Computers & Mathematics with Applications最新文献_第7页

MFPC-PIML: Physics-informed machine learning based on multiscale Fourier feature phase compensation MFPC-PIML：基于多尺度傅立叶特征相位补偿的物理信息机器学习

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-03 DOI: 10.1016/j.camwa.2025.03.026

Naixing Feng , Shuiqing Zeng , Xianpeng Wang , Jinfeng Zhu , Atef Z. Elsherbeni

{"title":"MFPC-PIML: Physics-informed machine learning based on multiscale Fourier feature phase compensation","authors":"Naixing Feng , Shuiqing Zeng , Xianpeng Wang , Jinfeng Zhu , Atef Z. Elsherbeni","doi":"10.1016/j.camwa.2025.03.026","DOIUrl":"10.1016/j.camwa.2025.03.026","url":null,"abstract":"<div><div>The paradigm of physics-driven forward electromagnetic computation holds significance for enhancing the accuracy of network approximations while reducing the dependence on large-scale datasets. However, challenges arise during the training process when dealing with objective functions characterized by high-frequency and multi-scale features. These challenges frequently occur as difficulties in effectively minimizing loss or encountering conflicts among competing objectives. To overcome these obstacles, we carried out analysis leveraging the Neural Tangent Kernel (NTK) as our theoretical framework for analysis. Through this, we propose a novel architectural solution: a Multi-scale Fourier Feature Phase Compensation (MFPC) technology, according to Gaussian kernel mapping. This architecture leverages a Gaussian kernel to enhance the spectral representation of coordinate data, expanding the frequency domain coverage of Fourier feature mapping. Additionally, by compensating for phase loss inherent in conventional Fourier mapping, our approach effectively mitigates training difficulties, accelerates convergence, and significantly improves the model's accuracy in capturing high-frequency components. Our research comprises a range of challenging examples, including the high-frequency Poisson equation and the isotropic layered medium scattering model. Through these examples, we demonstrate the proficiency of our proposed method in accurately solving high-frequency, multi-scale Partial Differential Equation (PDE) equations. This highlights its potential not only in forward modeling but also in solving evolution and inverse problems.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 166-180"},"PeriodicalIF":2.9,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759532","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

Improved accuracy of an analytical approximation for option pricing under stochastic volatility models using deep learning techniques 利用深度学习技术提高随机波动率模型下期权定价分析近似的准确性

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-02 DOI: 10.1016/j.camwa.2025.03.029

Donghyun Kim , Jeonggyu Huh , Ji-Hun Yoon

{"title":"Improved accuracy of an analytical approximation for option pricing under stochastic volatility models using deep learning techniques","authors":"Donghyun Kim , Jeonggyu Huh , Ji-Hun Yoon","doi":"10.1016/j.camwa.2025.03.029","DOIUrl":"10.1016/j.camwa.2025.03.029","url":null,"abstract":"<div><div>This paper addresses the challenge of pricing options under stochastic volatility (SV) models, where explicit formulae are often unavailable and parameter estimation requires extensive numerical simulations. Traditional approaches typically either rely on large volumes of historical (option) data (data-driven methods) or generate synthetic prices across wide parameter grids (model-driven methods). In both cases, the scale of data demands can be prohibitively high. We propose an alternative strategy that trains a neural network on the <em>residuals</em> between a fast but approximate pricing formula and numerically generated option prices, rather than learning the full pricing function directly. Focusing on these smaller, smoother residuals notably reduces the complexity of the learning task and lowers data requirements. We further demonstrate theoretically that the Rademacher complexity of the residual function class is significantly smaller, thereby improving generalization with fewer samples. Numerical experiments on fast mean-reverting SV models show that our residual-learning framework achieves accuracy comparable to baseline networks but uses only about one-tenth the training data. These findings highlight the potential of residual-based neural approaches to deliver efficient, accurate pricing and facilitate practical calibration of advanced SV models.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 150-165"},"PeriodicalIF":2.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143748609","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

Aubin–Nitsche-type estimates for space-time FOSLS for parabolic PDEs 抛物型偏微分方程时空FOSLS的aubin - nitsche型估计

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-01 DOI: 10.1016/j.camwa.2025.03.017

Thomas Führer , Gregor Gantner

引用次数: 0

Convergence analysis of variable-time-step BDF2/spectral approximations for optimal control problems governed by linear reaction-diffusion equations 线性反应扩散方程最优控制问题变时间步长BDF2/谱逼近的收敛性分析

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-01 DOI: 10.1016/j.camwa.2025.03.023

Tong Lyu, Xingyang Ye, Xiaoyue Liu

{"title":"Convergence analysis of variable-time-step BDF2/spectral approximations for optimal control problems governed by linear reaction-diffusion equations","authors":"Tong Lyu, Xingyang Ye, Xiaoyue Liu","doi":"10.1016/j.camwa.2025.03.023","DOIUrl":"10.1016/j.camwa.2025.03.023","url":null,"abstract":"<div><div>In this paper, we focus on the optimal control problem governed by a linear reaction-diffusion equation with constraints on the control variable. We construct an effective fully-discrete scheme to solve this problem by using the variable-time-step two-step backward differentiation formula (VSBDF2) in time combining with the Galerkin spectral methods in space. By using the recently developed techniques including the discrete orthogonal convolution (DOC) kernels, and the positive definiteness of BDF2 convolution kernels, we obtain an error estimate of order <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>−</mo><mi>p</mi></mrow></msup><mo>)</mo></math></span> under a mild restriction <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4.8645</mn></mrow></mfrac><mo>≤</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>≤</mo><mn>4.8645</mn></math></span> for the ratio of adjacent time steps <span><math><msub><mrow><mi>r</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span>, where <span><math><mi>τ</mi><mo>,</mo><mi>N</mi><mo>,</mo><mi>p</mi></math></span> are the maximum time step size, polynomial degree, and regularity of the exact solution respectively. Several numerical examples are provided to validate the theoretical results and to demonstrate the efficiency of the proposed method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"189 ","pages":"Pages 48-69"},"PeriodicalIF":2.9,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738387","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

Numerical simulation of pollutant concentration patterns of a two-dimensional congestion traffic 二维拥堵交通中污染物浓度模式的数值模拟

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-01 DOI: 10.1016/j.camwa.2025.03.020

Anis Chaari , Waleed Mouhali , Mohammed Louaked , Nacer Sellila , Houari Mechkour

{"title":"Numerical simulation of pollutant concentration patterns of a two-dimensional congestion traffic","authors":"Anis Chaari , Waleed Mouhali , Mohammed Louaked , Nacer Sellila , Houari Mechkour","doi":"10.1016/j.camwa.2025.03.020","DOIUrl":"10.1016/j.camwa.2025.03.020","url":null,"abstract":"<div><div>An accurate calculation of the traffic density is a key factor in understanding the formation and evolution of the traffic-related emission concentration in urban areas. We have developed a two-dimensional numerical model to solve traffic flow/pollution coupled problem whose pollution source is generated by the density of vehicles. The numerical solution of this problem is calculated via an algorithm that combines the Characteristic method for temporal discretization with the Lagrange-Galerkin finite element method for spatial discretization. This algorithm is validated by varying certain physical parameters of the model (effective viscosity). We study the pollutant concentration diffusion impacted by the presence of an obstacle in a bifurcation topology traffic. We draw attention to the influence of the wind velocity as well as its direction on the pollutant concentration diffusion, in several situations. The temporal evolution of pollutant concentration at various relevant locations in the domain (before and after an obstacle) is studied for a single velocity and two wind directions. Different regimes have been observed for transport pollution depending on time and the wind direction.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"188 ","pages":"Pages 97-114"},"PeriodicalIF":2.9,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738705","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 kind of fast successive permutation iterative algorithms with the relaxation factor for nonlinear radiation diffusion problem 非线性辐射扩散问题的一种带松弛因子的快速连续置换迭代算法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-31 DOI: 10.1016/j.camwa.2025.03.033

Qiuyan Xu, Zhiyong Liu

引用次数: 0

Phase-field computation for 3D shell reconstruction with an energy-stable and uniquely solvable BDF2 method 基于能量稳定且唯一可解BDF2方法的三维壳重建相场计算

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-31 DOI: 10.1016/j.camwa.2025.03.022

Dongting Cai, Boyi Fu, Renjun Gao, Xiangjie Kong, Junxiang Yang

{"title":"Phase-field computation for 3D shell reconstruction with an energy-stable and uniquely solvable BDF2 method","authors":"Dongting Cai, Boyi Fu, Renjun Gao, Xiangjie Kong, Junxiang Yang","doi":"10.1016/j.camwa.2025.03.022","DOIUrl":"10.1016/j.camwa.2025.03.022","url":null,"abstract":"<div><div>Three-dimensional (3D) reconstruction from points cloud is an important technique in computer vision and manufacturing industry. The 3D volume consists of a set of voxels which preserves the characteristics of scattered points. In this paper, a 3D shell (narrow volume) reconstruction algorithm based on the Allen–Cahn (AC) phase field model is proposed, aiming to efficiently and accurately generate 3D reconstruction models from point cloud data. The algorithm uses a linearized backward differentiation formula (BDF2) for time advancement and adopts the finite difference method to perform spatial discretization, unconditional energy stability and second-order time accuracy can be achieved. The present method is not only suitable for 3D reconstruction of unordered data but also has the effect of adaptive denoising and surface smoothing. In addition, theoretical derivation proves the fully discrete energy stability. In numerical experiments, the complex geometric models, such as Asian dragon, owl, and turtle, will be reconstructed to validate the energy stability. The temporal accuracy is validated by the numerical reconstructions of a Costa surface and an Amremo statue. Later, we reconstruct the Stanford dragon, teapot, and Thai statue to further investigate the capability of the proposed method. Finally, we implement a comparison study using a 3D happy Buddha. The numerical results show that the algorithm still has good numerical stability and reconstruction accuracy at large time steps, and can significantly preserve the detailed structure of the model. This research provides an innovative solution and theoretical support for scientific computing and engineering applications in the field of 3D reconstruction.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"189 ","pages":"Pages 1-23"},"PeriodicalIF":2.9,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738385","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 new error analysis of a linearized BDF2 Galerkin scheme for Schrödinger equation with cubic nonlinearity 具有三次非线性的Schrödinger方程线性化BDF2 Galerkin格式的新误差分析

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-31 DOI: 10.1016/j.camwa.2025.03.025

Huaijun Yang

引用次数: 0

Decoupled algorithms and analyses for an advection-reaction-diffusion model with stocking and harvesting 具有放养和收获的平流-反应-扩散模型的解耦算法与分析

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-31 DOI: 10.1016/j.camwa.2025.03.024

Mayesha Sharmim Tisha , Md. Kamrujjaman , Muhammad Mohebujjaman , Taufiquar Khan

{"title":"Decoupled algorithms and analyses for an advection-reaction-diffusion model with stocking and harvesting","authors":"Mayesha Sharmim Tisha , Md. Kamrujjaman , Muhammad Mohebujjaman , Taufiquar Khan","doi":"10.1016/j.camwa.2025.03.024","DOIUrl":"10.1016/j.camwa.2025.03.024","url":null,"abstract":"<div><div>We propose a time-dependent Advection Reaction Diffusion (ARD) <em>N</em>-species competition model to investigate the Stocking and Harvesting (SH) effect on population dynamics. For ongoing analysis, we explore the outcomes of a single species and competition between two competing species in a heterogeneous environment under no-flux boundary conditions, meaning no individual can cross the boundaries. We establish results concerning the existence, uniqueness, and positivity of the solutions. As a continuation, we propose, analyze, and test two novel fully discrete decoupled linearized algorithms for a nonlinearly coupled ARD <em>N</em>-species competition model with SH effort. The time-stepping algorithms are first and second order accurate in time and optimally accurate in space. Stability and optimal convergence theorems of the decoupled schemes are proved rigorously. We verify the predicted convergence rates of our analysis and the efficacy of the algorithms using numerical experiments and synthetic data for analytical test problems. We also study the effect of harvesting or stocking and diffusion parameters on the evolution of species population density numerically and observe the coexistence scenario subject to optimal stocking or harvesting.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"189 ","pages":"Pages 24-47"},"PeriodicalIF":2.9,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738386","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 semi-implicit second-order temporal scheme for solving the pressure head-based form of Richards' and advection-dispersion equations 求解基于压头形式的理查兹方程和平流色散方程的半隐式二阶时间格式

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-31 DOI: 10.1016/j.camwa.2025.03.011

Nour-Eddine Toutlini , Abdelaziz Beljadid , Azzeddine Soulaïmani

{"title":"A semi-implicit second-order temporal scheme for solving the pressure head-based form of Richards' and advection-dispersion equations","authors":"Nour-Eddine Toutlini , Abdelaziz Beljadid , Azzeddine Soulaïmani","doi":"10.1016/j.camwa.2025.03.011","DOIUrl":"10.1016/j.camwa.2025.03.011","url":null,"abstract":"<div><div>In this study, a semi-implicit finite element method is proposed to solve the coupled system of infiltration and solute transport in porous media. The Richards equation is used to describe unsaturated flow, while the advection-dispersion equation (ADE) is used for modeling solute transport. The proposed approach is applied to linearize the system in time, avoiding iterative processes. A free parameter is introduced to ensure the stability of the scheme. Numerical tests are conducted to analyze the accuracy of the proposed method in comparison with three second-order iterative schemes. The proposed scheme based on the optimal free parameter is accurate and efficient since it offers a considerable gain in computational time compared to the other methods. For reliability and effectiveness evaluation of the developed semi-implicit scheme, four showcase scenarios are used. The first two numerical tests focus on modeling water flow in heterogeneous medium and transient flow in variably saturated zones. The last numerical tests are carried out to simulate the salt and nitrate transport through unsaturated porous media. The simulation results are compared with reference solutions and laboratory data, and demonstrate the effectiveness of the proposed scheme in simulating infiltration and solute transport in porous media.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 106-131"},"PeriodicalIF":2.9,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739687","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