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First- and second-order adjoint methods for stochastic identification problems 随机辨识问题的一阶和二阶伴随方法
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-11-04 DOI: 10.21136/AM.2025.0151-25
Nguyen Thi Van Anh, Adrian Heldt, Akhtar Ali Khan, Christiane Tammer
{"title":"First- and second-order adjoint methods for stochastic identification problems","authors":"Nguyen Thi Van Anh,&nbsp;Adrian Heldt,&nbsp;Akhtar Ali Khan,&nbsp;Christiane Tammer","doi":"10.21136/AM.2025.0151-25","DOIUrl":"10.21136/AM.2025.0151-25","url":null,"abstract":"<div><p>We present a unified framework for estimating stochastic parameters in general variational problems. This nonlinear inverse problem is formulated as a stochastic optimization problem using the output least-squares (OLS) objective, which minimizes the discrepancy between observed data and the computed solution. A key challenge in OLS-based formulations is the efficient computation of first- and second-order derivatives of the OLS functional, which depend on the corresponding derivatives of the parameter-to-solution map often costly and difficult to evaluate, especially in stochastic settings. To address this, we develop a rigorous computational approach based on first- and second-order adjoint methods for inverse problems governed by stochastic variational problems. Specifically, we propose a new first-order adjoint method for computing the gradient of the OLS objective and introduce two novel second-order adjoint methods for Hessian evaluation. A stochastic Galerkin discretization framework is employed, enabling efficient implementation of the adjoint-based derivative computations. Numerical experiments demonstrate the accuracy and efficiency of the proposed computational framework.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 6","pages":"763 - 795"},"PeriodicalIF":0.7,"publicationDate":"2025-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Stable computation of Laplacian eigenfunctions corresponding to clustered eigenvalues 聚类特征值对应的拉普拉斯特征函数的稳定计算
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-10-30 DOI: 10.21136/AM.2025.0132-25
Ryoki Endo, Xuefeng Liu
{"title":"Stable computation of Laplacian eigenfunctions corresponding to clustered eigenvalues","authors":"Ryoki Endo,&nbsp;Xuefeng Liu","doi":"10.21136/AM.2025.0132-25","DOIUrl":"10.21136/AM.2025.0132-25","url":null,"abstract":"<div><p>The accurate computation of eigenfunctions corresponding to tightly clustered Laplacian eigenvalues remains an extremely difficult problem. Using the shape difference quotient of eigenvalues, we propose a stable computation method for the eigenfunctions of clustered eigenvalues caused by domain perturbation.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 5","pages":"595 - 609"},"PeriodicalIF":0.7,"publicationDate":"2025-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145442887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
An accelerated gradient descent method based on a non-monotone backtracking line search scheme for unconstrained optimization and image restoration problems 一种基于非单调回溯线搜索的加速梯度下降法，用于无约束优化和图像恢复问题
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-10-27 DOI: 10.21136/AM.2025.0131-25
Ali Ashrafi, Seyed Hamzeh Mirzaei
{"title":"An accelerated gradient descent method based on a non-monotone backtracking line search scheme for unconstrained optimization and image restoration problems","authors":"Ali Ashrafi,&nbsp;Seyed Hamzeh Mirzaei","doi":"10.21136/AM.2025.0131-25","DOIUrl":"10.21136/AM.2025.0131-25","url":null,"abstract":"<div><p>This study introduces an accelerated gradient descent method based on a non-monotone backtracking line search scheme. A simple adaptive quadratic model is enhanced by utilizing a real, positive definite scalar matrix derived from the Taylor expansion of the objective function, rather than relying on the exact Hessian. The global and superlinear convergence of the defined model is established under appropriate conditions. Numerical experiments on a set of standard unconstrained optimization problems and image restoration problems show that the new algorithm outperforms other comparable methods in terms of efficiency and robustness.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 5","pages":"711 - 728"},"PeriodicalIF":0.7,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145442886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
On parameter identification in the Stokes system with threshold leak boundary conditions 具有阈值泄漏边界条件的Stokes系统参数辨识
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-10-27 DOI: 10.21136/AM.2025.0142-25
Raino A. E. Mäkinen, Jaroslav Haslinger
{"title":"On parameter identification in the Stokes system with threshold leak boundary conditions","authors":"Raino A. E. Mäkinen,&nbsp;Jaroslav Haslinger","doi":"10.21136/AM.2025.0142-25","DOIUrl":"10.21136/AM.2025.0142-25","url":null,"abstract":"<div><p>This paper addresses the identification of the leak bound function <i>g</i> in the Stokes system with threshold leak boundary conditions, where <i>g</i> varies spatially. The state problem is solved using the dual formulation of the algebraic system, and the resulting optimization problem is formulated as a nonsmooth optimization problem. We establish the existence of solutions for both the continuous and discrete formulations of the problem. The theoretical developments are complemented by numerical experiments, which compare the performance of the nonsmooth optimization approach with traditional regularization-based methods and global optimization techniques.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 6","pages":"735 - 761"},"PeriodicalIF":0.7,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2025.0142-25.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754480","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Two-grid penalty Arrow-Hurwicz iterative finite element methods for the stationary magnetohydrodynamics flow 静止磁流体流动的双网格罚Arrow-Hurwicz迭代有限元方法
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-10-01 DOI: 10.21136/AM.2025.0141-23
Yun-Bo Yang, Yan-De Xia
{"title":"Two-grid penalty Arrow-Hurwicz iterative finite element methods for the stationary magnetohydrodynamics flow","authors":"Yun-Bo Yang,&nbsp;Yan-De Xia","doi":"10.21136/AM.2025.0141-23","DOIUrl":"10.21136/AM.2025.0141-23","url":null,"abstract":"<div><p>We propose and analyze three kinds of two-grid penalty Arrow-Hurwicz (A-H) iterative finite element methods for the stationary incompressible magnetohydrodynamic (MHD) equations, which adopt the existing A-H iterative method to obtain the coarse mesh solution, and then correct the solution by three different one-step schemes (Oseen type, Stokes type and Newton type) with the usual penalty method on the fine mesh. These methods combine the A-H iterative method, the penalty method and the two-grid strategy, maintaining the advantage of three methods and overcoming some of their limitations. Rigorous analysis of the optimal error estimate and stability for three methods are provided. Ample numerical experiments are reported to validate the theoretical results and the efficiency of the numerical schemes.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 5","pages":"611 - 646"},"PeriodicalIF":0.7,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145442884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A robust coefficient of determination based on implicit weighting 基于隐式加权的鲁棒决定系数
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-10-01 DOI: 10.21136/AM.2025.0105-25
Jan Kalina
{"title":"A robust coefficient of determination based on implicit weighting","authors":"Jan Kalina","doi":"10.21136/AM.2025.0105-25","DOIUrl":"10.21136/AM.2025.0105-25","url":null,"abstract":"<div><p>In the linear regression model, the standard coefficient of determination <i>R</i><sup>2</sup> and its weighted counterpart are commonly used to assess the quality of the linear fit. However, both metrics are susceptible to the influence of outliers and heteroskedasticity within the dataset. This paper introduces a robust version of <i>R</i><sup>2</sup>, based on the least weighted squares (LWS) estimator, and examines its statistical properties in detail. We investigate the impact of data quantization on <i>R</i><sup>2</sup> and its robust variants, and propose a hypothesis test for assessing the equality of expected values between two <i>R</i><sup>2</sup> versions. Numerical experiments on 29 publicly available datasets reveal that confidence intervals for the LWS-based coefficient of determination are generally narrower than those for existing measures, especially in homoskedastic settings. In contrast, under heteroskedasticity, narrower intervals do not necessarily imply greater robustness, highlighting the nuanced behavior of these estimators. The comparison with the well-known least trimmed squares (LTS) estimator underscores the promise of the LWS approach, which exhibits favorable efficiency properties and more reliable interval estimation in many practical scenarios.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 5","pages":"647 - 670"},"PeriodicalIF":0.7,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2025.0105-25.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145442885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Global weak solutions to a 3D self-consistent chemotaxis-Stokes system with nonlinear resource consumption 具有非线性资源消耗的三维自洽趋化- stokes系统的全局弱解
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-09-26 DOI: 10.21136/AM.2025.0041-25
Kwang-Ok Ri, Yong-Ho Kim, Jong-Chol Paek, Song-Chol Hong
{"title":"Global weak solutions to a 3D self-consistent chemotaxis-Stokes system with nonlinear resource consumption","authors":"Kwang-Ok Ri,&nbsp;Yong-Ho Kim,&nbsp;Jong-Chol Paek,&nbsp;Song-Chol Hong","doi":"10.21136/AM.2025.0041-25","DOIUrl":"10.21136/AM.2025.0041-25","url":null,"abstract":"<div><p>We study the self-consistent chemotaxis-fluid system with nonlinear resource consumption </p><div><div><span>$$left{{matrix{{{n_t} + u cdot nabla n = Delta {n^m} - nabla cdot (nnabla c) + nabla cdot (nnabla phi),} hfill &amp; {x in Omega,;t&gt;0,} hfill cr {{c_t} + u cdot nabla c = Delta c - {n^alpha}c,} hfill &amp; {x in Omega,;t&gt;0} hfill cr {{u_t} + nabla P = Delta u - nnabla phi + nnabla c,} hfill &amp; {x in Omega,;t&gt;0,} hfill cr {nabla cdot u = 0,} hfill &amp; {x in Omega,;t&gt;0,} hfill}}right.$$</span></div></div><p> under no-flux boundary conditions in a bounded domain Ω ⊂ ℝ<sup>3</sup> with smooth boundary. It is proved that this system possesses a global weak solution provided <i>m</i> &gt; 1 and <span>(alpha&gt;{4 over 3})</span>.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 5","pages":"695 - 709"},"PeriodicalIF":0.7,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145442883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Analysis and optimal control of a fractional tuberculosis model 分级结核模型的分析与最优控制
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-09-24 DOI: 10.21136/AM.2025.0075-25
Hamadoum Dicko, Ali Traoré, Rosaire Ouedraogo
{"title":"Analysis and optimal control of a fractional tuberculosis model","authors":"Hamadoum Dicko,&nbsp;Ali Traoré,&nbsp;Rosaire Ouedraogo","doi":"10.21136/AM.2025.0075-25","DOIUrl":"10.21136/AM.2025.0075-25","url":null,"abstract":"<div><p>A fractional model is developed to study the transmission dynamics of tuberculosis disease. The use of a fractional model provides a memory effect and long-term dynamics often observed in chronic infectious diseases such as tuberculosis, which is characterized by a prolonged incubation period and risks of reactivation. The basic reproduction number is computed and we derive the qualitative stability analysis of equilibria. A sensitivity analysis is conducted to assess the impact of the model parameters. Three control strategies are applied, namely treatment, vaccination, and infection rate management, to minimize the number of infected individuals. Numerical simulations are carried out to illustrate the theoretical results obtained.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 5","pages":"671 - 694"},"PeriodicalIF":0.7,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145442888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A note on eigenvalue of tensors and its application 张量的特征值及其应用
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-09-16 DOI: 10.21136/AM.2025.0022-25
Snigdhashree Nayak, Krushnachandra Panigrahy, Debasisha Mishra, Nachiketa Mishra
{"title":"A note on eigenvalue of tensors and its application","authors":"Snigdhashree Nayak,&nbsp;Krushnachandra Panigrahy,&nbsp;Debasisha Mishra,&nbsp;Nachiketa Mishra","doi":"10.21136/AM.2025.0022-25","DOIUrl":"10.21136/AM.2025.0022-25","url":null,"abstract":"<div><p>The tensor eigenvalue problem has been widely studied in recent years. In this paper, several new properties of eigenvalues and determinants of tensors are explored. We also proposed a formula to compute the determinant of a tensor as a mimic of the matrix determinant. The Perron-Frobenius theorem, one of the most important results in non-negative matrix theory, is proposed for the class of non-negative tensors in the Einstein product framework. Further, the power method, a widely used matrix iterative method for finding the largest eigenvalue, is framed for tensors using the Einstein product. The proposed higher-order power method is applied to calculate the largest eigenvalue of the Laplacian tensors associated with hyper-stars and hyper-trees. The numerical results show that the higher-order power method with the Einstein product is stable.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 4","pages":"563 - 594"},"PeriodicalIF":0.7,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145271565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A weighted hybrid conjugate gradient method for unconstrained multiobjective optimization problems 无约束多目标优化问题的加权混合共轭梯度法
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-09-11 DOI: 10.21136/AM.2025.0040-25
Yunchol Jong, Wonchol Hwang, Yungwang Rim
{"title":"A weighted hybrid conjugate gradient method for unconstrained multiobjective optimization problems","authors":"Yunchol Jong,&nbsp;Wonchol Hwang,&nbsp;Yungwang Rim","doi":"10.21136/AM.2025.0040-25","DOIUrl":"10.21136/AM.2025.0040-25","url":null,"abstract":"<div><p>We propose a weighted HS (Hestenes-Stiefel)-FR (Fletcher-Reeves) hybrid conjugate gradient method for unconstrained multiobjective optimization problem, in which a new positive coefficient of the multiobjective steepest descent direction is adaptively updated to keep its positiveness. The method takes advantage of a weighted hybrid of our modified HS and FR parameters and under the Armijo-type backtracking line search, it has global convergence to a Pareto critical point (point satisfying the first-order necessary condition for Pareto optimality) without convexity assumption on the objectives. Numerical experiments show that the practical performance of the method is competitive with the existing methods such as conjugate gradient method, steepest descent method, Newton method, and quasi-Newton method for unconstrained multiobjective optimization.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 4","pages":"537 - 561"},"PeriodicalIF":0.7,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145271592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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