms. This paper discusses the application of neural networks to control induction machines using direct torque control (DTC), A neural network is used to emulate the state selector of the DTC, The training algorithms used in this paper are the backpropagation, adaptive neuron model, extended Kalman filter, and the parallel recursive prediction error, Computer simulations of the motor and neural-network system using the four approaches are presented and compared, Discussions about the parallel recursive prediction error and the extended Kalman filter algorithms as the most promising training techniques is presented, giving their advantages and disadvantages.

关键词： adaptive neuron algorithm backpropagation algorithm direct torque control extended Kalman filter algorithm gradient descent algorithms induction machines neural-networks structure and training Newton algorithms parallel recursive prediction error algorithm

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DIMIX: DIMINISHING MIXING FOR SLOPPY AGENTS*

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SIAM JOURNAL ON OPTIMIZATION 2023年第2期33卷 978-1005页

作者： Reisizadeh, Hadi Touri, Behrouz Mohajer, Soheil Univ Minnesota Dept Elect & Comp Engn Minneapolis MN 55414 USA Univ Calif San Diego Dept Elect & Comp Engn La Jolla CA 92093 USA

We study nonconvex distributed optimization problems where a set of agents collaboratively solve a separable optimization problem that is distributed over a time-varying network. The existing methods to solve these problems rely on (at most) one-time-scale algorithms, where each agent performs a diminishing or constant step-size gradient descent at the average estimate of the agents in the network. However, if possible at all, exchanging exact information, which is required to evaluate these average estimates, potentially introduces a massive communication overhead. Therefore, a reasonable practical assumption to be made is that agents only receive a rough approximation of the neighboring agents' information. To address this, we introduce and study a two-time-scale decentralized algorithm with a broad class of lossy information sharing methods (which includes noisy, quantized, and/or compressed information sharing) over time-varying networks. In our method, one time-scale suppresses the (imperfect) incoming information from the neighboring agents, and one time-scale operates on local cost functions' gradients. We show that with a proper choices for the step-sizes' parameters, the algorithm achieves a convergence rate of \scrO (T - 1/3+\epsilon ) for nonconvex distributed optimization problems over time-varying networks for any \epsilon > 0.

关键词： Key words nonconvex optimization time-varying graphs distributed multiagent system distributed optimization gradient descent algorithms

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Distributed Optimization Over Time-Varying Graphs With Imperfect Sharing of Information

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2023年第7期68卷 4420-4427页

作者： Reisizadeh, Hadi Touri, Behrouz Mohajer, Soheil Univ Minnesota Minneapolis MN 55455 USA Univ Calif San Diego La Jolla 92093 CA USA

We study strongly convex distributed optimization problems where a set of agents are interested in solving a separable optimization problem collaboratively. In this article, we propose and study a two-time-scale decentralized gradient descent algorithm for a broad class of lossy sharing of information over time-varying graphs. One time-scale fades out the (lossy) incoming information from neighboring agents, and one time-scale regulates the local loss functions' gradients. We show that assuming a proper choice of step-size sequences, certain connectivity conditions, and bounded gradients along the trajectory of the dynamics, the agents' estimates converge to the optimal solution with the rate of O(T-1/2). We also provide novel tools to study distributed optimization with diminishing averaging weights over time-varying graphs.

关键词： Convex optimization distributed multiagent system distributed optimization gradient descent algorithms time-varying graphs

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Two-step gradient-based reinforcement learning for underwater robotics behavior learning

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ROBOTICS AND AUTONOMOUS SYSTEMS 2013年第3期61卷 271-282页

作者： El-Fakdi, Andres Carreras, Marc Univ Girona Dept Comp Engn Comp Vis & Robot Grp VICOROB Girona 17071 Spain

This article proposes a field application of a Reinforcement Learning (RL) control system for solving the action selection problem of an autonomous robot in a cable tracking task. The Ictineu Autonomous Underwater Vehicle (AUV) learns to perform a visual based cable tracking task in a two step learning process. First, a policy is computed by means of simulation where a hydrodynamic model of the vehicle simulates the cable following task. The identification procedure follows a specially designed Least Squares (LS) technique. Once the simulated results are accurate enough, in a second step, the learnt-in-simulation policy is transferred to the vehicle where the learning procedure continues in a real environment, improving the initial policy. The Natural Actor-Critic (NAC) algorithm has been selected to solve the problem. This Actor-Critic (AC) algorithm aims to take advantage of Policy gradient (PG) and Value Function (VF) techniques for fast convergence. The work presented contains extensive real experimentation. The main objective of this work is to demonstrate the feasibility of RL techniques to learn autonomous underwater tasks, the selection of a cable tracking task is motivated by an increasing industrial demand in a technology to survey and maintain underwater structures. (c) 2012 Elsevier B.V. All rights reserved.

关键词： Reinforcement learning Underwater robotics gradient descent algorithms Actor-Critic algorithms Model identification

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