Computers & Mathematics with Applications最新文献

英文中文

ITPINN : Integral-trainable physics informed neural network for solving high-dimensional evolution non-local partial differential equations 求解高维演化非局部偏微分方程的积分可训练物理通知神经网络

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-01 Epub Date: 2026-01-21 DOI: 10.1016/j.camwa.2026.01.019

Wenkai Liu , Fanhai Zeng , Hong Li , Yang Liu

In this paper, we develop a new physics informed neural network (PINN) method, named integral-trainable PINN (ITPINN), to solve high-dimensional non-local partial differential equations (PDEs), involving PDEs with fractional derivatives (Caputo derivative and Riemann-Liouville derivative) or multiple integral. In the ITPINN framework, we perform integration by parts on the original integral to obtain a new constraint condition, which forms a coupled system with the original equation. We consider the integral terms as unknown functions in the coupled system and construct a neural network with three output terms, one for predicting the exact solution, one for predicting the original integral term, and one for approximating the new integral obtained by integration by parts. The network is used as a surrogate model for fractional derivatives or multiple integral, which allows approximation of the fractional derivatives or multiple integral to be achieved by training the network. The proposed method omits the process of discretizing the integral term using traditional numerical methods, such as finite difference method or interpolation approximation. Moreover, the physical information obtained from integration by parts is used to construct a new supervised learning task to further constrain the surrogate model for the integral terms. Several experiments are used to illustrate the performance of the ITPINN. The numerical results confirm that our proposed method can effectively solve high-dimensional evolution non-local PDEs, such as 50D problems. Compared to fractional PINN (fPINN) and auxiliary PINN (A-PINN), the ITPINN can achieve higher prediction accuracy and save more training time. In particular, we also test the robustness of the ITPINN under interference with noise intensities ranging from 0.01% to 50% and further discuss its scalability in 100D and 1000D problems.

本文提出了一种新的物理通知神经网络（PINN）方法，称为积分可训练神经网络（ITPINN），用于求解含有分数阶导数（Caputo导数和Riemann-Liouville导数）或多重积分的高维非局部偏微分方程（PDEs）。在ITPINN框架中，我们对原积分进行分部积分，得到一个新的约束条件，与原方程形成一个耦合系统。我们将积分项视为耦合系统中的未知函数，并构造了一个具有三个输出项的神经网络，一个用于预测精确解，一个用于预测原始积分项，一个用于逼近由分部积分得到的新积分。该网络被用作分数阶导数或多重积分的代理模型，它允许通过训练网络来实现分数阶导数或多重积分的近似。该方法省去了用有限差分法或插值逼近等传统数值方法对积分项进行离散化的过程。此外，利用分部积分获得的物理信息构建新的监督学习任务，进一步约束积分项的代理模型。用几个实验说明了ITPINN的性能。数值结果表明，该方法可以有效地求解高维演化非局部偏微分方程，如50D问题。与分数PINN （fPINN）和辅助PINN （A-PINN）相比，ITPINN可以达到更高的预测精度，节省更多的训练时间。特别是，我们还测试了ITPINN在0.01%至50%噪声强度干扰下的鲁棒性，并进一步讨论了其在100D和1000D问题中的可扩展性。

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引用次数: 0

A discrete perfectly matched layer for peridynamic scalar waves in two-dimensional viscous media 二维粘性介质中周动力标量波的离散完美匹配层

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-01 Epub Date: 2025-12-29 DOI: 10.1016/j.camwa.2025.12.007

Yu Du , Yonglin Li , Jiwei Zhang

In this paper, we propose a discrete perfectly matched layer (PML) for the peridynamic scalar wave-type problems in viscous media. Constructing PMLs for nonlocal models is often challenging, mainly due to the fact that nonlocal operators are usually associated with various kernels. We first convert the continua model to a spatial semi-discretized version by adopting quadrature-based finite difference scheme, and then derive the PML equations from the semi-discretized equations using discrete analytic continuation. The harmonic exponential fundamental solutions (plane wave modes) of the semi-discretized equations are absorbed by the PML layer without reflection and are exponentially damped. The excellent efficiency and stability of discrete PML are demonstrated in numerical tests by comparison with exact absorbing boundary conditions.

本文提出了一种离散完美匹配层（PML），用于求解粘性介质中周期动力标量波型问题。为非局部模型构建pml通常具有挑战性，这主要是因为非局部操作符通常与各种核相关联。首先采用基于正交的有限差分格式将连续模型转换为空间半离散模型，然后利用离散解析延拓从半离散方程导出PML方程。半离散方程的谐波指数基解（平面波模式）被PML层不反射地吸收并呈指数阻尼。通过与精确吸收边界条件的比较，在数值试验中证明了离散PML具有良好的效率和稳定性。

引用次数: 0

Artificial Neural Network-Based Parameter Estimation in Lattice Boltzmann Simulations of MHD Nanofluid Natural Convection with Oscillating Wall Temperature 基于人工神经网络的MHD纳米流体自然对流振荡壁温晶格Boltzmann模拟参数估计

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-01 Epub Date: 2025-12-27 DOI: 10.1016/j.camwa.2025.12.020

C Venkata Lakshmi , Anuradha Aravapalli , K Venkatadri , Hakan F. Öztop

This study investigates magnetohydrodynamic natural convection of nanofluids in a square cavity subjected to sinusoidally varying thermal boundary conditions along the bottom wall. Understanding such flows is important for applications in thermal management, energy systems, and materials processing. The problem is solved using the lattice Boltzmann method coupled with an artificial neural network model to accelerate prediction of heat transfer responses. A comprehensive parametric analysis is performed for Rayleigh numbers up to

10^{6}

, Hartmann numbers up to 40, nanoparticle concentrations up to 4%, and a range of thermal wavelength parameters. The results show that the oscillatory thermal boundary significantly modifies flow structures and heat transfer characteristics: for example, at

R a = 10^{6}

and τ=0.5, the average Nusselt number is enhanced by nearly 28% compared with uniform heating, while strong magnetic damping (Ha=40) reduces it by about 35%. The neural network model reproduces LBM results with prediction errors below 2%, offering rapid estimation of Nusselt numbers across the studied parameter space. The novelty of this work lies in combining a high-fidelity lattice Boltzmann solver with data-driven prediction to study magnetically controlled nanofluid convection under oscillatory heating, an area not previously addressed in the literature. These findings provide new insights into the manipulation of convective transport in multiphysics thermal systems.

本文研究了沿底壁沿正弦变化的热边界条件下方形腔内纳米流体的磁流体力学自然对流。了解这种流动对于热管理、能源系统和材料加工的应用非常重要。采用晶格玻尔兹曼方法结合人工神经网络模型来加速传热响应的预测。一个全面的参数分析进行瑞利数高达106，哈特曼数高达40，纳米颗粒浓度高达4%，和热波长参数的范围。结果表明，振荡热边界显著改变了流动结构和换热特性：例如，在Ra=106和τ=0.5时，平均努塞尔数比均匀加热时提高了近28%，而强磁阻尼（Ha=40）使努塞尔数降低了约35%。神经网络模型以低于2%的预测误差再现LBM结果，在所研究的参数空间中提供对努塞尔数的快速估计。这项工作的新颖之处在于将高保真晶格玻尔兹曼解算器与数据驱动预测相结合，以研究振荡加热下的磁控纳米流体对流，这是以前文献中未涉及的领域。这些发现为多物理场热系统中对流输运的操纵提供了新的见解。

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引用次数: 0

Strong convergence analysis of time discretization for stochastic nonlinear diffusion-wave equations driven by fractional Brownian motion 分数阶布朗运动驱动随机非线性扩散波方程时间离散化的强收敛性分析

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-01 Epub Date: 2026-01-17 DOI: 10.1016/j.camwa.2026.01.011

Xing Liu , Yumeng Yang

This paper constructs a discretization for the stochastic nonlinear diffusion-wave equation involving the Caputo fractional derivative of order α ∈ (1, 2), driven by fractional Brownian motion with Hurst index 0 < H < 1. For time discretization, we propose a quadrature involving Mittag-Leffler functions

E_{β, η} (- t)

. The discretization method combines the integral representation of the solution, the approximation of Mittag-Leffler functions and numerical integration techniques. Two approximation methods for the Mittag-Leffler functions are developed to enhance computational efficiency. The mean square strong convergence order is established by utilizing the confirmed solution regularity. Numerical examples are presented to validate the theoretical results.

本文构造了包含阶α ∈ （1,2）的Caputo分数阶导数的随机非线性扩散波方程的离散化，该方程由Hurst指数为0 <； H <； 1的分数阶布朗运动驱动。对于时间离散，我们提出了一个涉及Mittag-Leffler函数Eβ，η(−t)的正交。离散化方法结合了解的积分表示、Mittag-Leffler函数的逼近和数值积分技术。为了提高计算效率，提出了两种逼近Mittag-Leffler函数的方法。利用确定的解正则性，建立了均方强收敛阶。数值算例验证了理论结果。

引用次数: 0

A novel evolutionary model using the Caputo time-fractional derivative and noise estimator for image denoising and contrast enhancement 一种基于卡普托时间分数阶导数和噪声估计的图像去噪和对比度增强的进化模型

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-02-15 Epub Date: 2026-01-24 DOI: 10.1016/j.camwa.2026.01.006

Anouar Ben-Loghfyry , Abderrahim Charkaoui , Anass Bouchriti , Nour Eddine Alaa

This paper proposes a novel fractional nonlinear parabolic model based on Caputo time-fractional derivative, designed to enhance the classical Perona-Malik model for image denoising and contrast improvement. A regularized diffusion mechanism is incorporated to control the diffusion rate and direction locally. The well-posedness of the model is analyzed, and two main existence results for weak solutions are established. The first, under a bounded reaction term, is proved using Schauder’s fixed-point theorem; the second, involving a nonlinear and weakly regular source term, ensures the existence of a weak SOLA solution via approximation techniques and new technical estimates. Numerical experiments on grayscale and MRI images validate the robustness and efficiency of the proposed model under various noise levels. The results show superior denoising and enhancement performance compared to state-of-the-art methods, preserving natural appearance and minimizing artifacts. This confirms the model’s potential for high-precision image restoration applications.

本文提出了一种基于Caputo时间-分数阶导数的分数阶非线性抛物模型，旨在对经典的Perona-Malik模型进行图像去噪和对比度改善。引入正则化扩散机制，局部控制扩散速率和扩散方向。分析了模型的适定性，建立了弱解的两个主要存在性结果。第一类，在有界反应项下，用Schauder不动点定理证明；第二，涉及一个非线性和弱正则源项，通过近似技术和新的技术估计确保弱SOLA解的存在。在灰度图像和MRI图像上的数值实验验证了该模型在不同噪声水平下的鲁棒性和有效性。结果显示，与最先进的方法相比，具有优越的去噪和增强性能，保留了自然外观并最大限度地减少了人工制品。这证实了该模型在高精度图像恢复应用中的潜力。

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引用次数: 0

A parameter-free approach for 3D staggered Lagrangian hydrodynamics 三维交错拉格朗日流体力学的无参数方法

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-02-15 Epub Date: 2026-01-20 DOI: 10.1016/j.camwa.2026.01.002

Xihua Xu , Xuan Zhou

In engineering applications, excessive artificial parameters can consume significant computational resources, particularly in 3D. This study presents a novel parameter-free approach for 3D staggered Lagrangian hydrodynamics that eliminates the need for artificial parameters and offers advantages over traditional methods. We construct a new form of artificial viscosity and give a new explanation for preventing the hourglass phenomenon. The proposed scheme ensures conservation of total mass, total momentum, and total energy through its unique formulation. Extensive testing has demonstrated the high robustness of this scheme, making it well-suited for multi-physics problems and various engineering applications.

在工程应用中，过多的人工参数会消耗大量的计算资源，特别是在3D中。该研究提出了一种新的三维交错拉格朗日流体动力学无参数方法，消除了对人工参数的需要，具有传统方法无法比拟的优点。我们构造了一种新的人工黏度形式，并对防止沙漏现象给出了新的解释。该方案通过其独特的公式保证了总质量、总动量和总能量的守恒。大量的测试证明了该方案的高鲁棒性，使其非常适合于多物理场问题和各种工程应用。

引用次数: 0

Macroscopic reconstruction of the lattice Boltzmann model for incompressible flows 不可压缩流晶格玻尔兹曼模型的宏观重建

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-02-15 Epub Date: 2025-12-16 DOI: 10.1016/j.camwa.2025.12.001

Jinhua Lu , Nikolaus A. Adams

The present work proposes a general framework that combines the good numerical stability of the lattice Boltzmann model for incompressible flows (LBM-IF) and the flexibility of finite difference/volume methods in using nonuniform meshes and removing higher-order deviation terms. By adopting the second-order non-equilibrium moment as fundamental variables and neglecting higher-order non-equilibrium moments, to approximately increase entropy in the collision process, the non-equilibrium-moment-based macroscopic equations of LBM-IF are derived. Numerical investigations demonstrate that discretized equations can achieve even better numerical stability than the single-relaxation-time LBM-IF. It is concluded that the good numerical stability of LBM-IF can be roughly interpreted as the entropy increase of the collision step and the diffusion process of the streaming step. However, the discretized non-equilibrium-moments-based macroscopic equations are found to have significant numerical errors at a fixed Reynolds number and very small kinematic viscosities. By combining the non-equilibrium-moments-based and equilibrium-moments-based macroscopic equations, the paper proposes a hybrid model that achieves good numerical stability and accuracy for both small and large kinematic viscosities, even for inviscid flow. The deviation term in the recovered momentum equation of LBM-IF can be easily removed in the hybrid model. Compared with LBM-IF, finite difference/volume solvers based on the hybrid model exhibit better numerical stability and accuracy, as well as superior efficiency in simulations using nonuniform meshes.

本文提出了一个综合了不可压缩流动的晶格玻尔兹曼模型（LBM-IF）良好的数值稳定性和有限差分/体积法在使用非均匀网格和去除高阶偏差项方面的灵活性的一般框架。采用二阶非平衡矩作为基本变量，忽略高阶非平衡矩，近似增加碰撞过程中的熵，推导了基于非平衡矩的LBM-IF宏观方程。数值研究表明，离散化方程比单松弛时间LBM-IF具有更好的数值稳定性。结果表明，LBM-IF良好的数值稳定性可以大致解释为碰撞步骤的熵增加和流步骤的扩散过程。然而，离散的基于非平衡矩的宏观方程在固定雷诺数和非常小的运动粘度下具有显著的数值误差。本文将基于非平衡矩和基于平衡矩的宏观方程结合起来，提出了一种混合模型，无论对大、小运动粘度，甚至对无粘流动，都具有良好的数值稳定性和精度。在混合模型中，可以很容易地去掉LBM-IF恢复动量方程中的偏差项。与LBM-IF相比，基于混合模型的有限差分/体积解具有更好的数值稳定性和精度，并且在非均匀网格下的模拟效率更高。

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引用次数: 0

An alternating approach for reconstructing the initial value and source term in a time-fractional diffusion-wave equation 一种交替重建时间分数扩散波方程初值和源项的方法

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-02-15 Epub Date: 2026-01-10 DOI: 10.1016/j.camwa.2026.01.004

Yun Zhang , Xiaoli Feng , Xiongbin Yan

This paper is dedicated to addressing the simultaneous inversion problem involving the initial value and space-dependent source term in a time-fractional diffusion-wave equation. Firstly, we establish the uniqueness of the inverse problem by leveraging the asymptotic expansion of Mittag-Leffler functions. Subsequently, we decompose the inverse problem into two subproblems and introduce an alternating iteration reconstruction method, complemented by a regularization strategy. Additionally, a comprehensive convergence analysis for this method is provided. To solve the inverse problem numerically, we introduce two semidiscrete schemes based on standard Galerkin method and lumped mass method, respectively. Furthermore, we establish error estimates that are associated with the noise level, iteration step, regularization parameter, and spatial discretization parameter. Finally, we present several numerical experiments in both one-dimensional and two-dimensional cases to validate the theoretical results and demonstrate the effectiveness of our proposed method.

研究了时间分数阶扩散波方程中包含初始值和空间相关源项的同时反演问题。首先，利用Mittag-Leffler函数的渐近展开式，建立了逆问题的唯一性。随后，我们将反问题分解为两个子问题，并引入交替迭代重建方法，并辅以正则化策略。并对该方法进行了全面的收敛性分析。为了在数值上解决反问题，我们分别引入了基于标准伽辽金法和集总质量法的两种半离散格式。此外，我们建立了与噪声水平、迭代步长、正则化参数和空间离散化参数相关的误差估计。最后，我们在一维和二维情况下进行了数值实验来验证理论结果并证明了我们所提出方法的有效性。

引用次数: 0

Hygro-thermo-mechanical-electro coupling inhomogeneous isogeometric analysis of functionally graded piezoelectric structures under hygrothermal environment 湿热环境下功能梯度压电结构的水热机电耦合非均匀等几何分析

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-02-15 Epub Date: 2025-12-22 DOI: 10.1016/j.camwa.2025.12.002

Zhong Zhang, Bo Cui, Pengxu Chen, Liming Zhou, Yue Wu

The functionally graded piezoelectric structure (FGPS) is one of the core structures for the design and development of new intelligent components, and has excellent piezoelectric effect and gradient distribution characteristics. Since FGPS has a complex structure and often operates in complex environments, it is essential to propose an efficient algorithm for solving the multi-physics coupling problem of FGPS. Based on the structural characteristics of FGPS, this study introduces NURBS basis functions, proposes hygro-thermo-mechanical-electro coupling inhomogeneous isogeometric analysis (HTMEI-IGA) combining the constitutive equations and boundary conditions of FGPS, and derives the control equations and motion equations of HTMEI-IGA. The free vibration, transient response and harmonic response of FGPS in the hygrothermal field are solved using the subspace iteration method and the Newmark method. The convergence and accuracy of HTMEI-IGA are verified through multiple numerical examples. The influence of exponential factors, moisture and thermal on the FGPS structure is also studied, providing a new means for design and development of FGPS.

功能梯度压电结构（FGPS）具有优异的压电效应和梯度分布特性，是设计和开发新型智能元件的核心结构之一。由于FGPS结构复杂，工作环境复杂，因此有必要提出一种有效的算法来解决FGPS的多物理场耦合问题。基于FGPS的结构特点，引入NURBS基函数，结合FGPS的本构方程和边界条件，提出了湿热机电耦合非齐次等几何分析（HTMEI-IGA），推导了HTMEI-IGA的控制方程和运动方程。采用子空间迭代法和Newmark法求解了FGPS在湿热场中的自由振动、瞬态响应和谐波响应。通过多个数值算例验证了HTMEI-IGA算法的收敛性和精度。研究了指数因子、水分和热量对FGPS结构的影响，为FGPS的设计和开发提供了新的手段。

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引用次数: 0

Nonconforming finite element method and reduced order algorithm for poroelasticity problem 孔隙弹性问题的非协调有限元法及降阶算法

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-02-15 Epub Date: 2026-01-01 DOI: 10.1016/j.camwa.2025.12.022

Xue Wang , Hongxing Rui , Xiaozhe Hu

In this work, we develop a nonconforming finite element method for the three-field Biot model, where the variables are displacement, Darcy velocity, and pore pressure. The discretization employs the lowest-order Crouzeix-Raviart (CR) element for both displacement and Darcy velocity, and piecewise constant element for pressure. We establish the well-posedness of the discrete problem with respect to a carefully chosen weighted norm, ensuring robustness with respect to both discretization and physical parameters. Furthermore, we prove optimal convergence of the proposed scheme. To improve computational efficiency, we introduce a reduced-order CR method based on the proper orthogonal decomposition (POD) technique. Numerical experiments are provided to verify the theoretical convergence rates and to demonstrate the effectiveness of the reduced-order approach.

在这项工作中，我们为三场Biot模型开发了一种非一致性有限元方法，其中变量是位移，达西速度和孔隙压力。对位移和达西速度均采用最低阶Crouzeix-Raviart （CR）元，对压力采用分段常数元。我们建立了关于一个精心选择的加权范数的离散问题的适定性，确保了关于离散化和物理参数的鲁棒性。进一步证明了该方案的最优收敛性。为了提高计算效率，我们引入了一种基于正交分解（POD）技术的降阶CR方法。数值实验验证了理论收敛速度和降阶方法的有效性。

引用次数: 0

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