Journal of Computational Physics最新文献_第8页

iPINNER: An iterative physics-informed neural network with ensemble Kalman filter 基于集成卡尔曼滤波的迭代物理信息神经网络

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2025-12-13 DOI: 10.1016/j.jcp.2025.114592

Binghang Lu , Changhong Mou , Guang Lin

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving forward and inverse problems involving partial differential equations (PDEs) by incorporating physical laws into the training process. However, the performance of PINNs is often hindered in real-world scenarios involving noisy observational data and missing physics, particularly in inverse problems. In this work, we propose an iterative multi-objective PINN ensemble Kalman filter (iPINNER) framework that improves the robustness and accuracy of PINNs in both forward and inverse problems by using the ensemble Kalman filter and the non-dominated sorting genetic algorithm III (NSGA-III). Specifically, NSGA-III is used as a multi-objective optimizer that can generate various ensemble members of PINNs along the optimal Pareto front, while accounting the model uncertainty in the solution space. These ensemble members are then utilized within the EnKF to assimilate noisy observational data. The EnKF’s analysis is subsequently used to refine the data loss component for retraining the PINNs, thereby iteratively updating their parameters. The iterative procedure generates improved solutions to the PDEs. The proposed method is tested on two benchmark problems: the one-dimensional viscous Burgers equation and the time-fractional mixed diffusion-wave equation (TFMDWE). The numerical results show it outperforms standard PINNs in handling noisy data and missing physics.

物理信息神经网络（pinn）通过将物理定律纳入训练过程，已经成为解决涉及偏微分方程（PDEs）的正解和逆问题的强大工具。然而，在涉及噪声观测数据和物理缺失的现实场景中，特别是在逆问题中，pin - n的性能经常受到阻碍。在这项工作中，我们提出了一个迭代多目标PINN集成卡尔曼滤波器（iPINNER）框架，该框架通过使用集成卡尔曼滤波器和非支配排序遗传算法III (NSGA-III)，提高了PINN在正向和逆问题中的鲁棒性和准确性。具体来说，NSGA-III作为一个多目标优化器，可以沿最优Pareto前沿生成各种pinn的集成成员，同时考虑解空间中的模型不确定性。然后在EnKF内利用这些集合成员来吸收有噪声的观测数据。EnKF的分析随后用于细化数据丢失组件，以重新训练pin，从而迭代更新其参数。迭代过程生成pde的改进解。在一维粘性Burgers方程和时间分数混合扩散波方程（TFMDWE）两个基准问题上对该方法进行了测试。数值结果表明，该方法在处理噪声数据和物理缺失方面优于标准pin。

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引用次数: 0

Low-cost operator splitting based parallel data assimilation methods with the application in phase-field simulation 基于低成本算子分割的并行数据同化方法及其在相场仿真中的应用

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2025-12-13 DOI: 10.1016/j.jcp.2025.114580

Fenglian Zheng, Xufeng Xiao, Xinlong Feng

The phase-field simulation is quite sensitive to the settings of model parameters and initial conditions, as different settings may yield significantly different simulation results. However, in practical phase-field simulation, model errors may arise from the initial input to the model. Therefore, utilizing available real-time observations for data assimilation to enhance the accuracy of numerical simulation has become an important research topic. Traditional data assimilation methods, such as three-dimensional variational data assimilation and Ensemble Kalman Filter, face challenges due to the need for computing high-dimensional covariance matrices or solving high-dimensional optimization problems, which result in low computational efficiency and high storage requirements. To address these challenges, this paper proposes and compares three parallel data assimilation methods based on the operator splitting method: nudging, three-dimensional variational data assimilation, and Ensemble Kalman Filter. Although the three methods all reduce computational costs and storage requirements, each has its own specific advantages. By comparing the three methods and integrating their strengths, this paper further proposes a more comprehensive hybrid data assimilation method, which significantly improves simulation accuracy and avoids the limitations of using a single data assimilation method. Meanwhile, the effectiveness of the hybrid method in improving simulation accuracy is validated using the phase-field dendritic growth model as a test case.

相场仿真对模型参数和初始条件的设置非常敏感，不同的设置可能会产生明显不同的仿真结果。然而，在实际的相场仿真中，模型的初始输入可能会产生模型误差。因此，利用现有的实时观测资料进行同化，提高数值模拟的精度已成为一个重要的研究课题。传统的数据同化方法，如三维变分数据同化和集成卡尔曼滤波，由于需要计算高维协方差矩阵或解决高维优化问题，导致计算效率低，存储要求高，面临挑战。为了解决这些问题，本文提出并比较了三种基于算子分裂方法的并行数据同化方法：微推、三维变分数据同化和集成卡尔曼滤波。虽然这三种方法都降低了计算成本和存储需求，但每种方法都有其特定的优势。通过比较三种方法并综合其优点，本文进一步提出了一种更全面的混合数据同化方法，该方法显著提高了仿真精度，避免了使用单一数据同化方法的局限性。同时，以相场枝晶生长模型为例，验证了混合方法提高仿真精度的有效性。

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引用次数: 0

LSTM-PINN: An hybrid method for prediction of steady-state electrohydrodynamic flow LSTM-PINN：一种用于稳态电流体流动预测的混合方法

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2025-12-12 DOI: 10.1016/j.jcp.2025.114586

Ze Tao , Ke Xu , Fujun Liu

Physics-Informed Neural Networks (PINNs) have demonstrated considerable success in solving complex fluid dynamics problems. However, their performance often deteriorates in regimes characterized by steep gradients, intricate boundary conditions, and stringent physical constraints, leading to convergence failures and numerical instabilities. To overcome these limitations, we propose a hybrid framework that integrates Long Short-Term Memory (LSTM) networks into the PINN architecture, enhancing its ability to capture spatial correlations in the steady-state velocity field of a two-dimensional charged fluid under an external electric field. Our results demonstrate that the LSTM-enhanced PINN model significantly outperforms conventional Multilayer Perceptron (MLP)-based PINNs in terms of convergence rate, numerical stability, and predictive accuracy. This innovative approach offers improved computational efficiency and reliability for modeling electrohydrodynamic flows, providing new insights and strategies for applications in microfluidics and nanofluidics.

物理信息神经网络（pinn）在解决复杂流体动力学问题方面取得了相当大的成功。然而，在陡峭的梯度、复杂的边界条件和严格的物理约束条件下，它们的性能往往会恶化，导致收敛失效和数值不稳定。为了克服这些限制，我们提出了一种混合框架，将长短期记忆（LSTM）网络集成到PINN架构中，增强了其在外电场下二维带电流体稳态速度场中捕获空间相关性的能力。我们的研究结果表明，lstm增强的PINN模型在收敛速度、数值稳定性和预测精度方面显著优于传统的基于多层感知器（MLP）的PINN模型。这种创新的方法为电流体动力学建模提供了更高的计算效率和可靠性，为微流体和纳米流体的应用提供了新的见解和策略。

引用次数: 0

Score-based physics-informed learning framework for stochastic dynamics 基于分数的随机动力学物理知识学习框架

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2025-12-12 DOI: 10.1016/j.jcp.2025.114585

Hanbo Kou , Feng Liu , Faguo Wu , Xiao Zhang

The Fokker-Planck equation is crucial for characterizing the dynamics of stochastic systems and predicting their evolutionary behavior. In practice, the forward problem of the Fokker-Planck equation becomes ill-posed when the system dynamics and initial conditions are incompletely known. Meanwhile, the inverse problem for inferring dynamical coefficients is fundamentally constrained by the inherent unobservability of probability densities, which restricts available data to discrete-time particle observations. To address these challenges, we propose a novel Score-based Physics-informed Learning Framework that leverages score matching to connect particle observations with the forward and inverse problems of the Fokker-Planck equation, without requiring density reference solution or complete system dynamics. Experimental results demonstrate that our method achieves superior accuracy, computational efficiency, scalability to high dimensions, and robustness to data sparsity and noise.

福克-普朗克方程对于描述随机系统的动力学和预测它们的演化行为是至关重要的。在实际应用中，当系统动力学和初始条件不完全已知时，Fokker-Planck方程的正问题会变得不适定。同时，推导动力系数的逆问题从根本上受到概率密度固有的不可观测性的限制，这使得可用的数据仅限于离散时间的粒子观测。为了解决这些挑战，我们提出了一种新的基于分数的物理信息学习框架，该框架利用分数匹配将粒子观测与Fokker-Planck方程的正反问题联系起来，而不需要密度参考解或完整的系统动力学。实验结果表明，该方法具有较高的精度、计算效率、高维可扩展性以及对数据稀疏性和噪声的鲁棒性。

引用次数: 0

A variable-separation method based on the frequency domain for time-domain Maxwell’s equations with random inputs 基于频域的随机输入时域麦克斯韦方程组变量分离方法

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2025-12-12 DOI: 10.1016/j.jcp.2025.114579

Yuming Ba , Qiuqi Li

This paper presents a Variable-separation (VS) method based on frequency-domain techniques for solving time-domain Maxwell systems with random inputs. The goal is to obtain a separated representation of the Galerkin solution to Maxwell’s equations. To achieve this, we use a numerically efficient, parallelizable approach that employs Fourier transforms to solve the problem in the space-frequency domain, rather than in the space-time domain. The VS method utilizes an offline-online decomposition to efficiently solve the derived equations in the space-frequency domain. In this formulation, both stochastic and deterministic basis functions belong to complex-valued spaces. A key component of the proposed method is the construction of optimal stochastic basis functions during the offline stage. These functions are derived incrementally, with the real and imaginary parts determined through coupled linearized stochastic equations at each enrichment step. Furthermore, the frequency variable is treated as a one-dimensional random parameter, which enables the VS model to be constructed once and then reused for all frequencies involved in the inverse Fourier transform. This approach significantly enhances the computational efficiency by eliminating the need for repeated model construction. Finally, we present four numerical examples to illustrate the efficacy of the proposed method. These examples include the 2D transverse electric (TE) and transverse magnetic (TM) modes, as well as the 3D time-domain Maxwell equations.

本文提出了一种基于频域技术的时域随机输入麦克斯韦系统的变分离方法。目标是获得麦克斯韦方程组伽辽金解的分离表示。为了实现这一目标，我们使用了一种数值上有效的、可并行化的方法，该方法使用傅里叶变换在空频域中而不是在空时域中解决问题。该方法利用离线-在线分解方法在空频域有效地求解导出方程。在这个公式中，随机基函数和确定性基函数都属于复值空间。该方法的一个关键部分是在离线阶段构造最优随机基函数。这些函数是增量导出的，实部和虚部在每个富集步骤通过耦合线性化随机方程确定。此外，频率变量被视为一维随机参数，这使得VS模型可以构造一次，然后对傅里叶反变换中涉及的所有频率重复使用。该方法消除了重复构建模型的需要，大大提高了计算效率。最后，我们给出了四个数值例子来说明所提出方法的有效性。这些例子包括二维横向电（TE）和横向磁（TM）模式，以及三维时域麦克斯韦方程组。

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引用次数: 0

Data assimilation with physics-informed neural network surrogates constructed against prediction uncertainty 数据同化与物理通知神经网络代理构建预测不确定性

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2025-12-11 DOI: 10.1016/j.jcp.2025.114587

Takashi Misaka, Yusuke Mizuno, Shogo Nakasumi, Yoshiyuki Furukawa

A physics-informed neural network (PINN) surrogate is developed to represent the discrepancy between computational fluid dynamics (CFD) simulations and observations, enabling surrogate-based data assimilation. Utilizing the multi-block CFD framework of the Building Cube Method (BCM), the PINN surrogate is constructed and trained in parallel only in the subdomains where it is required for data assimilation. One-dimensional problems illustrate the overlapping strategy between finite-difference solutions and PINN surrogates for estimating uncertain parameters in governing equations. Low- and high-Reynolds-number flows are then investigated using the three-dimensional incompressible Navier-Stokes equations within the BCM framework, where a porous region is introduced and its macroscopic porous drag is estimated from observations. In the Navier-Stokes cases, a time-averaged PINN surrogate is constructed in combination with the mean flow field obtained from a large eddy simulation (LES) to perform data assimilation based on the mean flow field. The drag parameters of the porous region located in the wake of a circular cylinder are successfully estimated by superimposing the LES flow field and the PINN surrogate.

开发了一种物理信息神经网络（PINN）代理来表示计算流体动力学（CFD）模拟与观测之间的差异，从而实现基于代理的数据同化。利用构建立方体方法（BCM）的多块CFD框架，仅在数据同化所需的子域中并行构建和训练PINN代理。一维问题说明了有限差分解与PINN代理之间的重叠策略，用于估计控制方程中的不确定参数。然后使用BCM框架内的三维不可压缩Navier-Stokes方程研究了低雷诺数和高雷诺数流动，其中引入了多孔区域，并根据观测估计了其宏观多孔阻力。在Navier-Stokes情况下，结合大涡模拟（LES）得到的平均流场构造时间平均的PINN代理，在平均流场的基础上进行数据同化。通过将LES流场与PINN代理函数叠加，成功地估计了圆柱尾迹中多孔区域的阻力参数。

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引用次数: 0

A thermodynamically consistent and conservative diffuse-interface model for surfactant-laden two-phase dynamics 负载表面活性剂的两相动力学热力学一致且保守的扩散界面模型

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2025-12-11 DOI: 10.1016/j.jcp.2025.114584

Hong Liang , Sen Tong , Lu Wang , Chuang Zhang , Baochang Shi

Numerical modelling of surfactant-laden multiphase flows has become a widely sought methodology due to its scientific relevance and multiple industrial applications. In this paper, we propose a mass-conserved Allen-Cahn phase field model for the transport of the order parameter and surfactant component. Two nonlocal Lagrange multipliers are incorporated in this model to preserve the mass conservation for both phase field variable and surfactant, meanwhile satisfying the energy dissipation law. Unlike the traditional Cahn-Hilliard type model, the proposed model only contains a second-order spacial derivative at most and achieves in theory lower numerical dissipation. The thermodynamic equilibrium profiles for the order parameter and surfactant are derived analytically and a novel surface tension formulation with the inclusion of the surfactant effect is also constructed. Further, the two Allen-Cahn-like equations are utilized to be coupled with the nonlinear hydrodynamic equations for describing the surfactant-covered two-phase dynamics with density contrasts. Numerical simulations of some benchmark two-phase problems with soluble surfactant are carried out to demonstrate the feasibility of the proposed phase field model.

表面活性剂负载多相流的数值模拟由于其科学相关性和多种工业应用而成为一种广泛寻求的方法。本文提出了阶参量和表面活性剂组分输运的质量守恒的Allen-Cahn相场模型。在该模型中加入两个非局部拉格朗日乘子，既保证了相场变量和表面活性剂的质量守恒，又满足了能量耗散规律。与传统的Cahn-Hilliard型模型不同，该模型最多只包含一个二阶空间导数，理论上实现了较低的数值耗散。解析导出了阶参数和表面活性剂的热力学平衡曲线，并构造了包含表面活性剂效应的新型表面张力公式。此外，利用这两个类allen - cahn方程与非线性流体动力学方程耦合，描述了表面活性剂覆盖的两相密度对比动力学。通过对一些具有可溶性表面活性剂的基准两相问题的数值模拟，验证了所提相场模型的可行性。

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引用次数: 0

A simple, fully-discrete, unconditionally energy-stable method for the two-phase Navier-Stokes Cahn-Hilliard model with arbitrary density ratios 具有任意密度比的两相Navier-Stokes Cahn-Hilliard模型的一种简单、完全离散、无条件能量稳定方法

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2025-12-11 DOI: 10.1016/j.jcp.2025.114558

A. Brunk , M.F.P. ten Eikelder

The two-phase Navier-Stokes Cahn-Hilliard (NSCH) mixture model is a key framework for simulating multiphase flows with non-matching densities. Developing fully discrete, energy-stable schemes for this model remains challenging, due to the possible presence of negative densities. While various methods have been proposed, ensuring provable energy stability under phase-field modifications, like positive extensions of the density, remains an open problem. We propose a simple, fully discrete, energy-stable method for the NSCH mixture model that ensures stability with respect to the energy functional, where the density in the kinetic energy is positively extended. The method is based on an alternative but equivalent formulation using mass-averaged velocity and volume-fraction-based order parameters, simplifying implementation while preserving theoretical consistency. Numerical results demonstrate that the proposed scheme is robust, accurate, and stable for large density ratios, addressing key challenges in the discretization of NSCH models.

两相Navier-Stokes - Cahn-Hilliard （NSCH）混合流模型是模拟密度不匹配多相流的关键框架。由于可能存在负密度，为该模型开发完全离散的能量稳定方案仍然具有挑战性。虽然已经提出了各种方法，但确保相场修改下可证明的能量稳定性，如密度的正扩展，仍然是一个悬而未决的问题。我们提出了一种简单的、完全离散的、能量稳定的NSCH混合模型方法，以确保相对于能量泛函的稳定性，其中动能中的密度是正扩展的。该方法基于另一种等效的公式，使用质量平均速度和基于体积分数的顺序参数，简化了实现过程，同时保持了理论一致性。数值结果表明，该方法在大密度比下具有鲁棒性、准确性和稳定性，解决了NSCH模型离散化的关键问题。

引用次数: 0

Localized Schrödinger bridge sampler 本地化Schrödinger桥采样器

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2025-12-10 DOI: 10.1016/j.jcp.2025.114583

Georg A. Gottwald , Sebastian Reich

We consider the problem of sampling from an unknown distribution for which only a sufficiently large number of training samples are available. In this paper, we build on previous work combining Schrödinger bridges and plug & play Langevin samplers. A key bottleneck of these approaches is the exponential dependence of the required training samples on the dimension, d, of the ambient state space. We propose a localization strategy which exploits conditional independence of conditional expectation values. Localization thus replaces a single high-dimensional Schrödinger bridge problem by d low-dimensional Schrödinger bridge problems over the available training samples. As for the original Schrödinger bridge sampling approach, the localized sampler is stable and geometrically ergodic. The sampler also naturally extends to conditional sampling and to Bayesian inference. We demonstrate the performance of our proposed scheme through experiments on a high-dimensional Gaussian problem, on a temporal stochastic process, and on a stochastic subgrid-scale parametrization conditional sampling problem. We also extend the idea of localization to plug & play Langevin samplers using kernel-based denoising in combination with Tweedie’s formula.

我们考虑从一个未知分布中抽样的问题，其中只有足够多的训练样本可用。在本文中，我们建立在先前的工作结合Schrödinger桥和即插即用朗格万采样器。这些方法的一个关键瓶颈是所需的训练样本对环境状态空间维数d的指数依赖性。我们提出了一种利用条件期望值的条件独立性的定位策略。因此，本地化用可用训练样本上的d个低维Schrödinger桥问题取代了单个高维Schrödinger桥问题。对于原来的Schrödinger桥采样方法，局部采样器是稳定的和几何遍历的。采样器也自然地扩展到条件采样和贝叶斯推理。我们通过在高维高斯问题、时间随机过程和随机子网格尺度参数化条件采样问题上的实验证明了我们提出的方案的性能。我们还将本地化的想法扩展到使用基于核的去噪与Tweedie公式相结合的插拔式朗格万采样器。

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引用次数: 0

A sharp-interface discontinuous Galerkin method for simulation of two-phase flow of real gases based on implicit shock tracking 基于隐式激波跟踪的真实气体两相流模拟的锐界面不连续Galerkin方法

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2025-12-09 DOI: 10.1016/j.jcp.2025.114556

Charles Naudet , Brian Taylor , Matthew J. Zahr

We present a high-order, sharp-interface method for simulation of two-phase flow of real gases using implicit shock tracking. The method is based on a phase-field formulation of two-phase, compressible, inviscid flow with a trivial mixture model. Implicit shock tracking is a high-order, optimization-based discontinuous Galerkin method that automatically aligns mesh faces with non-smooth flow features to represent them perfectly with inter-element jumps. It is used to accurately approximate shocks and rarefactions without stabilization and converge the phase-field solution to a sharp interface one by aligning mesh faces with the material interface. Time-dependent problems are formulated as steady problems in a space-time domain where complex wave interactions (e.g., intersections and reflections) manifest as space-time triple points. The space-time formulation avoids complex re-meshing and solution transfer that would be required to track moving waves with mesh faces using the method of lines. The approach is applied to several two-phase flow Riemann problems involving gases with ideal, stiffened gas, and Becker-Kistiakowsky-Wilson (BKW) equations of state, including a spherically symmetric underwater explosion problem. In all cases, the method aligns element faces with all shocks (including secondary shocks that form at time t > 0), rarefactions, and material interfaces, and accurately resolves the flow field on coarse space-time grids.

本文提出了一种高阶、清晰界面的方法，利用隐式激波跟踪来模拟真实气体的两相流动。该方法基于具有平凡混合模型的两相、可压缩、无粘流的相场公式。隐式激波跟踪是一种高阶、基于优化的不连续Galerkin方法，它自动对齐网格面，使其具有非光滑的流动特征，并通过元素间跳跃完美地表示它们。该方法用于精确地逼近无稳定化的冲击和稀疏，并通过将网格面与材料界面对齐，将相场解收敛到一个尖锐的界面解。时间相关问题被表述为时空域中的稳定问题，其中复杂的波相互作用（例如，交叉和反射）表现为时空三重点。时空公式避免了使用线法跟踪具有网格面的运动波所需的复杂的重新网格划分和解转移。该方法应用于几种两相流Riemann问题，包括理想气体、强化气体和Becker-Kistiakowsky-Wilson （BKW）状态方程，包括球对称水下爆炸问题。在所有情况下，该方法将元素面与所有冲击（包括在时间t >； 0形成的二次冲击）、区域和材料界面对齐，并在粗糙的时空网格上精确地解析流场。

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引用次数: 0