Numerical simulation of impact and shock-wave interactions of deformable solids is an urgent problem. The key to the adequacy and accuracy of simulation is the material model that links the yield strength with accumulated plastic strain, strain rate,...
Ghost imaging is an indirect optical imaging technique, which retrieves object information by calculating the intensity correlation between reference and bucket signals. However, in existing correlation functions, a high number of measurements is req...
This paper proposes a novel mathematical theory of adaptation to convexity of loss functions based on the definition of the condense-discrete convexity (CDC) method. The developed theory is considered to be of immense value to stochastic settings and...
Aiming at the problem of the weak dynamic performance of the gradient descent method in the attitude and heading reference system, the susceptibility to the interference of accelerometers and magnetometers, and the complex calculation of the nonlinea...
In this paper, we mainly consider two kinds of perturbed accelerated gradient descents driven by Lévy perturbations, which is of great importance for enhancing the global search ability. By using Lévy representation, Lévy perturb...
Motivated by the weighted averaging method for training neural networks, we study the time-fractional gradient descent (TFGD) method based on the time-fractional gradient flow and explore the influence of memory dependence on neural network training....
In this paper, we present a rapid gradient descent method for solving low-rank matrix recovery problems. Our method extends the conventional gradient descent framework by exploiting the problem’s unique features to develop an innovative fast gr...
This research proposes and investigates some improvements in gradient descent iterations that can be applied for solving system of nonlinear equations (SNE). In the available literature, such methods are termed improved gradient descent methods. We u...
For a high-power slab solid-state laser, obtaining high output power and high output beam quality are the most important indicators. Adaptive optics systems can significantly improve beam qualities by compensating for the phase distortions of the las...
Stochastic gradient descent (SGD) is an optimization method typically used in deep learning to train deep neural network (DNN) models. In recent studies for DNN training, pipeline parallelism, a type of model parallelism, is proposed to accelerate SG...
Stochastic gradient descent is the method of choice for solving large-scale optimization problems in machine learning. However, the question of how to effectively select the step-sizes in stochastic gradient descent methods is challenging, and can gr...
This paper mainly proposes some improved stochastic gradient descent (SGD) algorithms with a fractional order gradient for the online optimization problem. For three scenarios, including standard learning rate, adaptive gradient learning rate, and mo...
Data heterogeneity may significantly deteriorate the performance of federated learning since the client’s data distribution is divergent. To mitigate this issue, an effective method is to partition these clients into suitable clusters. However,...
Attitude estimation methods provide modern consumer, industrial, and space systems with an estimate of a body orientation based on noisy sensor measurements. The gradient descent algorithm is one of the most recent methods for optimal attitude estima...
Non-convex optimization problems often challenge gradient-based algorithms, such as Gradient Descent. Neural network training, a prominent application of gradient-based methods, heavily relies on their computational efficiency. However, the cost func...
We are proposing an adaptation of the gradient descent method to optimize the position and orientation of sensors for the sensor placement problem. The novelty of the proposed method lies in the combination of gradient descent optimization with a rea...
Enhancing the effectiveness of clustering methods has always been of great interest. Therefore, inspired by the success story of the gradient descent approach in supervised learning in the current research, we proposed an effective clustering method...
During the interaction process of a manipulator executing a grasping task, to ensure no damage to the object, accurate force and position control of the manipulator’s end-effector must be concurrently implemented. To address the computationally...
We investigate the mathematical model of the 2D acoustic waves propagation in a heterogeneous domain. The hyperbolic first order system of partial differential equations is considered and solved by the Godunov method of the first order of approximati...
Existing tensor completion methods all require some hyperparameters. However, these hyperparameters determine the performance of each method, and it is difficult to tune them. In this paper, we propose a novel nonparametric tensor completion method,...
First-order methods such as stochastic gradient descent (SGD) have recently become popular optimization methods to train deep neural networks (DNNs) for good generalization; however, they need a long training time. Second-order methods which can lowe...
This paper is a step towards developing a geometric understanding of a popular algorithm for training deep neural networks named stochastic gradient descent (SGD). We built upon a recent result which observed that the noise in SGD while training typi...
This paper establishes a model of economic growth for all the G7 countries from 1973 to 2016, in which the gross domestic product (GDP) is related to land area, arable land, population, school attendance, gross capital formation, exports of goods and...
Tracking moving objects is one of the most promising yet the most challenging research areas pertaining to computer vision, pattern recognition and image processing. The challenges associated with object tracking range from problems pertaining to cam...
Accurate monitoring of estuarine turbidity patterns is important for maintaining aquatic ecological balance and devising informed estuarine management strategies. This study aimed to enhance the prediction of estuarine turbidity patterns by enhancing...
This paper introduces a broad class of Mirror Descent (MD) and Generalized Exponentiated Gradient (GEG) algorithms derived from trace-form entropies defined via deformed logarithms. Leveraging these generalized entropies yields MD and GEG algorithms...
In the age of artificial intelligence, the best approach to handling huge amounts of data is a tremendously motivating and hard problem. Among machine learning models, stochastic gradient descent (SGD) is not only simple but also very effective. This...
The high accuracy attainment, using less complex architectures of neural networks, remains one of the most important problems in machine learning. In many studies, increasing the quality of recognition and prediction is obtained by extending neural n...
This paper describes an improved method of calculating reactivity ratios by applying the neuronal networks optimization algorithm, named gradient descent. The presented method is integral and has been compared to the following existing methods: Finem...
Water quality control and the control of contaminant spill in water in particular are becoming a primary need today. Gradient descent sensitivity methods based on the adjoint formulation have proved to be encouraging techniques in this context for ri...
We propose a novel variant of the gradient descent bit-flipping (GDBF) algorithm for decoding low-density parity-check (LDPC) codes over the binary symmetric channel. The new bit-flipping rule is based on the reliability information passed from neigh...
In this study, the harbor aquaculture area tested is Zhanjiang coast, and for the remote sensing data, we use images from the GaoFen-1 satellite. In order to achieve a superior extraction performance, we propose the use of an integration-enhanced gra...
For the last 20 years, it has been common lore that the free energy of RNA duplexes formed from canonical Watson–Crick base pairs (bps) can be largely approximated with dinucleotide bp parameters and a few simple corrective constants that are duplex...
In recent years, deep neural networks (DNN) have been widely used in many fields. Lots of effort has been put into training due to their numerous parameters in a deep network. Some complex optimizers with many hyperparameters have been utilized to ac...
The efficient utilization of structural information in High-Range Resolution Profiles (HRRPs) is of great significance for improving recognition performance. This paper proposes a size estimation method based on L1-norm variable fractional-order grad...
This paper proposes a novel sine step size for warm-restart stochastic gradient descent (SGD). For the SGD based on the new proposed step size, we establish convergence rates for smooth non-convex functions with and without the Polyak–Łoja...
Task offloading in satellite networks, which involves distributing computational tasks among heterogeneous satellite nodes, is crucial for optimizing resource utilization and minimizing system latency. However, existing approaches such as static offl...
The uncertainty in the new power system has increased, leading to limitations in traditional stability analysis methods. Therefore, considering the perspective of the three-dimensional static security region (SSR), we propose a novel approach for sys...
The Gerchberg–Saxton (GS) algorithm is a Fourier iterative algorithm that can effectively optimize phase-only computer-generated holograms (CGHs). This study proposes a new optimization technique for phase-only CGHs based on the gradient descent meth...
This paper presents an adaptive PID using stochastic gradient descent with momentum (SGDM) for a proton exchange membrane fuel cell (PEMFC) power system. PEMFC is a nonlinear system that encounters external disturbances such as inlet gas pressures an...
The escalating demand for power load is increasingly prone to triggering power quality (PQ) issues, leading to severe economic losses. Aiming at reducing the economic losses, this paper focuses on the coordinated relationship between PQ and economic...
Wavefront aberrations caused by thermal flows or arising from the quality of optical components can significantly impair wireless communication links. Such aberrations may result in an increased error rate in the received signal, leading to data loss...
We propose a novel dynamic gradient descent (DGD) framework integrated with reinforcement learning (RL) for AI-enhanced indoor environmental simulation, addressing the limitations of static optimization in dynamic settings. The proposed method combin...
Maximum correntropy criterion (MCC) has been an important method in machine learning and signal processing communities since it was successfully applied in various non-Gaussian noise scenarios. In comparison with the classical least squares method (L...
Projective Norms are a class of tensor norms that map from the input to the output spaces. These norms are useful for providing a measure of entanglement. Calculating the projective norms is an NP-hard problem, which creates challenges in computing d...
Precision matrices can efficiently exhibit the correlation between variables and they have received much attention in recent years. When one encounters large datasets stored in different locations and when data sharing is not allowed, the implementat...
In this paper, we introduce a novel gradient descent bit-flipping algorithm with a finite state machine (GDBF-wSM) for iterative decoding of low-density parity-check (LDPC) codes. The algorithm utilizes a finite state machine to update variable node...
This article uses the projected gradient method (PG) for a non-negative matrix factorization problem (NMF), where one or both matrix factors must have orthonormal columns or rows. We penalize the orthonormality constraints and apply the PG method via...
Numerical simulations of protein folding enable the design of protein-based nanomachines and nanorobots by predicting folded three-dimensional protein structures with high accuracy and revealing the protein conformation transitions during folding and...
Prior work has introduced a form of explainable artificial intelligence that is able to precisely explain, in a human-understandable form, why it makes decisions. It is also able to learn to make better decisions without potentially learning illegal...
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