Journal of Computational Physics最新文献_第6页

Goal-oriented real-time Bayesian inference for linear autonomous dynamical systems with application to digital twins for tsunami early warning 面向目标的线性自主动力系统实时贝叶斯推理及其在数字孪生体海啸预警中的应用

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

Journal of Computational Physics

Pub Date : 2026-05-01 Epub Date: 2026-01-14 DOI: 10.1016/j.jcp.2026.114682

Stefan Henneking , Sreeram Venkat , Omar Ghattas

We present a goal-oriented framework for constructing digital twins with the following properties: (1) they employ discretizations of high-fidelity partial differential equation (PDE) models governed by autonomous dynamical systems, leading to large-scale forward problems; (2) they solve a linear inverse problem to assimilate observational data to infer uncertain model components followed by a forward prediction of the evolving dynamics; and (3) the entire end-to-end, data-to-inference-to-prediction computation is carried out without approximation and in real time through a Bayesian framework that rigorously accounts for uncertainties. Several challenges must be overcome to realize this framework, including the large scale of the forward problem, the high dimensionality of the parameter space, and for a class of problems including those we target, the slow decay of the singular values of the parameter-to-observable map. Here we introduce a methodology to overcome these challenges by exploiting the autonomous structure of the forward model to decompose the solution of the inverse problem into a one-time-only offline phase in which the PDE model is solved a limited number of times (equal to the number of sensors), and an online phase that maps well onto GPUs and computes the parameter inference and prediction of quantities of interest in real time, given observational data. Our ultimate goal is to apply this framework to construct digital twins for subduction zones, including Cascadia, to provide early warning for tsunamis generated by megathrust earthquakes. To this end, we demonstrate how our methodology can be used to employ seafloor pressure observations, along with the coupled acoustic–gravity wave equations, to infer the earthquake-induced spatiotemporal seafloor motion (discretized with

O (10^{9})

parameters) and forward predict the tsunami propagation. We present results of an end-to-end inference, prediction, and uncertainty quantification for a representative test problem with

O (10^{8})

inversion parameters for which goal-oriented Bayesian inference is accomplished exactly and in real time, that is, in a matter of seconds.

我们提出了一个目标导向的框架，用于构建具有以下性质的数字孪生：(1)它们采用由自主动力系统控制的高保真偏微分方程（PDE）模型的离散化，导致大规模的正演问题；(2)求解线性逆问题，吸收观测数据推断不确定模型分量，然后对演化动力学进行正演预测；(3)整个端到端，从数据到推理到预测的计算都是通过严格考虑不确定性的贝叶斯框架进行的，没有近似值，而且是实时的。实现这一框架必须克服几个挑战，包括前向问题的大规模，参数空间的高维，以及对于包括我们目标在内的一类问题，参数到可观测映射的奇异值的缓慢衰减。在这里，我们引入了一种方法来克服这些挑战，通过利用前向模型的自治结构将逆问题的解分解为一个仅一次性离线阶段，其中PDE模型求解有限次数（等于传感器数量），以及一个在线阶段，该阶段很好地映射到gpu上，并在给定观测数据的情况下实时计算感兴趣数量的参数推断和预测。我们的最终目标是应用这个框架为包括卡斯卡迪亚在内的俯冲带构建数字孪生体，为大型逆冲地震引发的海啸提供早期预警。为此，我们展示了如何使用我们的方法来利用海底压力观测，以及耦合声重力波方程来推断地震引起的海底时空运动（用O（109）参数离散化）并正演预测海啸的传播。我们提出了一个具有0（108）个反演参数的代表性测试问题的端到端推理、预测和不确定性量化的结果，针对该问题，目标导向的贝叶斯推理可以精确地实时完成，即在几秒钟内完成。

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引用次数: 0

An online interactive physics-informed diffusion-adversarial network for solving mean field games 用于求解平均场博弈的在线交互式物理信息扩散对抗网络

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

Journal of Computational Physics

Pub Date : 2026-05-01 Epub Date: 2026-01-20 DOI: 10.1016/j.jcp.2026.114700

Longqiang Xu , Weishi Yin , Pinchao Meng , Zhengxuan Shen , Hongyu Liu

High-dimensional, complex, and dynamic environments pose significant challenges in solving mean field games (MFGs). To address these challenges, we propose an online interactive physics-informed diffusion-adversarial network (IPIDAN), which offers enhanced interpretability and flexibility by leveraging a novel agent strategy generator based on diffusion models. This generator utilizes a noise process to improve its ability to escape local optima, while a stepwise optimization process during the denoising phase generates refined agent strategies, thereby enhancing the quality and diversity of the generated results. The discriminator perceives the distribution and strategies of agents in MFGs by extracting the physical information exchange from agent interactions. By using variational techniques, the typical MFG problem is transformed into a static optimization problem, which is then efficiently approximated using a generative adversarial framework through adversarial training. IPIDAN, with its diffusion generation model architecture, provides the network with greater tunability and significantly enhances its ability to model randomness in high-dimensional strategy spaces. Furthermore, by establishing a connection between the diffusion process and the agents’ motion dynamics, the network achieves improved interpretability and robustness. Numerical experiments and comparisons with experimental results validate the effectiveness of the novel agent strategy generator based on diffusion models, particularly demonstrating its superior performance through quadrotor obstacle avoidance experiments conducted in various complex scenarios.

高维、复杂和动态的环境对求解平均场博弈（mfg）提出了重大挑战。为了应对这些挑战，我们提出了一个在线交互式物理信息扩散对抗网络（IPIDAN），它通过利用基于扩散模型的新型代理策略生成器提供了增强的可解释性和灵活性。该生成器利用噪声过程来提高其逃避局部最优的能力，而在去噪阶段的逐步优化过程生成精细的代理策略，从而提高了生成结果的质量和多样性。鉴别器通过从agent交互中提取物理信息交换来感知agent在mfg中的分布和策略。通过变分技术，将典型的MFG问题转化为静态优化问题，然后通过对抗性训练，使用生成式对抗性框架有效地逼近该问题。IPIDAN的扩散生成模型架构为网络提供了更大的可调性，显著增强了网络在高维策略空间中对随机性的建模能力。此外，通过建立扩散过程与智能体运动动力学之间的联系，网络具有更好的可解释性和鲁棒性。数值实验以及与实验结果的对比验证了基于扩散模型的新型智能体策略生成器的有效性，特别是通过在各种复杂场景下的四旋翼避障实验证明了其优越的性能。

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引用次数: 0

Analysis and elimination of numerical pressure dependency in coupled Stokes-Darcy problem 耦合Stokes-Darcy问题中数值压力依赖性的分析与消除

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

Journal of Computational Physics

Pub Date : 2026-05-01 Epub Date: 2026-01-26 DOI: 10.1016/j.jcp.2026.114710

Jiachuan Zhang

This paper analyses the classical mixed finite element method (FEM) and a pressure-robust variant with divergence-free reconstruction operators for the coupled Stokes-Darcy problem. Its main contribution is to provide viscosity-explicit a priori error estimates that clearly distinguish the pressure dependence of the two discretizations: the velocity error of the classical scheme depends on both the exact pressure and the viscosity, whereas the pressure-robust method eliminates both entirely. Moreover, we derive pressure error estimates and quantify their dependence on the exact solution and model parameters. Two-dimensional numerical experiments validate the theoretical findings, including higher-order tests up to polynomial degree three and a lid-driven cavity benchmark with a piecewise linear interface. The implementation code is made publicly available to facilitate reproducibility.

本文分析了耦合Stokes-Darcy问题的经典混合有限元法和无发散重构算子的压力鲁棒变体。它的主要贡献是提供粘度显式先验误差估计，清楚地区分了两种离散化的压力依赖性：经典方案的速度误差取决于精确压力和粘度，而压力鲁棒方法完全消除了两者。此外，我们导出了压力误差估计，并量化了它们对精确解和模型参数的依赖。二维数值实验验证了理论结果，包括多项式三次的高阶测试和分段线性界面的盖驱动腔基准测试。实现代码是公开的，以促进再现性。

引用次数: 0

A positive and asymptotic preserving scheme for the multi-group radiative equations 多群辐射方程的一个正渐近保持格式

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

Journal of Computational Physics

Pub Date : 2026-05-01 Epub Date: 2026-01-15 DOI: 10.1016/j.jcp.2026.114691

Clément Lasuen

In this paper, we propose a finite volume scheme for the grey and multi-group radiative equations. We present it in one space dimension but it can be easily generalized to the two dimensional case using the ideas from Lasuen [1]. This scheme is designed as an upwind scheme where the velocity is modified so as to recover the correct diffusion limit. The resulting scheme is asymptotic preserving, positive under a classical CFL condition and conservative. We also add a reconstruction procedure so as to make it second order consistent. Besides, its computational cost is similar to an explicit scheme.

本文提出了灰色多群辐射方程的有限体积格式。我们在一维空间中表示它，但它可以很容易地推广到二维情况，使用Lasuen[1]的思想。该方案被设计为一个逆风方案，其中速度被修改，以恢复正确的扩散极限。所得到的格式是渐近保持的，在经典CFL条件下是正的，并且是保守的。我们还增加了一个重建程序，使其二阶一致。此外，其计算成本与显式方案相似。

引用次数: 0

A high-order, conservative and positivity-preserving intersection-based remapping method between meshes with isoparametric curvilinear cells 一种高阶、保守、保正的等参曲线单元网格重映射方法

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

Journal of Computational Physics

Pub Date : 2026-04-15 Epub Date: 2026-01-15 DOI: 10.1016/j.jcp.2026.114669

Nuo Lei , Juan Cheng , Chi-Wang Shu

This paper presents a novel two-dimensional intersection-based remapping method for isoparametric curvilinear meshes within the indirect arbitrary Lagrangian-Eulerian (ALE) framework, addressing the challenges of transferring physical quantities between high-order curved-edge meshes. Our method leverages the Weiler-Atherton clipping algorithm to compute intersections between curved-edge quadrangles, enabling robust handling of arbitrary order isoparametric curves. By integrating multi-resolution weighted essentially non-oscillatory (WENO) reconstruction, we achieve high-order accuracy while suppressing numerical oscillations near discontinuities. A positivity-preserving limiter is further applied to ensure physical quantities such as density remain non-negative without compromising conservation or accuracy. Notably, the computational cost of handling higher-order curved meshes, such as cubic or even higher-degree parametric curves, does not significantly increase compared to second-order curved meshes. This ensures that our method remains efficient and scalable, making it applicable to arbitrary two-dimensional high-order isoparametric curvilinear cells without compromising performance. Numerical experiments demonstrate that the proposed method achieves high-order accuracy, strict conservation (with errors approaching machine precision), essential non-oscillation and positivity-preserving. The proposed approach is currently restricted to two-dimensional meshes, and an extension to fully three-dimensional curved polyhedral mesh is beyond the scope of the present work.

本文提出了一种在间接任意拉格朗日-欧拉（ALE）框架下等参曲线网格的二维交叉重映射方法，解决了高阶曲线边缘网格之间物理量传递的难题。我们的方法利用Weiler-Atherton裁剪算法来计算弯曲边缘四边形之间的交叉点，从而实现对任意阶等参曲线的鲁棒处理。通过积分多分辨率加权非振荡（WENO）重建，我们在抑制不连续点附近的数值振荡的同时获得了高阶精度。正保持限制器进一步应用，以确保物理量，如密度保持非负，而不损害守恒或准确性。值得注意的是，处理高阶曲线网格（如三次甚至更高次参数曲线）的计算成本与处理二阶曲线网格相比并没有显著增加。这确保了我们的方法保持高效和可扩展性，使其适用于任意二维高阶等参数曲线细胞而不影响性能。数值实验表明，该方法具有高阶精度、严格守恒（误差接近机器精度）、基本不振荡和保正等优点。所提出的方法目前仅限于二维网格，扩展到全三维弯曲多面体网格超出了本工作的范围。

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引用次数: 0

On ground states of spin-1 dipolar Bose-Einstein condensate: Dimension reduction and numerical computation 自旋-1偶极玻色-爱因斯坦凝聚的基态：降维和数值计算

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

Journal of Computational Physics

Pub Date : 2026-04-15 Epub Date: 2026-01-11 DOI: 10.1016/j.jcp.2026.114671

Zhixuan Li , Qinglin Tang , Hanquan Wang , Yong Zhang

We perform a dimension reduction for spin-1 dipolar Bose-Einstein condensate (BEC), which is described by the mean-field Gross-Pitaevskii equations (GPEs) coupled with dipole-dipole interaction (DDI), under strongly anisotropic external confining potentials. The original three dimensions (3D) problem is then reduced to quasi-2D and quasi-1D models for pancake- and cigar-shaped trapping potentials respectively. To compute the ground state, we propose an efficient and accurate algorithm by incorporating the kernel truncation method (KTM) for the dipolar potential evaluation into the projected gradient flow (PGF) method. The long-range dipolar potential is computed efficiently and accurately by KTM with optimal zero-padding factor, and the resulted PGF-KTM algorithm achieves spectral accuracy in the ground states. We compute the ground states in different space dimensions, and confirm the convergence and rates of dimension reduction from 3D to quasi-2D and from 3D to quasi-1D. Extensive numerical results of ground states for BECs with ferromagnetic/antiferromagnetic interaction and various external potentials in 1D/2D/3D are reported.

在强各向异性外约束势下，用平均场Gross-Pitaevskii方程（gpe）耦合偶极-偶极相互作用（DDI）描述自旋-1偶极玻色-爱因斯坦凝聚体（BEC），对其进行了降维。然后将原来的三维问题分别简化为饼形和雪茄形捕获势的准二维和准一维模型。为了计算基态，我们将偶极势计算的核截断法（KTM）结合到投影梯度流（PGF）方法中，提出了一种高效、准确的算法。利用最优补零因子的KTM高效、准确地计算了远距离偶极势，得到的PGF-KTM算法在基态下实现了光谱精度。我们计算了不同空间维度的基态，并确定了从三维到准二维和从三维到准一维的收敛性和降维率。本文报道了具有铁磁/反铁磁相互作用和一维/二维/三维各种外部电位的bec基态的大量数值结果。

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引用次数: 0

A structure-preserving multiscale solver for particle-wave interaction in non-uniform magnetized plasmas 非均匀磁化等离子体中粒子波相互作用的保结构多尺度求解器

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

Journal of Computational Physics

Pub Date : 2026-04-15 Epub Date: 2026-01-13 DOI: 10.1016/j.jcp.2026.114670

Kun Huang , Irene M. Gamba , Chi-Wang Shu

Particle-wave interaction is of fundamental interest in plasma physics, especially in the study of runaway electrons in magnetic confinement fusion. Analogous to the concept of photons and phonons, wave packets in plasma can also be treated as quasi-particles, called plasmons. To model the “mixture” of electrons and plasmons in plasma, a set of “collisional” kinetic equations has been derived, based on weak turbulence limit and the Wentzel-Kramers-Brillouin (WKB) approximation.

There are two main challenges in solving the electron-plasmon kinetic system numerically. Firstly, non-uniform plasma density and magnetic field results in high dimensionality and the presence of multiple time scales. Secondly, a physically reliable numerical solution requires a structure-preserving scheme that enforces the conservation of mass, momentum, and energy.

In this paper, we propose a structure-preserving multiscale solver for particle-wave interaction in non-uniform magnetized plasmas. The solver combines a conservative local discontinuous Galerkin (LDG) scheme for the interaction part with a trajectory averaging method for the plasmon Hamiltonian flow part. Numerical examples for a non-uniform magnetized plasma in an infinitely long symmetric cylinder are presented. It is verified that the LDG scheme rigorously preserves all the conservation laws, and the trajectory averaging method significantly reduces the computational cost.

粒子-波相互作用是等离子体物理学的一个重要研究方向，特别是在磁约束聚变中失控电子的研究中。与光子和声子的概念类似，等离子体中的波包也可以被视为准粒子，称为等离子体激元。为了模拟等离子体中电子和等离子体的“混合物”，基于弱湍流极限和Wentzel-Kramers-Brillouin （WKB）近似，导出了一组“碰撞”动力学方程。用数值方法求解电子-等离子体动力学系统有两个主要的挑战。首先，等离子体密度和磁场的不均匀导致了高维度和多时间尺度的存在。其次，一个物理上可靠的数值解需要一个结构保持方案，以保证质量、动量和能量的守恒。本文提出了一个非均匀磁化等离子体中粒子波相互作用的多尺度保结构求解器。求解器结合了相互作用部分的保守局部不连续伽辽金格式和等离子体哈密顿流部分的轨迹平均法。给出了无限长对称圆柱体中非均匀磁化等离子体的数值算例。验证了LDG方案严格保持了所有的守恒定律，且轨迹平均法显著降低了计算量。

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引用次数: 0

Theory and computation of plasmon hybridization modes for multi-layered complex media 多层复杂介质等离子体杂化模式的理论与计算

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

Journal of Computational Physics

Pub Date : 2026-04-15 Epub Date: 2026-01-14 DOI: 10.1016/j.jcp.2026.114672

Youjun Deng, Lingzheng Kong, Gongsheng Tong

Multi-layered structures have attracted increasing attention due to their potential applications in imaging and cloaking. Such structures, which include GPT-vanishing and SC-vanishing configurations, are known to exhibit significant non-uniqueness in inverse problems under low-frequency or slowly oscillating incident fields. Unique recovery in these settings typically requires high-order incident waves, resulting in severe ill-posedness and instability. Motivated by these insights and the hybridization behavior of plasmon modes across interfaces in multi-layered media, we develop a mathematical framework for plasmon hybridization theory in multi-layered structures of general shape based on perturbation theory. Our analysis yields a spectral expansion of the shape sensitivity functional, providing a foundation for highly sensitive shape reconstruction. Numerical simulations are presented to corroborate the theoretical findings and show new plasmon hybridization phenomena.

多层结构由于其在成像和隐身方面的潜在应用而受到越来越多的关注。这种结构，包括gpt消失和sc消失构型，已知在低频或慢振荡入射场的反问题中表现出显著的非唯一性。在这些环境中，独特的恢复通常需要高阶入射波，导致严重的不适和不稳定。基于这些见解和等离子体模式在多层介质中跨界面的杂化行为，我们基于微扰理论建立了一般形状多层结构中等离子体杂化理论的数学框架。我们的分析产生了形状灵敏度函数的光谱扩展，为高灵敏度形状重建提供了基础。数值模拟证实了理论结果，并展示了新的等离子体杂化现象。

引用次数: 0

Fast recovery of parametric eigenvalues depending on several parameters and location of high order exceptional points 基于多个参数和高阶异常点位置的参数特征值快速恢复

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

Journal of Computational Physics

Pub Date : 2026-04-15 Epub Date: 2026-01-14 DOI: 10.1016/j.jcp.2026.114692

Benoit Nennig , Martin Ghienne , Emmanuel Perrey-Debain

A numerical algorithm is proposed to deal with parametric eigenvalue problems involving non-Hermitian matrices and is exploited to find location of defective eigenvalues in the parameter space of non-Hermitian parametric eigenvalue problems. These non-Hermitian degeneracies also called exceptional points (EP) have raised considerable attention in the scientific community as these can have a great impact in a variety of physical problems. The method first requires the computation of high order derivatives of a few selected eigenvalues with respect to each parameter involved. The second step is to recombine these quantities to form new coefficients associated with a partial characteristic polynomial (PCP). By construction, these coefficients are regular functions in a large domain of the parameter space which means that the PCP allows one to recover the selected eigenvalues as well as the localization of high order EPs by simply using standard root-finding algorithms.

The versatility of the proposed approach is tested on several applications, from mass-spring systems to guided acoustic waves with absorbing walls and room acoustics. The scalability of the method to large sparse matrices arising from conventional discretization techniques such as the finite element method is demonstrated. The proposed approach can be extended to a large number of applications where EPs play an important role in quantum mechanics, optics and photonics or in mechanical engineering.

提出了一种处理非厄米矩阵参数特征值问题的数值算法，并利用该算法在非厄米矩阵参数特征值问题的参数空间中寻找缺陷特征值的位置。这些非厄米简并也被称为异常点（EP），在科学界引起了相当大的关注，因为它们可以对各种物理问题产生重大影响。该方法首先需要计算几个选定的特征值对所涉及的每个参数的高阶导数。第二步是重新组合这些量以形成与部分特征多项式（PCP）相关的新系数。通过构造，这些系数是参数空间大域中的正则函数，这意味着PCP允许人们通过简单地使用标准寻根算法来恢复所选择的特征值以及高阶ep的定位。所提出的方法的多功能性在几个应用中进行了测试，从质量弹簧系统到带吸收壁和房间声学的引导声波。证明了该方法对传统离散化技术如有限元法产生的大型稀疏矩阵的可扩展性。所提出的方法可以扩展到大量应用中，其中EPs在量子力学，光学和光子学或机械工程中发挥重要作用。

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引用次数: 0

A dual physics-informed neural network for topology optimization 拓扑优化的双物理信息神经网络

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

Journal of Computational Physics

Pub Date : 2026-04-15 Epub Date: 2026-01-08 DOI: 10.1016/j.jcp.2026.114666

Ajendra Singh , Souvik Chakraborty , Rajib Chowdhury

We propose a novel dual physics-informed neural network for topology optimization (DPNN-TO), which merges physics-informed neural networks (PINNs) with the traditional SIMP-based topology optimization (TO) algorithm. This approach leverages two interlinked neural networks–a displacement network and an implicit density network-connected through an energy-minimization-based loss function derived from the variational principles of the governing equations. By embedding deep learning within the physical constraints of the problem, DPNN-TO eliminates the need for large-scale data and analytical sensitivity analysis, addressing key limitations of traditional methods. The framework efficiently minimizes compliance through energy-based objectives while enforcing volume fraction constraints, producing high-resolution designs for both 2D and 3D optimization problems. Extensive numerical validation demonstrates that DPNN-TO outperforms conventional methods, solving complex structural optimization scenarios with greater flexibility and computational efficiency, while addressing challenges such as multiple load cases and three-dimensional problems without compromising accuracy.

本文提出了一种新的双物理通知神经网络拓扑优化（DPNN-TO），它将物理通知神经网络（pinn）与传统的基于simp的拓扑优化（TO）算法相结合。这种方法利用了两个相互连接的神经网络——位移网络和隐式密度网络，它们通过由控制方程的变分原理导出的基于能量最小化的损失函数连接起来。通过将深度学习嵌入到问题的物理约束中，DPNN-TO消除了对大规模数据和分析灵敏度分析的需求，解决了传统方法的关键局限性。该框架通过基于能量的目标有效地减少了合规性，同时实施了体积分数限制，为2D和3D优化问题提供了高分辨率设计。大量的数值验证表明，DPNN-TO优于传统方法，以更大的灵活性和计算效率解决复杂的结构优化方案，同时在不影响精度的情况下解决多种载荷情况和三维问题等挑战。

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引用次数: 0