Applied Numerical Mathematics最新文献_第4页

On the growth factor of Hadamard matrices of order 20 论 20 阶哈达玛矩阵的增长因子

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.01.019

Emmanouil Lardas, Marilena Mitrouli

引用次数: 0

The weak Galerkin finite element method for Stokes interface problems with curved interface

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.10.004

Lin Yang, Qilong Zhai, Ran Zhang

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An augmented Lagrangian approach for cardinality constrained minimization applied to variable selection problems 应用于变量选择问题的心数受限最小化的增强拉格朗日方法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2023.12.006

N. Krejić , E.H.M. Krulikovski , M. Raydan

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On the efficacy of conditioned and progressive Latin hypercube sampling in supervised machine learning 论监督式机器学习中条件式和渐进式拉丁超立方采样的功效

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2023.12.016

Ioannis Iordanis, Christos Koukouvinos, Iliana Silou

{"title":"On the efficacy of conditioned and progressive Latin hypercube sampling in supervised machine learning","authors":"Ioannis Iordanis, Christos Koukouvinos, Iliana Silou","doi":"10.1016/j.apnum.2023.12.016","DOIUrl":"10.1016/j.apnum.2023.12.016","url":null,"abstract":"<div><div><span>In this paper, Latin Hypercube Sampling<span> (LHS) method is compared as per its effectiveness in supervised machine learning procedures. Employing LHS saves computer's processing time and in conjunction with Latin hypercube design properties and space filling ability, is considered as one of the most advanced mechanisms in terms of sampling. Although more data usually deliver better results, when using LHS techniques, same quality outputs can be produced with less data and, as a result, </span></span>storage cost<span> and training time are reduced. Conditioned Latin Hypercube Sampling (cLHS) is one of those techniques, successfully performing in supervised machine learning tasks. Unfortunately, the minimum sufficient training dataset size cannot be known in advance. In this case, progressive sampling is recommended since it begins with a small sample and progressively increases its size until model accuracy no longer improves. Combining Latin hypercube sampling and the idea of sequentially incrementing sampling, we test Progressive Latin Hypercube Sampling (PLHS) while monitoring the performance of the sampling-based training as the sample size grows. PLHS and cLHS algorithms are applied in datasets with discrete variables securing that each sample is provided with the Latin hypercube design properties and preserves the principal ability of LHS for space filling, as illustrated in respective sample projecting diagrams. The performance of the above LHS methods in supervised machine learning is evaluated by the degree of training of the model, which is certified through the accuracy of the produced confusion matrices in test files. The results from the use of the above Latin Hypercube Sampling techniques compared against benchmark sampling method empirically prove that machine learning training process becomes less costfull, while remaining reliable.</span></div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 256-270"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139094504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Regularisation and iterated regularisation of Hamiltonian systems of the second quasi-Painlevé equation

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.10.012

Galina Filipuk

引用次数: 0

Penalty hyperparameter optimization with diversity measure for nonnegative low-rank approximation

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.10.002

Nicoletta Del Buono , Flavia Esposito , Laura Selicato , Rafał Zdunek

{"title":"Penalty hyperparameter optimization with diversity measure for nonnegative low-rank approximation","authors":"Nicoletta Del Buono , Flavia Esposito , Laura Selicato , Rafał Zdunek","doi":"10.1016/j.apnum.2024.10.002","DOIUrl":"10.1016/j.apnum.2024.10.002","url":null,"abstract":"<div><div>Learning tasks are often based on penalized optimization problems in which a sparse solution is desired. This can lead to more interpretative results by identifying a smaller subset of important features or components and reducing the dimensionality of the data representation, as well. In this study, we propose a new method to solve a constrained Frobenius norm-based nonnegative low-rank approximation, and the tuning of the associated penalty hyperparameter, simultaneously. The penalty term added is a particular diversity measure that is more effective for sparseness purposes than other classical norm-based penalties (i.e., <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> or <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></math></span> norms). As it is well known, setting the hyperparameters of an algorithm is not an easy task. Our work drew on developing an optimization method and the corresponding algorithm that simultaneously solves the sparsity-constrained nonnegative approximation problem and optimizes its associated penalty hyperparameters. We test the proposed method by numerical experiments and show its promising results on several synthetic and real datasets.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 189-204"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Orthogonal designs for computer experiments constructed from sequences with zero autocorrelation 由零自相关序列构建的计算机实验正交设计

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2023.09.010

Omar A. Alhelali , S.D. Georgiou , C. Koukouvinos , S. Stylianou

引用次数: 0

A new class of symplectic methods for stochastic Hamiltonian systems 随机哈密顿系统的新一类交映法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.01.021

Cristina Anton

引用次数: 0

Krylov subspace methods for large multidimensional eigenvalue computation 用于大型多维特征值计算的克雷洛夫子空间方法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.01.017

Anas El Hachimi , Khalide Jbilou , Ahmed Ratnani

引用次数: 0

An inverse problem of determining the parameters in diffusion equations by using fractional physics-informed neural networks

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.10.016

M. Srati , A. Oulmelk , L. Afraites , A. Hadri , M.A. Zaky , A. Aldraiweesh , A.S. Hendy

{"title":"An inverse problem of determining the parameters in diffusion equations by using fractional physics-informed neural networks","authors":"M. Srati , A. Oulmelk , L. Afraites , A. Hadri , M.A. Zaky , A. Aldraiweesh , A.S. Hendy","doi":"10.1016/j.apnum.2024.10.016","DOIUrl":"10.1016/j.apnum.2024.10.016","url":null,"abstract":"<div><div>In this study, we address an inverse problem in nonlinear time-fractional diffusion equations using a deep neural network. The challenge arises from the equation's nonlinear behavior, the involvement of time-based fractional Caputo derivatives, and the need to estimate parameters influenced by space or the solution of the fractional PDE. Our solution involves a fractional physics-informed neural network (FPINN). Initially, we use FPINN to solve a straightforward problem. Then, we apply FPINN to the inverse problem of estimating parameter and model non-linearity. For the inverse problem, we enhance our method by including the mean square error of final observations in the FPINN's cost function. This adjustment helps effectively in tackling the unique challenges of the time-fractional diffusion equation. Numerical tests involving regular and singular examples demonstrate the effectiveness of the physics-informed neural network approach in accurately recovering parameters. We reinforce this finding through a numerical comparison with alternative methods such as the alternating direction multiplier method (ADMM), the gradient descent, and the DeepONets (deep operator networks) method.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 189-213"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143141227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0