Computers & Mathematics with Applications最新文献_第3页

Stabilize physics-informed neural networks for stiff differential equations: Re-spacing layer 稳定硬微分方程的物理信息神经网络：重新间隔层

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-22 DOI: 10.1016/j.camwa.2025.09.014

Eunsuh Kim , Heejae Kwon , Sungha Cho , Kyongmin Yeo , Minseok Choi

{"title":"Stabilize physics-informed neural networks for stiff differential equations: Re-spacing layer","authors":"Eunsuh Kim , Heejae Kwon , Sungha Cho , Kyongmin Yeo , Minseok Choi","doi":"10.1016/j.camwa.2025.09.014","DOIUrl":"10.1016/j.camwa.2025.09.014","url":null,"abstract":"<div><div>Approximating the solution of stiff differential equations, which exhibit abrupt changes in certain regions, using physics-informed neural networks (PINNs) is challenging. Typically, training PINNs involves using a larger number of samples concentrated around regions of rapid changes to resolve the sharp gradients. However, this strategy leads to data imbalance, resulting in slower convergence and reduced solution quality. Here, we propose Re-spacing layer (RS-layer) to mitigate these challenges. RS-layer is a pre-trained encoding layer designed to map the skewed distribution of sampling points onto a uniform distribution, maintaining the desirable statistical properties of the input data for effective PINN training. We demonstrate that RS-layer improves PINN training by regularizing the solution gradient in the transformed space. The efficacy of our method is validated through numerical experiments on one-dimensional singularly perturbed equations, the ROBER problem, and the Akzo Nobel problem. Our results show that RS-layer not only accelerates convergence, but also enhances accuracy.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"200 ","pages":"Pages 167-179"},"PeriodicalIF":2.5,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110183","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

A local weak form of the generalized finite difference method (GFDM) with control volume in heat conduction problems 热传导问题中具有控制体积的广义有限差分法的局部弱形式

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-22 DOI: 10.1016/j.camwa.2025.09.015

Tao Zhang , Xiaofeng Zhou

引用次数: 0

Approximation of unknown sources in a time fractional PDE by the optimal ones and their reconstruction 时间分数阶偏微分方程中未知源的最优逼近及其重构

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-22 DOI: 10.1016/j.camwa.2025.09.020

Mourad Hrizi , Ravi Prakash , Antonio André Novotny

引用次数: 0

A bond-based nonlocal anisotropic diffusion model with variable matrix-valued coefficients and its asymptotically compatible meshfree discretization 基于键的变矩阵值系数非局部各向异性扩散模型及其渐近相容的无网格离散化

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-22 DOI: 10.1016/j.camwa.2025.09.018

Xiaofang Wang , Hao Tian

{"title":"A bond-based nonlocal anisotropic diffusion model with variable matrix-valued coefficients and its asymptotically compatible meshfree discretization","authors":"Xiaofang Wang , Hao Tian","doi":"10.1016/j.camwa.2025.09.018","DOIUrl":"10.1016/j.camwa.2025.09.018","url":null,"abstract":"<div><div>We propose a bond-based nonlocal anisotropic diffusion model with variable matrix-valued coefficients. In previous studies, the non-ordinary state-based nonlocal diffusion model <span><span>[37]</span></span> has been used effectively for simulating anisotropic diffusion. However, it encounters challenges such as high computational costs, complexities in implementing boundary conditions, and numerical oscillation of zero-energy mode. In this paper, we propose a novel bond-based, nonlocal anisotropic diffusion model, and the key idea is that incorporates a nonlocal operator via a kernel function, integrating matrix-valued diffusion coefficients. The influence region of our model consists of two parts: an elliptical region determined by the variable diffusion coefficient at a material point and an irregular region shaped by the coefficient at neighboring points. Furthermore, we confirm the well-posedness of the proposed model and deduce various properties, such as weak convergence and mass conservation. For computational implementation, we introduce a meshfree method that is shown to be asymptotically compatible and relies on the quadrature rule, which is compatible with the proposed nonlocal diffusion model and can effectively solve the model. To evaluate the precision and efficiency of the model, we performed comprehensive numerical experiments in both two and three dimensions. We have also confirmed the discrete maximum principle through experimental validation simultaneously.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"199 ","pages":"Pages 148-166"},"PeriodicalIF":2.5,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145109776","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

hp-version discontinuous Galerkin time-stepping schemes for diffusive-viscous wave equation 扩散-粘性波动方程的hp型间断Galerkin时步格式

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-22 DOI: 10.1016/j.camwa.2025.09.021

Min Zhang , Zhaonan Dong , Wenjing Yan

引用次数: 0

Hybrid active-passive control of multiphase composite shells through high-order Chebyshev frequency response modeling 基于高阶切比雪夫频率响应建模的多相复合材料壳体混合主动被动控制

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-22 DOI: 10.1016/j.camwa.2025.09.012

Duy-Khuong Ly , Huy-Cuong Vu-Do , Trung-Hau Dang , T. Nguyen-Thoi

{"title":"Hybrid active-passive control of multiphase composite shells through high-order Chebyshev frequency response modeling","authors":"Duy-Khuong Ly , Huy-Cuong Vu-Do , Trung-Hau Dang , T. Nguyen-Thoi","doi":"10.1016/j.camwa.2025.09.012","DOIUrl":"10.1016/j.camwa.2025.09.012","url":null,"abstract":"<div><div>This paper presents a high-efficiency approach for controlled frequency response analysis of laminated multi-phase composite shells, employing high-order Chebyshev finite elements. A key feature of the composite material used in this study is its three-phase composition, consisting of a polymer matrix, carbon fiber, and carbon nanotube nanofillers embedded within the matrix phase. The inclusion of carbon nanotube nanofillers significantly enhances the mechanical and dynamic properties of the overall material. The proposed approach addresses shear/membrane locking and the computational expense of discrete layerwise models, ensuring both efficiency and precision in analyzing complex composite shells. By using high-order shape functions derived from Chebyshev polynomials, this approach achieves rapid convergence without sacrificing accuracy. The developed numerical model captures the frequency response of laminated shells across varying geometric configurations, while incorporating the effects of two-layer control patches that introduce active or passive damping. Additionally, the model accounts for the layerwise effect of the composite, allowing for accurate prediction of structural behavior under excited loads. Numerical validation confirms the robustness and versatility of the high-order Chebyshev finite elements, effectively overcoming common computational challenges such as locking and spurious modes, while providing highly accurate and reliable frequency response predictions for practical engineering applications. This study highlights the potential of using advanced numerical techniques in combination with innovative composite materials for improved dynamic performance in aerospace, automotive, and civil engineering applications.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"199 ","pages":"Pages 184-202"},"PeriodicalIF":2.5,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145109778","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

Bound-preserving physics-informed neural networks for steady-state convection-diffusion-reaction problems 用于稳态对流扩散反应问题的保界物理信息神经网络

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-22 DOI: 10.1016/j.camwa.2025.09.009

Marina Matthaiou , Volker John , Marwa Zainelabdeen

{"title":"Bound-preserving physics-informed neural networks for steady-state convection-diffusion-reaction problems","authors":"Marina Matthaiou , Volker John , Marwa Zainelabdeen","doi":"10.1016/j.camwa.2025.09.009","DOIUrl":"10.1016/j.camwa.2025.09.009","url":null,"abstract":"<div><div>Numerical approximations of solutions of convection-diffusion-reaction problems should take only physically admissible values. Provided that bounds for the admissible values are known, this paper presents several approaches within physics-informed neural networks (PINNs) and <em>hp</em>-variational PINNs (<em>hp</em>-VPINNs) to preserve these bounds for convection-dominated problems. These approaches comprise the inclusion of the requirement for bound preservation in the cost functional, a simple cut-off strategy for the unphysical values, and two methods that enforce bound preservation via the activation function of the output layer of the neural network. Numerical simulations are performed for convection-dominated problems defined in two-dimensional domains. A variety of choices for several hyperparameters is explored. Enforcing bound preservation with the sine activation function in the output layer turned out to be superior to all other methods with respect to the accuracy of the computed solutions, and in particular, the results are much more accurate than those obtained with the standard PINNs and <em>hp</em>-VPINNs.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"199 ","pages":"Pages 167-183"},"PeriodicalIF":2.5,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145109777","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

Shape derivative of the Laplacian eigenvalue problem 拉普拉斯特征值问题的形状导数

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-19 DOI: 10.1016/j.camwa.2025.09.013

Zhengfang Zhang , Lulu Guo , Xiangjing Gao , Weifeng Chen , Xiaoliang Cheng

引用次数: 0

An averaged L1 ADI compact difference scheme for the three-dimensional time-fractional mobile/immobile transport equation with weakly singular solutions 具有弱奇异解的三维时间分数阶可动/不可动输运方程的平均L1 - ADI紧致差分格式

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-19 DOI: 10.1016/j.camwa.2025.09.019

Kai Liu, Haixiang Zhang, Xuehua Yang

引用次数: 0

Pricing American options with exogenous and endogenous transaction costs 考虑外生和内生交易成本的美式期权定价