Journal of Scientific Computing最新文献_第3页

Neural Active Manifolds: Nonlinear Dimensionality Reduction for Uncertainty Quantification. 神经活动流形：不确定性量化的非线性降维。

IF 2.6 2区数学

Journal of Scientific Computing Pub Date : 2025-01-01 Epub Date: 2025-11-04 DOI: 10.1007/s10915-025-03113-7

Andrea Zanoni, Gianluca Geraci, Matteo Salvador, Alison L Marsden, Daniele E Schiavazzi

{"title":"Neural Active Manifolds: Nonlinear Dimensionality Reduction for Uncertainty Quantification.","authors":"Andrea Zanoni, Gianluca Geraci, Matteo Salvador, Alison L Marsden, Daniele E Schiavazzi","doi":"10.1007/s10915-025-03113-7","DOIUrl":"10.1007/s10915-025-03113-7","url":null,"abstract":"We present a new approach for nonlinear dimensionality reduction, specifically designed for computationally expensive mathematical models. We leverage autoencoders to discover a one-dimensional neural active manifold (NeurAM) capturing the model output variability, through the aid of a simultaneously learnt surrogate model with inputs on this manifold. Our method only relies on model evaluations and does not require the knowledge of gradients. The proposed dimensionality reduction framework can then be applied to assist outer loop many-query tasks in scientific computing, like sensitivity analysis and multifidelity uncertainty propagation. In particular, we prove, both theoretically under idealized conditions, and numerically in challenging test cases, how NeurAM can be used to obtain multifidelity sampling estimators with reduced variance by sampling the models on the discovered low-dimensional and shared manifold among models. Several numerical examples illustrate the main features of the proposed dimensionality reduction strategy and highlight its advantages with respect to existing approaches in the literature.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"105 3","pages":"79"},"PeriodicalIF":2.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12586266/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145460495","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

Surrogate Modeling of Resonant Behavior in Scattering Problems Through Adaptive Rational Approximation and Sketching. 基于自适应理性逼近和素描的散射问题共振行为代理建模。

IF 3.3 2区数学

Journal of Scientific Computing Pub Date : 2025-01-01 Epub Date: 2025-08-09 DOI: 10.1007/s10915-025-03020-x

Davide Pradovera, Ralf Hiptmair, Ilaria Perugia

{"title":"Surrogate Modeling of Resonant Behavior in Scattering Problems Through Adaptive Rational Approximation and Sketching.","authors":"Davide Pradovera, Ralf Hiptmair, Ilaria Perugia","doi":"10.1007/s10915-025-03020-x","DOIUrl":"10.1007/s10915-025-03020-x","url":null,"abstract":"This paper describes novel algorithms for the identification of (almost-)resonant behavior in scattering problems. Our methods, relying on rational approximation, aim at building surrogate models of what we call \"field amplification\", defined as the norm of the solution operator of the scattering problem, which we express through boundary-integral equations. To provide our techniques with theoretical foundations, we first derive results linking the field amplification to the spectral properties of the operator that defines the scattering problem. Such results are then used to justify the use of rational approximation in the surrogate-modeling task. Some of our proposed methods apply rational approximation in a \"standard\" way, building a rational approximant for either the solution operator directly or, in the interest of computational efficiency, for a randomly \"sketched\" version of it. Our other \"hybrid\" approaches are more innovative, combining rational-approximation-assisted root-finding with approximation using radial basis functions. Three key features of our methods are that (i) they are agnostic of the strategy used to discretize the scattering problem, (ii) they do not require any computations involving non-real wavenumbers, and (iii) they can adjust to different settings through the use of adaptive sampling strategies. We carry out some numerical experiments involving 2D scatterers to compare our approaches. In our tests, two of our approaches (one standard, one hybrid) emerge as the best performers, with one or the other being preferable, depending on whether emphasis is placed on accuracy or efficiency.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"104 3","pages":"104"},"PeriodicalIF":3.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12335407/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144823108","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

A Posteriori Error Analysis for a Coupled Stokes-Poroelastic System with Multiple Compartments. 多隔室stokes -孔隙弹性耦合系统的后验误差分析。

IF 2.8 2区数学

Journal of Scientific Computing Pub Date : 2025-01-01 Epub Date: 2025-03-08 DOI: 10.1007/s10915-025-02814-3

Ivan Fumagalli, Nicola Parolini, Marco Verani

{"title":"A Posteriori Error Analysis for a Coupled Stokes-Poroelastic System with Multiple Compartments.","authors":"Ivan Fumagalli, Nicola Parolini, Marco Verani","doi":"10.1007/s10915-025-02814-3","DOIUrl":"10.1007/s10915-025-02814-3","url":null,"abstract":"The computational effort entailed in the discretization of fluid-poromechanics systems is typically highly demanding. This is particularly true for models of multiphysics flows in the brain, due to the geometrical complexity of the cerebral anatomy-requiring a very fine computational mesh for finite element discretization-and to the high number of variables involved. Indeed, this kind of problems can be modeled by a coupled system encompassing the Stokes equations for the cerebrospinal fluid in the brain ventricles and Multiple-network Poro-Elasticity (MPE) equations describing the brain tissue, the interstitial fluid, and the blood vascular networks at different space scales. The present work aims to rigorously derive a posteriori error estimates for the coupled Stokes-MPE problem, as a first step towards the design of adaptive refinement strategies or reduced order models to decrease the computational demand of the problem. Through numerical experiments, we verify the reliability and optimal efficiency of the proposed a posteriori estimator and identify the role of the different solution variables in its composition.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"103 1","pages":"22"},"PeriodicalIF":2.8,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11890245/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143598197","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

Fast Reflected Forward-Backward algorithm: achieving fast convergence rates for convex optimization with linear cone constraints. 快速反射前向后算法：实现快速收敛率凸优化与线性锥约束。

IF 3.3 2区数学

Journal of Scientific Computing Pub Date : 2025-01-01 Epub Date: 2025-11-03 DOI: 10.1007/s10915-025-03103-9

Radu Ioan Boţ, Dang-Khoa Nguyen, Chunxiang Zong

{"title":"Fast Reflected Forward-Backward algorithm: achieving fast convergence rates for convex optimization with linear cone constraints.","authors":"Radu Ioan Boţ, Dang-Khoa Nguyen, Chunxiang Zong","doi":"10.1007/s10915-025-03103-9","DOIUrl":"https://doi.org/10.1007/s10915-025-03103-9","url":null,"abstract":"In this paper, we derive a Fast Reflected Forward-Backward (Fast RFB) algorithm to solve the problem of finding a zero of the sum of a maximally monotone operator and a monotone and Lipschitz continuous operator in a real Hilbert space. Our approach extends the class of reflected forward-backward methods by introducing a Nesterov momentum term and a correction term, resulting in enhanced convergence performance. The iterative sequence of the proposed algorithm is proven to converge weakly, and the Fast RFB algorithm demonstrates impressive convergence rates, achieving <math><mrow><mi>o</mi> <mfenced><mfrac><mn>1</mn> <mi>k</mi></mfrac> </mfenced> </mrow> </math> as <math><mrow><mi>k</mi> <mo>→</mo> <mo>+</mo> <mi>∞</mi></mrow> </math> for both the discrete velocity and the tangent residual at the last-iterate. When applied to minimax problems with a smooth coupling term and nonsmooth convex regularizers, the resulting algorithm demonstrates significantly improved convergence properties compared to the current state of the art in the literature. For convex optimization problems with linear cone constraints, our approach yields a fully splitting primal-dual algorithm that ensures not only the convergence of iterates to a primal-dual solution, but also a last-iterate convergence rate of <math><mrow><mi>o</mi> <mfenced><mfrac><mn>1</mn> <mi>k</mi></mfrac> </mfenced> </mrow> </math> as <math><mrow><mi>k</mi> <mo>→</mo> <mo>+</mo> <mi>∞</mi></mrow> </math> for the objective function value, feasibility measure, and complementarity condition. This represents the most competitive theoretical result currently known for algorithms addressing this class of optimization problems. Numerical experiments are performed to illustrate the convergence behavior of Fast RFB.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"105 3","pages":"73"},"PeriodicalIF":3.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12583384/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145453877","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

An Efficient Quasi-Newton Method with Tensor Product Implementation for Solving Quasi-Linear Elliptic Equations and Systems. 求解拟线性椭圆方程和系统的有效的张量积拟牛顿法。

IF 2.8 2区数学

Journal of Scientific Computing Pub Date : 2025-01-01 Epub Date: 2025-04-30 DOI: 10.1007/s10915-025-02897-y

Wenrui Hao, Sun Lee, Xiangxiong Zhang

{"title":"An Efficient Quasi-Newton Method with Tensor Product Implementation for Solving Quasi-Linear Elliptic Equations and Systems.","authors":"Wenrui Hao, Sun Lee, Xiangxiong Zhang","doi":"10.1007/s10915-025-02897-y","DOIUrl":"10.1007/s10915-025-02897-y","url":null,"abstract":"In this paper, we introduce a quasi-Newton method optimized for efficiently solving quasi-linear elliptic equations and systems, with a specific focus on GPU-based computation. By approximating the Jacobian matrix with a combination of linear Laplacian and simplified nonlinear terms, our method reduces the computational overhead typical of traditional Newton methods while handling the large, sparse matrices generated from discretized PDEs. We also provide a convergence analysis demonstrating local convergence to the exact solution under optimal choices for the regularization parameter, ensuring stability and efficiency in each iteration. Numerical experiments in two- and three-dimensional domains validate the proposed method's robustness and computational gains with tensor product implementation. This approach offers a promising pathway for accelerating quasi-linear elliptic equations and systems solvers, expanding the feasibility of complex simulations in physics, engineering, and other fields leveraging advanced hardware capabilities.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"103 3","pages":"89"},"PeriodicalIF":2.8,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12043795/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144057248","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

Nonlinear Hierarchical Matrix Factorization-Based Tensor Ring Approximation for Multi-dimensional Image Recovery 基于非线性层次矩阵因数分解的张量环逼近法实现多维图像复原

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-09-16 DOI: 10.1007/s10915-024-02670-7

Wei-Hao Wu, Ting-Zhu Huang, Xi-Le Zhao, Hao Zhang, Zhi-Long Han

{"title":"Nonlinear Hierarchical Matrix Factorization-Based Tensor Ring Approximation for Multi-dimensional Image Recovery","authors":"Wei-Hao Wu, Ting-Zhu Huang, Xi-Le Zhao, Hao Zhang, Zhi-Long Han","doi":"10.1007/s10915-024-02670-7","DOIUrl":"https://doi.org/10.1007/s10915-024-02670-7","url":null,"abstract":"Recently, tensor ring (TR) approximation has received increasing attention in multi-dimensional image processing. In TR approximation, the key backbone is the shallow matrix factorizations, which approximate the circular unfolding of the multi-dimensional image. However, the shallow matrix factorization limits the standard TR approximation’s ability to represent images with complex details and textures. To address this limitation, we propose a nonlinear hierarchical matrix factorization-based tensor ring (NHTR) approximation. Specifically, instead of the shallow matrix factorization, we introduce the nonlinear hierarchical matrix factorization in NHTR approximation to approximate circularly (lceil frac{N}{2}rceil )-modes unfoldings of an N-th order tensor. Benefiting from the powerful expressive capability of the nonlinear hierarchical matrix factorization, the proposed NHTR approximation can faithfully capture fine details of the clean image compared to classical tensor ring approximation. Empowered with the proposed NHTR, we build a multi-dimensional image recovery model and establish a theoretical error bound between the recovered image and the clean image based on the proposed model. To solve the highly nonlinear and hierarchical optimization problem, we develop an efficient alternating minimization-based algorithm. Experiments on multispectral images and color videos conclusively demonstrate the superior performance of our method over the compared state-of-the-art methods in multi-dimensional image recovery.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"51 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256274","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

Fully Discrete Finite Difference Schemes for the Fractional Korteweg-de Vries Equation 分数科特韦格-德-弗里斯方程的完全离散有限差分方案

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-09-14 DOI: 10.1007/s10915-024-02672-5

Mukul Dwivedi, Tanmay Sarkar

引用次数: 0

Curvature-Dependent Elastic Bending Total Variation Model for Image Inpainting with the SAV Algorithm 利用 SAV 算法绘制图像的曲率相关弹性弯曲总变化模型

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-09-12 DOI: 10.1007/s10915-024-02666-3

Caixia Nan, Zhonghua Qiao, Qian Zhang

引用次数: 0

The Optimal Weights of Non-local Means for Variance Stabilized Noise Removal 方差稳定除噪的非局部均值的最佳权重

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-09-12 DOI: 10.1007/s10915-024-02668-1

Yu Guo, Caiying Wu, Yuan Zhao, Tao Wang, Guoqing Chen, Qiyu Jin, Yiqiu Dong

{"title":"The Optimal Weights of Non-local Means for Variance Stabilized Noise Removal","authors":"Yu Guo, Caiying Wu, Yuan Zhao, Tao Wang, Guoqing Chen, Qiyu Jin, Yiqiu Dong","doi":"10.1007/s10915-024-02668-1","DOIUrl":"https://doi.org/10.1007/s10915-024-02668-1","url":null,"abstract":"The Non-Local Means (NLM) algorithm is a fundamental denoising technique widely utilized in various domains of image processing. However, further research is essential to gain a comprehensive understanding of its capabilities and limitations. This includes determining the types of noise it can effectively remove, choosing an appropriate kernel, and assessing its convergence behavior. In this study, we optimize the NLM algorithm for all variations of independent and identically distributed (i.i.d.) variance-stabilized noise and conduct a thorough examination of its convergence behavior. We introduce the concept of the optimal oracle NLM, which minimizes the upper bound of pointwise (L_{1}) or (L_{2}) risk. We demonstrate that the optimal oracle weights comprise triangular kernels with point-adaptive bandwidth, contrasting with the commonly used Gaussian kernel, which has a fixed bandwidth. The computable optimal weighted NLM is derived from this oracle filter by replacing the similarity function with an estimator based on the similarity patch. We present theorems demonstrating that both the oracle filter and the computable filter achieve optimal convergence rates under minimal regularity conditions. Finally, we conduct numerical experiments to validate the performance, accuracy, and convergence of (L_{1}) and (L_{2}) risk minimization for NLM. These convergence theorems provide a theoretical foundation for further advancing the study of the NLM algorithm and its practical applications.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"8 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183705","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

Quaternion-Aware Low-Rank Prior for Blind Color Image Deblurring 用于盲彩色图像去模糊的四元数感知低库优先级

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-09-11 DOI: 10.1007/s10915-024-02671-6

Hao Zhang, Te Qi, Tieyong Zeng

{"title":"Quaternion-Aware Low-Rank Prior for Blind Color Image Deblurring","authors":"Hao Zhang, Te Qi, Tieyong Zeng","doi":"10.1007/s10915-024-02671-6","DOIUrl":"https://doi.org/10.1007/s10915-024-02671-6","url":null,"abstract":"Blind image deblurring is a critical and challenging task in the field of imaging science due to its severe ill-posedness. Appropriate prior information and regularizations are normally introduced to alleviate this problem. Inspired by the fact that the matrix representing a natural image is intrinsically low-rank or approximately low-rank, we employ the low-rank matrix approximation (LRMA) approach for tackling blind image deblurring problems with unknown kernels. When applied to color image restoration tasks, making use of the quaternion representation in the hypercomplex domain enables us to better illustrate the inner relationships among color channels and thus more accurately characterize color image structure. Following this idea, we develop a novel model for color image blind deblurring by implementing the quaternion representation to the LRMA method. This proposed model facilitates better results for blur kernel estimation through preserving the sharper color intermediate latent image, which is first implemented for addressing the blind color image deblurring problem. Extensive numerical experiments demonstrate that our proposed quaternion-aware low-rank prior model greatly improves the performance when compared with the conventional low-rank based scheme and outperforms some of the state-of-the-art methods in terms of some criteria and visual quality.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"10 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183704","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