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

Uncertainty analysis framework of MPS and implementation in the simulation of MCCI phenomenon MPS的不确定性分析框架及其在MCCI现象模拟中的实现

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-28 DOI: 10.1016/j.camwa.2026.01.031

Xinkun Xiao , Qinghang Cai , Tianrui Li , Ronghua Chen , Guanghui Su

This study establishes the Moving Particle Semi-implicit Plus Uncertainty (MPSPU) framework to enable rigorous uncertainty quantification (UQ) for particle-based simulations in nuclear reactor safety analysis. Designed to extend the Best Estimate Plus Uncertainty (BEPU) methodology, MPSPU addresses the specific challenges of Lagrangian particle methods while maintaining compatibility with existing regulatory assessment protocols. The framework is validated using the SURC-4 experiment, which simulates the Molten Core–Concrete Interaction (MCCI) phenomenon. A critical advancement is the formulation of a time-dependent sensitivity analysis, which reveals that melt temperature is the dominant driver governing early-stage MCCI behavior. Furthermore, a comparative evaluation of surrogate models for MPS time-series data identifies Long Short-Term Memory (LSTM) networks as the optimal architecture, outperforming conventional polynomial and neural network approaches. To demonstrate the framework's practical utility, an end-to-end calculation example is presented, illustrating the complete workflow from raw simulation data to regulatory-grade risk metrics. This example explicitly quantifies the conditional failure probability of concrete ablation depth against safety limits, showcasing the framework's ability to support risk-informed decision-making. Ultimately, this work provides a systematic pathway for integrating particle methods into safety analysis.

本研究建立了移动粒子半隐式加不确定性（MPSPU）框架，为核反应堆安全分析中基于粒子的模拟提供严格的不确定性量化（UQ）。MPSPU旨在扩展最佳估计加不确定性（BEPU）方法，解决拉格朗日粒子方法的特定挑战，同时保持与现有监管评估协议的兼容性。使用SURC-4实验对该框架进行了验证，该实验模拟了熔融核-混凝土相互作用（MCCI）现象。一个关键的进步是制定了一个时间依赖的敏感性分析，这表明熔体温度是控制早期MCCI行为的主要驱动因素。此外，对MPS时间序列数据的替代模型进行了比较评估，发现长短期记忆（LSTM）网络是最优架构，优于传统的多项式和神经网络方法。为了展示该框架的实用性，本文给出了一个端到端计算示例，说明了从原始模拟数据到监管级风险指标的完整工作流程。这个例子明确地量化了混凝土消融深度相对于安全限制的条件失效概率，展示了框架支持风险知情决策的能力。最终，这项工作为将粒子方法整合到安全分析中提供了一个系统的途径。

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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 : 2026-01-24 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

Error estimates of the weak Galerkin mixed finite element method for parabolic interface problems 抛物界面问题的弱Galerkin混合有限元法误差估计

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-24 DOI: 10.1016/j.camwa.2026.01.024

Amit Kumar Pal , Jhuma Sen Gupta , Rajen Kumar Sinha

This paper aims to study a priori error analysis of the weak Galerkin mixed finite element method (WG-MFEM) for parabolic interface problems in a two-dimensional bounded convex polygonal domain. While discontinuous functions are employed for the approximation of spatial variable, an implicit backward Euler scheme is used for the time variable. Due to the presence of the discontinuous coefficient across the interface, the solution of parabolic interface problems possesses very low global regularity. Using the Stein extension operator and the H¹(div)-extension operator leads to the novel approximation results for the L² projection operators for both the scalar and the vector-valued functions, respectively. With the help of mixed elliptic projection operator and the new approximation properties combined with the standard energy argument, an almost optimal order a priori error bounds are derived for both the solution and the flux variables in the L^∞(L²) norm. Numerical outcomes for some test problems are reported to confirm the theoretical analysis.

本文研究了二维有界凸多边形区域中抛物界面问题的弱Galerkin混合有限元法的先验误差分析。空间变量采用不连续函数逼近，时间变量采用隐式后向欧拉格式逼近。由于界面上存在不连续系数，抛物型界面问题的解具有很低的全局正则性。使用Stein扩展算子和H1(div)-扩展算子分别可以得到标量函数和向量值函数的L2投影算子的新的近似结果。利用混合椭圆投影算子和新的近似性质，结合标准能量参数，导出了L∞(L2)范数上的解和通量变量的几乎最优阶先验误差界。文中还报道了一些试验问题的数值结果，以证实理论分析。

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引用次数: 0

Least-squares enhanced physics-informed learning for singular and ill-posed partial differential equations 最小二乘增强了奇异和不适定偏微分方程的物理知识学习

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-23 DOI: 10.1016/j.camwa.2026.01.027

Eunjung Lee

Partial differential equations that exhibit reduced regularity due to geometric singularities or possess nontrivial null space components arising from intrinsic properties of the differential operator pose serious challenges for both conventional numerical methods and standard physics-informed neural networks (PINNs). Least-squares finite element methods (LSFEM) have long provided robust tools for addressing such issues through weighted norm formulations and null-space projection techniques. In this work, we propose a hybrid PINN framework that systematically incorporates key elements of LSFEM to overcome limitations of existing PINNs. By embedding weighted least-squares functionals or projection mechanisms into the PINN architecture, the proposed method effectively handles singularities and ill-posedness within a deep learning paradigm. This approach enhances solution stability, avoids pollution from singular modes, and improves accuracy in problems where standard PINNs struggle.

偏微分方程由于几何奇异性而表现出降低的规律性，或者由于微分算子的固有性质而具有非平凡的零空间分量，这对传统的数值方法和标准的物理信息神经网络（pinn）都提出了严峻的挑战。长期以来，最小二乘有限元方法（LSFEM）通过加权范数公式和零空间投影技术为解决此类问题提供了强大的工具。在这项工作中，我们提出了一个混合PINN框架，该框架系统地结合了LSFEM的关键元素，以克服现有PINN的局限性。通过将加权最小二乘函数或投影机制嵌入到PINN架构中，该方法有效地处理了深度学习范式中的奇异性和病态性。这种方法提高了解的稳定性，避免了奇异模式的污染，并提高了标准pin难以解决的问题的准确性。

引用次数: 0

EM propagation analysis of multilayered fully anisotropic media with an efficacious model equivalent approach 基于有效模型等效方法的多层全各向异性介质电磁传播分析

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-23 DOI: 10.1016/j.camwa.2026.01.022

Huan Wang , Naixing Feng , Chong-Zhi Han , Jinfeng Zhu , Lixia Yang , Atef Z. Elsherbeni

In this paper, the model equivalent approach is developed for full-wave analysis of electromagnetic propagation in multilayered fully anisotropic lossy media. In the process of geometric simulation, the 3D planar layered model is projected onto an axial stratified structure, effectively reducing spatial complexity. Then, the mesh free scheme is adopted for discretization, thus significantly decreasing the resource consumption. To accommodate generalized electromagnetic media, the governing equation for the electric field is formulated based on fully anisotropic media, characterized by full tensor parameters. The Galerkin method is employed to generate weak form partial differential equations (PDEs), then, the FEM is adopted to address the equations. To ensure accuracy in the FEM implementation, the divergence condition is imposed as a constraint on the PDEs, effectively eliminating spurious solutions from the computational domain. Finally, three numerical examples are presented to verify the effectiveness of the proposed method.

本文建立了多层全各向异性有耗介质中电磁传播全波分析的模型等效方法。在几何模拟过程中，将三维平面分层模型投影到轴向分层结构上，有效降低了空间复杂度。然后，采用无网格格式进行离散化，从而大大降低了资源消耗。为了适应广义电磁介质，在全各向异性介质的基础上建立了以全张量参数为特征的电场控制方程。采用伽辽金法生成弱形式偏微分方程，然后采用有限元法求解。为了保证有限元实现的准确性，对偏微分方程施加了发散条件作为约束，有效地消除了计算域中的伪解。最后给出了三个数值算例，验证了所提方法的有效性。

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引用次数: 0

Peristaltic transport of non-Newtonian hybrid nanofluid flow through an inclined porous tube under a magnetic field and thermal radiation in a fuzzy environment 模糊环境下磁场和热辐射作用下非牛顿混合纳米流体流过倾斜多孔管的蠕动输运

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-21 DOI: 10.1016/j.camwa.2026.01.020

Bivas Bhaumik , Soumini Dolui , Mrutyunjaya Sahoo , Snehashish Chakraverty , Soumen De

In advanced studies of bionanoscience, magnetic nanomaterials serve as therapeutic transporters for treating vascular disorders, such as carotid and peripheral artery diseases, along with other biomedical applications. This study explores the theoretical behavior of hybrid nanoparticles (Cu-Fe₂O₃) in two-dimensional peristaltic blood flow through an inclined, catheterized artery, accounting for outer wall slip in an uncertain environment. The non-Newtonian Jeffrey nanofluid model is employed, incorporating nonlinear thermal radiation and an externally induced magnetic field to capture novel aspects of nanofluid behavior. However, uncertainty in velocity and temperature patterns may arise due to variations in nanoparticle volume fraction, which cannot be ignored. To address this, these distributions are analyzed within a fuzzy framework, treating them as triangular fuzzy numbers (TFNs). Within this framework, the dimensionless nonlinear flow equations are converted into fuzzy differential equations by introducing symmetrical TFNs, where the nanoparticle volume fractions serve as fuzzy parameters. The Homotopy Perturbation Method (HPM) is then applied to derive fuzzy semi analytical solutions for temperature and velocity profiles using a double parametric approach for fuzzy numbers. Additionally, a comprehensive graphical analysis is presented, incorporating triangular fuzzy representations in both two-dimensional (2D) and three-dimensional (3D) frameworks for the fuzzy solutions of temperature and velocity profiles. The obtained fuzzy solutions are validated by comparing a special case of the present solution with existing precise solutions. An in-depth analysis of key flow characteristics such as wall shear stress, the Nusselt number, and the skin friction coefficient is conducted for the special case under various emerging parameters. It is observed that as the Darcy parameter increases, both the upper and lower bounds of fuzzy velocity improve. Meanwhile, an increase in the thermal radiation parameter leads to a significant drop in the fuzzy temperature profile due to enhanced heat dissipation through radiation.

在生物纳米科学的高级研究中，磁性纳米材料作为治疗性转运体用于治疗血管疾病，如颈动脉和外周动脉疾病，以及其他生物医学应用。本研究探讨了混合纳米粒子（Cu-Fe2O3）在二维蠕动血液流过倾斜导管动脉时的理论行为，考虑了不确定环境下外壁滑移的影响。采用非牛顿杰弗里纳米流体模型，结合非线性热辐射和外部感应磁场来捕捉纳米流体行为的新方面。然而，由于纳米颗粒体积分数的变化，速度和温度模式的不确定性可能会产生，这是不可忽视的。为了解决这个问题，在模糊框架内分析这些分布，将它们视为三角模糊数（tfn）。在此框架内，通过引入对称tfn将无量纲非线性流动方程转换为模糊微分方程，其中纳米颗粒体积分数作为模糊参数。然后应用同伦摄动法（HPM）对模糊数采用双参数方法推导温度和速度曲线的模糊半解析解。此外，还提出了一个全面的图形分析，在二维（2D）和三维（3D）框架中结合三角形模糊表示来获得温度和速度剖面的模糊解。通过与已有精确解的比较，验证了所得到的模糊解的正确性。针对各种新出现参数下的特殊情况，深入分析了壁面剪应力、努塞尔数、表面摩擦系数等关键流动特性。观察到，随着Darcy参数的增大，模糊速度的上界和下界都增大。同时，随着热辐射参数的增大，由于辐射散热增强，模糊温度廓线明显下降。

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引用次数: 0

A geometry aware arbitrary order collocation boundary element method solver for the potential flow past three dimensional lifting surfaces 三维升力面势流的几何感知任意阶配置边界元法求解

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-21 DOI: 10.1016/j.camwa.2026.01.021

Luca Cattarossi , Filippo Guido Davide Sacco , Nicola Giuliani , Nicola Parolini , Andrea Mola

This work presents a numerical model for the simulation of potential flow past three dimensional lifting surfaces. The solver is based on the collocation Boundary Element Method, combined with Galerkin variational formulation of the nonlinear Kutta condition imposed at the trailing edge. A similar Galerkin variational formulation is also used for the computation of the fluid velocity at the wake collocation points, required by the relaxation algorithm which aligns the wake with the local flow. The use of such a technique, typically associated with the Finite Element Method, allows in fact for the evaluation of the solution derivatives in a way that is independent of the local grid topology. As a result of this choice, combined with the direct interface with CAD surfaces, the solver is able to use arbitrary order Lagrangian elements on automatically refined grids. Numerical results on a rectangular wing with NACA 0012 airfoil sections are presented to compare the accuracy improvements obtained refining the grid or increasing the polynomial degree. Finally, numerical results on rectangular and swept wings with NACA 0012 airfoil section confirm that the model is able to reproduce experimental data with good accuracy.

本文提出了一个三维升力面势流的数值模拟模型。求解方法基于配置边界元法，结合后缘非线性库塔条件的伽辽金变分公式。类似的伽辽金变分公式也用于计算尾迹配点处的流体速度，这是使尾迹与局部流动对齐的松弛算法所要求的。这种技术的使用，通常与有限元法相关联，实际上允许以一种独立于局部网格拓扑结构的方式评估解的导数。由于这种选择，结合与CAD曲面的直接接口，求解器能够在自动细化的网格上使用任意阶的拉格朗日元素。给出了NACA 0012翼型截面矩形机翼的数值计算结果，比较了细化网格和增加多项式度所获得的精度改进。最后，对NACA 0012翼型截面矩形翼和后掠翼的数值计算结果证实了该模型能够较好地再现实验数据。

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引用次数: 0

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 : 2026-01-21 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 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 : 2026-01-20 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

MS-PINN: A physics-informed neural network for multi-field coupled evolution modeling in metal solidification MS-PINN：用于金属凝固多场耦合演化建模的物理信息神经网络

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-20 DOI: 10.1016/j.camwa.2026.01.015

Chen Bai , Yunhu Zhang , Hongxing Zheng , Quan Qian

Simulating the metal solidification process is crucial for improving product quality, optimizing manufacturing processes, and developing new materials. Traditional numerical methods like the Finite Element Method (FEM) and Physics-Informed Neural Networks (PINNs) face significant challenges when applied to metal solidification simulations due to inefficiencies and inaccuracies in dealing with multiphysics coupling, nonlinearity, and spatio-temporal complexity. Despite their potential, PINNs require further optimization to accurately capture complex physical phenomena in practical simulations. In this study, we propose a novel method based on PINNs, termed MS-PINN, which integrates Fourier Feature Embedding (FFE), Residual-based Adaptive Resampling (RAD), and Self-adaptive Loss Balanced methods (SAL) to significantly enhance simulation accuracy and efficiency. FFE improves the model’s ability to capture high-frequency features, RAD increases learning efficiency in high-gradient regions, and SAL dynamically adjusts loss function weights to optimize the training process. Experimental results show that MS-PINN outperforms traditional PINNs and other advanced approaches, achieving average error reductions of approximately 81.00% compared to Conv-LSTM, 77.11% compared to TCN, and 61.56% compared to PINN in reconstruction experiments. In predictive experiments, MS-PINN reduces errors by 53.23%, 68.81%, and 72.54% compared to PINN, TCN, and CONV-LSTM methods, respectively. Additionally, we developed a general PDE-solving software, NeuroPDE, based on this method. NeuroPDE has demonstrated success not only in the solidification process of Cu-1wt.%Ag alloy but also in solving Burgers, diffusion, and Navier-Stokes (NS) equations, including turbulent datasets characterized by high Reynolds numbers, and their inverse problems. This highlights NeuroPDE’s versatility and broad applicability in solving complex forward and inverse problems in fluid dynamics and other fields.

模拟金属凝固过程对于提高产品质量、优化制造工艺和开发新材料至关重要。传统的数值方法，如有限元法（FEM）和物理信息神经网络（pinn），由于在处理多物理场耦合、非线性和时空复杂性方面的低效率和不准确性，在应用于金属凝固模拟时面临着重大挑战。尽管具有潜力，但在实际模拟中需要进一步优化才能准确捕获复杂的物理现象。在这项研究中，我们提出了一种基于pinn的新方法，称为MS-PINN，它集成了傅里叶特征嵌入（FFE），基于残差的自适应重采样（RAD）和自适应损失平衡方法（SAL），以显着提高仿真精度和效率。FFE提高了模型捕获高频特征的能力，RAD提高了高梯度区域的学习效率，SAL动态调整损失函数权值以优化训练过程。实验结果表明，MS-PINN优于传统的PINN和其他先进的方法，在重建实验中，与convl - lstm相比，MS-PINN的平均误差降低约81.00%，与TCN相比，MS-PINN的平均误差降低约77.11%，与PINN相比，MS-PINN的平均误差降低约61.56%。在预测实验中，MS-PINN比PINN、TCN和convl - lstm方法分别降低了53.23%、68.81%和72.54%的误差。此外，我们还基于该方法开发了通用的pde求解软件NeuroPDE。NeuroPDE不仅在Cu-1wt的凝固过程中取得了成功。%Ag合金，但也在解决汉堡，扩散，和Navier-Stokes （NS）方程，包括湍流数据集特征的高雷诺数，和他们的反问题。这突出了NeuroPDE在解决流体动力学和其他领域复杂的正反问题方面的多功能性和广泛适用性。

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引用次数: 0