Low Convergence Rate Research Articles

Implementation of Chernobyl disaster optimizer based feature selection approach to predict software defects

Background Software Defect Prediction (SDP) enables developers to investigate unscrambled faults in the inaugural parts of the software progression mechanism. However, SDP faces the threat of high dimensionality. Feature selection (FS) selects the finest features while carefully discarding others. Several meta-heuristic algorithms, like Genetic Algorithm, Particle Swarm Optimization, Differential Evolution, and Ant Colony Optimization, have been used to develop defect prediction models. However, these models have drawbacks like high cost, local optima trap, lower convergence rate, and higher parameter tuning. This study applies an innovative FS technique (FSCOA) rooted in Chernobyl Disaster Optimizer (CDO) technique. The proposed procedure intends to unwrap the best features for a prediction model while minimizing errors. Methods The proposed FSCOA investigated twelve public NASA software datasets from the PROMISE archive on Decision Tree, K-nearest neighbor, Naive Bayes, and Quantitative Discriminant Analysis classifiers. Furthermore, the accuracy of the recommended FSCOA method was correlated with existing FS techniques, like FSDE, FSPSO, FSACO, and FSGA. The statistical merit of the proposed measure was verified using Friedman and Holm tests. Results The experiment indicated that the proposed FSCOA approach bettered the accuracy in majority of the instances and achieved an average rank of 1.75 among other studied FS approaches while applying the Friedman test. Furthermore, the Holm test showed that the p-value was lower than or equivalent to the value of α/(A-i), except for the FSCOA and FSGA and FSCOA and FSACO models. Conclusion The results illustrated the supremacy of the prospective FSCOA procedure over extant FS techniques with higher accuracy in almost all cases due to its advantages like enhanced accuracy, the ability to deal with convoluted, high-magnitude datasets not grounded in local optima, and a faster convergence rate. These advantages empower the suggested FSCOA method to overcome the challenges of the other studied FS techniques.

Conservative numerical algorithm for simulating thermoelectrical semiconductor device with unconditional optimal convergence analysis

We propose conservative type numerical method to simulate thermoelectrical semiconductor device problem, in which mixed finite element method used for electric potential equation, conservative characteristic finite element method for electron and hole concentration equations, and standard finite element method for heat conduction equation. By temporal-spatial error splitting argument, the optimal error estimates without certain time step restriction are derived, and low order convergence rate of electrostatic potential and electric field intensity will not affect the accuracy of the electron, hole density and temperature. Numerical tests are performed to validate the theoretical results and application performance of the given method.

A novel multi-objective robust optimization method based on improved Gray Wolf optimizer and Kriging model

A novel multi-objective robust optimization method for mechanical structure products is introduced. Firstly, the method introduces Bernoulli Dynamic Adaptive Gray Wolf Optimizer (BDAGWO) to address inherent limitations within the original Gray Wolf Optimizer (GWO), such as falling into local optimal solutions and low convergence rate. Subsequently, BDAGWO is utilized to search optimal correlation coefficients of Kriging. The proposed surrogate model exhibits high fitting accuracy on different test cases, with coefficients of determination reaching above 0.99 on the test set, and mean relative error, mean absolute error, mean absolute percentage error and root mean squared error are all close to 0. To solve multi-objective optimization problems, an improved NSGA-II is introduced to amplify search capabilities. Then based on robust optimization method, combine BDAGWO-Kriging and improved NSGA-II to establish a multi-objective robust optimization framework with high accuracy and high solution efficiency. The proposed method is implemented to an EMU bogie frame, demonstrating that the robust optimization scheme reduces the maximum equivalent stress and mass, and exhibits lower fluctuation compared to deterministic optimization. This substantiates the method’s effectiveness and provides an optimization approach of large and complex mechanical products.

An Information Theoretic Learning Artificial Immune Network for Alternative Clustering

Clustering is an unsupervised task employed when there is no prior knowledge about the structure and information contained in the data. Nowadays the amount of information and the dimensionality of data increased. Due to this, several datasets contain samples that can be clustered in different ways, presenting different partitions. Classical algorithms tend to obtain a single partition per execution and also require information like the number of clusters. Immuno-inspired algorithms were developed to reduce some of these drawbacks. They can find alternative solutions without knowing the number of clusters, but high dimensionality reduces their performance leading to low convergence rates. Information Theoretic Learning (ITL) uses statistical information of the data regardless of prior knowledge of the structure of these data and the dimensionality involved. Applied in several papers for clustering, ITL-based algorithms tend to present good performance for this task. This paper presents an immuno-inspired ITL-based algorithm (ITL-aiNet) capable of finding and maintaining high-quality and diverse solutions for datasets regardless of their dimensionality and structure. Real-world image and document datasets of varying dimensions were used in the experiments, allowing different ways of clustering. The results were evaluated using external indices. The proposed approach was capable of maintaining high-quality and diverse solutions, compared to other strategies found in the literature. The indices used to measure the quality and diversity of solutions indicated that the algorithm is capable of finding and maintaining good solutions. Solutions that have greater diversity than other algorithms in some datasets and higher quality in others.

Optimization of vehicle conceptual design problems using an enhanced hunger games search algorithm

Abstract Electric vehicles have become a standard means of transportation in the last 10 years. This paper aims to formalize design optimization problems for electric vehicle components. It presents a tool conceptual design technique with a hunger games search optimizer that incorporates dynamic adversary-based learning and diversity leader (referred to as HGS-DOL-DIL) to overcome the local optimum trap and low convergence rate limitations of the Hunger Games search algorithm to improve the convergence rate. The performance of the proposed algorithms is studied on six widely used engineering design problems, complex constraints, and discrete variables. For the HGS-DOL-DIL practical feasibility analysis, a case study of shape optimization of an electric car suspension arm from the industry is carried out. Overall, the inclusion of the OL strategy has proven its superiority in solving real-world problems, especially in solving real-world problems such as shape optimization of an electric vehicle automobile suspension arm, showing that the algorithm improves the search space improves the solution quality, and reflects its potential to find global optimum solutions in a well-balanced exploration and exploitation phase.

A Combined Quasi-Newton-Type Method Using 4th-Order Directional Derivatives for Solving Degenerate Problems of Unconstrained Optimization

Introduction. Methods of unconstrained optimization play a significant role in machine learning [1–6]. When solving practical problems in machine learning, such as tuning nonlinear regression models, the extremum point of the chosen optimality criterion is often degenerate, which significantly complicates its search. Therefore, degenerate problems are the most challenging in optimization. Known numerical methods for solving the general unconstrained optimization problem, up to the second order, have very low convergence rates when solving degenerate problems [7, 8]. This is explained by the fact that for a significant improvement in convergence rate in this case, it is necessary to use higher-order derivatives in the method than the second order [10]. The purpose of the paper is to develop an efficient quasi-Newton method for solving degenerate unconstrained optimization problems, the idea of which (unlike regularization) involves dividing the entire space into the sum of two orthogonal subspaces. This idea was introduced in [23]. The space division at each iteration of the method is based on the spectral decomposition of the matrix approximating the Hessian of the objective function using the BFGS formula [3]. Each subspace exhibits its own behavior of the objective function, and therefore, an appropriate minimization method is applied on it. Results. A combined quasi-Newton method is presented for solving degenerate unconstrained optimization problems, based on orthogonal decomposition of the Hessian approximation matrix and division of the entire space into the sum of two orthogonal subspaces. On one subspace (the kernel of the Hessian approximation matrix), a method is applied where derivatives in the direction of the 4th order are computed, while on the orthogonal complement to it, a quasi-Newtonian method is applied. A separate one-dimensional search is applied on each of these subspaces to determine the step multiplier in the respective direction. The effectiveness of the presented combined method is confirmed by numerical experiments conducted on widely accepted test functions for unconstrained optimization problems. The proposed method allows obtaining fairly accurate solutions to test tasks in case of degeneracy of the minimum point with significantly lower computational costs for gradient calculations compared to optimization procedures of well-known mathematical packages. Conclusions. The idea of dividing the entire space into the sum of two (or possibly more) orthogonal subspaces when solving complex optimization problems is quite promising in terms of applying a combination of different numerical methods on separate subspaces. In the future, it is planned to conduct theoretical research on the convergence rate of the presented combined method in solving degenerate unconstrained optimization problems. Keywords: unconstrained optimization, quasi-Newton methods, degenerate minimum point, spectral matrix decomposition, Machine Learning.

A nested non-intrusive stochastic isogeometric method for nonlinear thermal vibration of FGM plates under random loading

This paper introduces an adaptive nested non-invasive dynamic SIGA method based on RBFNN for the nonlinear thermal vibration analysis of FGM plates under random loading. This method is robust and accurate in high-dimensional input spaces regardless of the sample sequence, addresses the low convergence rate of QMCS, and solves the stochastic dynamic response probability density function under random loading. Firstly, the multidimensional input space for random loading is constructed based on several mutually independent random variables via the stationary Gaussian stochastic process simulation technique. The nonlinear FGM plate model subjected to random loading in the thermal environment is modeled using HSDT with von Kármán strain-displacement relation within the IGA framework. Subsequently, a nested non-invasive dynamic response surface analysis method, SIGA-RBFNN, is proposed based on the RBFNN technique. Analysis of the FGM plate response under random loading demonstrates that SIGA-RBFNN, compared to tensor-product-based SIGA methods, is less affected by sample sequence types. It effectively addresses high-dimensional stochasticity and offers significant advantages in robustness, accuracy, and efficiency. Finally, SIGA-RBFNN compensates for the low convergence speed of QMCS and successfully solves the FGM plate displacement response statistics and probability density function under random loading.

Vibration based dual-criteria damage detection method using deep neural networks in highway bridges with steel girders

This article introduces a new method for assessing the damage in steel girders of highway bridges using deep neural networks. The method uses modified forms of modal strain energy damage index and modal flexibility damage index to train the neural network and prevent unsafe decisions. The neural network is trained using damage indexes achieved from numerical simulations of the bridge with different damage scenarios. Three types of neural networks, including convolutional neural network (CNN), Long short-term memory (LSTM) neural network, and conventional artificial neural network (ANN) are compared to achieve the best performance. The proposed method overcomes previous detection problems such as false-positive indications, limited damage locations, and scenarios, and insufficient accuracy in cases with multiple damage scenarios. The results show that the proposed method and CNN can accurately identify unspecified damage locations and severity in multi-span highway bridges. The new training method of the CNN deep neural network systems overcomes some shortcomings in ANN, such as being time-consuming, having a low convergence rate, and experiencing data overfitting. Additionally, the CNN training scheme can limit the need for massive amounts of input data and increase the speed and accuracy of network training, especially in multiple damage scenarios.

Geodynamic modeling on continental collision in Qilian orogenic belt

The Qilian orogenic belt (QOB) located in the northeast margin of the Tibetan Plateau is featured by remarkable crustal thrusting and shortening, providing a key natural example to understand the lithospheric deformation of the Tibetan Plateau. Two types of continental collision are observed in the QOB: lithosphere subduction beneath Southern Qilian and crust underthrusting of Alxa terrain along the North Border Thrust (NBT). Deep seismic reflection profiles reveal complex stress field evolution, including compressional deformation in the lower crust, extensional deformation in the upper crust, and detachment deformation in the middle crust. In this study, we use 2D numerical modeling to investigate the dynamics of these two different collision types and the evolution of Qilian uplift. Model results suggest three patterns of continental collision, i.e., crust underthrusting follows lithosphere subduction, lithosphere subduction and the failed underthrusting/subduction. The key factors that may influence model evolution, including crustal rheology, convergence direction and rate, are systematically investigated. Our model results are further compared to observations, suggesting that lower convergence rate and crust underthrusting along NBT likely control the uplift and crust stress stratification of the QOB.

An improved Genghis Khan optimizer based on enhanced solution quality strategy for global optimization and feature selection problems

Feature selection (FS) is the activity of defining the most contributing feature subset among all used features to improve the superiority of datasets with a large number of dimensions by selecting significant features and eliminating redundant and irrelevant ones. Therefore, this process can be seen as an optimization process. The primary goals of feature selection are to decrease the number of dimensions and enhance classification accuracy in many domains, such as text classification, large-scale data analysis, and pattern recognition. Several metaheuristics, such as the Genghis Khan Shark Optimizer Algorithm (GKSO), can assist in optimizing the FS issue. However, these methods tend to converge towards local solutions with a low convergence rate. In order to address this issue in GKSO, a more refined version called I-GKSO is implemented. The I-GKSO suggested introducing a new approach to modify solutions that have low fitness values. In addition, it employs the Enhanced Solution Quality (ESQ) strategy to enhance the exploration phase. It utilizes Quasi-opposite-based learning (QOBL) to enhance the best solution obtained and, consequently, the entire population. The algorithm presented aims to solve the FS problem and has been assessed using benchmark optimization problems from the CEC’2017 and CEC’2022. To assess the efficacy of the I-GKSO, it has been subjected to comparisons with multiple different algorithms. The trials conducted using FS datasets yield a quantitative consideration of the I-GKSO's capacity to attain the most optimal subset of features. Furthermore, Wilcoxon and Friedman's non-parametric tests were accomplished to support the performance of the proposed method.

Implementation of Chernobyl optimization algorithm based feature selection approach to predict software defects

Background Software defects can have catastrophic consequences. Therefore, fixing these defects is crucial for the evolution of software. Software Defect Prediction (SDP) enables developers to investigate unscramble faults in the inaugural parts of the software progression mechanism. However, SDP faces many challenges, including the high magnitude of attributes in the datasets, which can degrade the prognostic performance of a defect forecasting model. Feature selection (FS), a compelling instrument for overcoming high dimensionality, selects only the relevant and best features while carefully discarding others. Over the years, several meta-heuristic algorithms such as the Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE), and Ant Colony Optimization (ACO) have been used to develop defect prediction models. However, these models suffer from several drawbacks, such as high cost, local optima trap, lower convergence rate, and higher parameter tuning. To overcome the above shortcomings, this study aims to develop an innovative FS technique, namely, the Chernobyl Optimization Algorithm (FSCOA), to unwrap the most informative features that can produce a precise prediction model while minimizing errors. Methods The proposed FSCOA approach mimicked the process of nuclear radiation while attacking humans after an explosion. The proposed FSCOA approach was combined with four widely used classifiers, namely Decision Tree (DT), K-nearest neighbor (KNN), Naive Bayes (NB), and Quantitative Discriminant Analysis (QDA), to determine the finest attributes from the SDP datasets. Furthermore, the accuracy of the recommended FSCOA method is correlated with existing FS techniques, such as FSDE, FSPSO, FSACO, and FSGA. The statistical merit of the proposed measure was verified using Friedman and Holm tests. Results The experimental findings showed that the proposed FSCOA approach yielded the best accuracy in most cases and achieved an average rank of 1.75, followed by the other studied FS approaches. Furthermore, the Holm test showed that the p-value was lower than or equivalent to the value of α/(A-i), except for the FSCOA and FSGA and FSCOA and FSACO models. Conclusion The experimental findings showed that the prospective FSCOA procedure eclipsed alternative FS techniques with higher accuracy in almost all cases while selecting optimal features.

Parameter Optimization Method for Metal Surface pBRDF Model Based on Improved Strawberry Algorithm

To study the polarization reflection characteristics of metal surfaces, a parameter optimization method for the polarization bidirectional reflection distribution function (pBRDF) model of metal surfaces based on the improved strawberry algorithm has been proposed. Firstly, the light scattering characteristics of metal surfaces were analyzed and a multi-parameter pBRDF model was constructed. Then, the working mechanism of the strawberry optimization algorithm was investigated and improved by introducing the chaotic mapping and Levy flight strategy to overcome the shortcomings, such as low convergence rate and easily falling into local optimum. Finally, the method proposed in this paper was validated by simulating open-source data from references and the obtained ones with a self-built experimental platform. The results show that the proposed method outperforms those by nonlinear least squares, particle swarm optimization and the original strawberry algorithm in fitting the detected degree of polarization (DOP) data, indicating the modeling accuracy was significantly improved and better suited to characterize the polarized reflection properties of metal surfaces.

Intelligent planning of fire evacuation routes in buildings based on improved adaptive ant colony algorithm

Intelligent planning of fire evacuation routes is an important guarantee for rapid emergency response. Ant colony optimization, as an intelligent bionic algorithm, has notable advantages in route planning. However, traditional ant colony optimization corresponds to a low convergence rate, is easily caught in local optimal solution, and regards route length as the only constraint. To resolve these problems, an improved adaptive ant colony optimization (IAACO) algorithm was proposed in this study. Risk, energy consumption, and route length were taken as key factors to improve the heuristic function, optimize the pheromone update function, and establish multi-objective constraints, The standards for fire evacuation better align with practical requirements. Meanwhile, the adaptive pheromone volatile coefficient was introduced to balance convergence and global searching ability. In addition, the hazard range on the grid map was visualized. The results indicate that under various complex obstacle grid maps, the path inferiority of IAACO is reduced by 61.7% and 58.4%, 43.6% and 36.7%, and 41.6% and 67.7% compared to ACO and IACO, respectively; under the condition of multiple exits, the inferiority is reduced by 63.8% and 54.6%; under the condition of multiple fire sources, the inferiority is reduced by 40.1% and 34.6%; compared with other algorithms, IAACO shows the lowest path inferiority index, 26.6. IAACO is applicable to both the dynamic planning of fire evacuation routes and the evacuation simulation software, Pathfinder, and it performs better than the built-in algorithms of Pathfinder. Facts have proved that the IAACO algorithm significantly improves the safety level of evacuation compared to traditional evacuation methods and other optimization algorithms.

An improved genetic algorithm for robot path planning

The conventional genetic algorithm (GA) for path planning exists several drawbacks, such as uncertainty in the direction of robot movement, circuitous routes, low convergence rates, and prolonged search time. To solve these problems, this study introduces an improved GA-based path-planning algorithm that adopts adaptive regulation of crossover and mutation probabilities. This algorithm uses a hybrid selection strategy that merges elite, tournament, and roulette wheel selection methods. An adaptive approach is implemented to control the speed of population evolution through crossover and mutation. Combining with a local search operation enhances the optimization capability of the algorithm. The proposed algorithm was compared with the traditional GA through simulations, demonstrating shorter path lengths and reduced search times.

A novel framework for online supervised learning with feature selection

Current online learning methods suffer issues such as lower convergence rates and limited capability to select important features compared to their offline counterparts. In this paper, a novel framework for online learning based on running averages is proposed. Many popular offline regularised methods such as Lasso, Elastic Net, Minimax Concave Penalty (MCP), and Feature Selection with Annealing (FSA) have their online versions introduced in this framework. The equivalence between the proposed online methods and their offline counterparts is proved, and then novel theoretical true support recovery and convergence guarantees are provided for some of the methods in this framework. Numerical experiments indicate that the proposed methods enjoy high true support recovery accuracy and a faster convergence rate compared with conventional online and offline algorithms. Finally, applications to large datasets are presented, where again the proposed framework shows competitive results compared to popular online and offline algorithms.

A compact artificial bee colony metaheuristic for global optimization problems

AbstractComputationally efficient and time‐memory saving compact algorithms become a keystone for solving global optimization problems, particularly the real world problems; which involve devices with limited memory or restricted use of battery power. Compact optimization algorithms represent a probabilistic view of the population to simulate the population behaviour as they broadly explores the decision space at the beginning of the optimization process and keep focus on to search the most promising solution, therefore narrows the search space, moreover few number of parameters need be stored in the memory thus require less space and time to compute efficiently. Role of population‐based algorithms remain inevitable as compact algorithms make use of the efficient search ability of these population based algorithms for optimization but only through a probabilistic representation of the population space in order to optimize the real world problems. Artificial bee colony (ABC) algorithm has shown to be competitive over other population‐based algorithms for solving optimization problems, however its solution search equation contributes to its insufficiency due to poor exploitation phase coupled with low convergence rate. This paper, presents a compact Artificial bee colony (cABC) algorithm with an improved solution search equation, which will be able to search an optimal solution to improve its exploitation capabilities, moreover in order to increase the global convergence of the proposed algorithm, an improved approach for population sampling is introduced through a compact distribution which helps in maintaining a good balance between exploration and exploitation search abilities of the proposed compact algorithm with least memory requirements, thus became suitable for limited hardware access devices. The proposed algorithm is evaluated extensively on a standard set of benchmark functions proposed at IEEE CEC'13 for large‐scale global optimization (LSGO) problems. Numerical results prove that the proposed compact algorithm outperforms other standard optimization algorithms.

Colour Image Enhancement Model of Retinal Fundus Image for Diabetic Retinopathy Recognition

Diabetic retinopathy (DR) features are typically identified through ophthalmologist eye examinations, but these images often facechallenges like low contrast, non-uniform illumination, and colour inconsistency, affecting the diagnosis accuracy. Therefore, this studyintroduces two novel techniques to improve image quality. One is applying colour image processing techniques to original retinalfundus images, overcoming existing algorithm limitations. Firstly, a new colour correction algorithm was proposed based on TunedBrightness Controlled Single-Scale Retinex (TBCSSR) named Fuzzy TBCSSR Histogram Matching (fTBCSSRhm) to address the issue of colour inconsistency in the dataset. Secondly, based on hybrid particle swarm optimisation-contrast stretch (HPSOCS), the hybridof TBCSSR and HPSOCS named eTBCSSR-HPSOCS algorithm is introduced to tackle the limitations of the standard Particle SwarmOptimisation (PSO) algorithm in HPSOCS, which is prone to local optima and exhibits low convergence rates. This technique combinesthe L-component of the LAB colour model with an enhanced velocity mechanism in PSO and contrast stretching (lavHPSOCS). Its goalis to fine-tune parameters automatically, reduce over-enhancement, avoid unwanted artefacts, and preserve intricate details. This approach improves optimisation by balancing exploration and exploitation and refining velocity control. The proposed algorithm underwent both qualitative and quantitative evaluations. Tests on 100 retinal fundus images from primary datasets were performed to benchmark the algorithm against three existing approaches. The results show that the qualitative performance of the proposed enhancement is more favourable to ophthalmologist specialists than other images. Quantitatively, eTBCSSR-HPSOCS outperforms others with the lowest mean squared error (MSE) of 42.72859, the highest peak signal-to-noise ratio (PSNR) of 32.768, and entropy of 0.977.

Stochastic gradient descent without full data shuffle: with applications to in-database machine learning and deep learning systems

Modern machine learning (ML) systems commonly use stochastic gradient descent (SGD) to train ML models. However, SGD relies on random data order to converge, which usually requires a full data shuffle. For in-DB ML systems and deep learning systems with large datasets stored on block-addressable secondary storage such as HDD and SSD, this full data shuffle leads to low I/O performance—the data shuffling time can be even longer than the training itself, due to massive random data accesses. To balance the convergence rate of SGD (which favors data randomness) and its I/O performance (which favors sequential access), previous work has proposed several data shuffling strategies. In this paper, we first perform an empirical study on existing data shuffling strategies, showing that these strategies suffer from either low performance or low convergence rate. To solve this problem, we propose a simple but novel two-level data shuffling strategy named CorgiPile, which can avoid a full data shuffle while maintaining comparable convergence rate of SGD as if a full shuffle were performed. We further theoretically analyze the convergence behavior of CorgiPile and empirically evaluate its efficacy in both in-DB ML and deep learning systems. For in-DB ML systems, we integrate CorgiPile into PostgreSQL by introducing three new physical operators with optimizations. For deep learning systems, we extend single-process CorgiPile to multi-process CorgiPile for the parallel/distributed environment and integrate it into PyTorch. Our evaluation shows that CorgiPile can achieve comparable convergence rate with the full-shuffle-based SGD for both linear models and deep learning models. For in-DB ML with linear models, CorgiPile is 1.6×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes $$\\end{document}-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-$$\\end{document}12.8×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes $$\\end{document} faster than two state-of-the-art systems, Apache MADlib and Bismarck, on both HDD and SSD. For deep learning models on ImageNet, CorgiPile is 1.5×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes $$\\end{document} faster than PyTorch with full data shuffle.

A variable diagonal-matrix-step-size APA robust to impulsive noises

This study introduces a variable diagonal-matrix-step-size affine projection algorithm (APA), which shows robustness against to impulsive noises. Unlike the normal scalar step-size method, the independent step size for each input vector is used as the entry of the diagonal matrix, and the optimal step size at each time step is ascertained by conducting mean-square-deviation (MSD) analysis. In addition, a recursive equation of weight update has been derived without approximating posteriori error as priori error. Using the Lagrange multiplier method, we formulate a scalar step size affine projection algorithm that shows resilience to impulsive noises. This algorithm emerges as a solution to a constrained optimization problem. To further enhance convergence performance, a diagonal-matrix-step size is introduced and its MSD is analyzed. The step size at each time step is optimized by interpreting the MSD mathematically, resulting in the variable diagonal-matrix-step size APA (VDMSS-APA). Various simulations exhibit low steady-state error and fast convergence rate of the proposed algorithm.

Magmatic fingerprints of subduction initiation and mature subduction: numerical modelling and observations from the Izu-Bonin-Mariana system

Understanding the formation of new subduction zones is important because they have been proposed as the main driving mechanism for plate tectonics and they are crucial for geochemical cycles on Earth. However, the conditions needed to facilitate subduction zone initiation and the associated magmatic evolution are still poorly understood. Using a natural case study, we conducted a series of high-resolution 2D petrological-thermomechanical (i2VIS) subduction models assuming visco-plastic rheology. We aim to model the initiation and early stage of an intra-oceanic subduction zone connected to the gravitational collapse of a weak transform zone and compare it to the natural example of the Izu-Bonin-Mariana subduction zone. We also analysed the influence of low convergence rates on magmatic evolution. We propose a viable transition from initiation to mature subduction zone divided into distinct stages that include initiation by gravitational collapse of the subducting slab, development of a near-trench spreading centre, gradual build-up of asthenospheric mantle return flow, and maturation of a volcanic arc. We further show that mantle flow variations and shear instabilities, producing thermal perturbations and depleted interlayers, influence the temporal and spatial distribution of asthenospheric mantle composition and fertility in the mantle wedge. Our modelling results are in good agreement with geological and geochemical observations of the early stages of the Izu-Bonin-Mariana subduction zone.