Journal of Computational Physics最新文献

{"title":"Isoparametric finite element methods for mean curvature flow and surface diffusion","authors":"Harald Garcke ,&nbsp;Robert Nürnberg ,&nbsp;Simon Praetorius ,&nbsp;Ganghui Zhang","doi":"10.1016/j.jcp.2025.114248","DOIUrl":"10.1016/j.jcp.2025.114248","url":null,"abstract":"<div><div>We propose higher-order isoparametric finite element approximations for mean curvature flow and surface diffusion. The methods are natural extensions of the piecewise linear finite element methods introduced by Barrett, Garcke, and Nürnberg (BGN) in a series of papers in 2007 and 2008. The proposed schemes exhibit unconditional energy stability and inherit the favorable mesh quality of the original BGN methods. Moreover, in the case of surface diffusion we present structure-preserving higher-order isoparametric finite element methods. In addition to being unconditionally stable, these also conserve the enclosed volume. Extensive numerical results demonstrate the higher-order spatial accuracy, the unconditional energy stability, the volume preservation for surface diffusion, and the good mesh quality.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"539 ","pages":"Article 114248"},"PeriodicalIF":3.8,"publicationDate":"2025-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144712956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An explainable operator approximation framework under the guideline of Green’s function","authors":"Jianghang Gu ,&nbsp;Ling Wen ,&nbsp;Yuntian Chen ,&nbsp;Shiyi Chen","doi":"10.1016/j.jcp.2025.114244","DOIUrl":"10.1016/j.jcp.2025.114244","url":null,"abstract":"<div><div>Compared to traditional methods such as the finite element and finite volume methods, the Green’s function approach offers the advantage of providing analytical solutions to linear partial differential equations (PDEs) with varying boundary conditions and source terms, without the need for repeated iterative solutions. Nevertheless, deriving Green’s functions analytically remains a non-trivial task. In this study, we develop a framework inspired by the architecture of deep operator networks (DeepONet) to learn embedded Green’s functions and solve PDEs through integral formulation, termed the Green’s operator network (GON). Specifically, the Trunk Net within GON is designed to approximate the unknown Green’s functions of the system, while the Branch Net are utilized to approximate the auxiliary gradients of the Green’s function. These outputs are subsequently employed to perform surface integrals and volume integrals, incorporating user-defined boundary conditions and source terms, respectively. The effectiveness of the proposed framework is demonstrated on three types of PDEs in 3D bounded domains: Poisson equations, reaction-diffusion equations, and Stokes equations. Comparative results in these cases demonstrate that GON’s accuracy and generalization ability surpass those of existing methods, including Physics-Informed Neural Networks (PINN), DeepONet, Physics-Informed DeepONet (PI-DeepONet), and Fourier Neural Operators (FNO). Code and data is available at <span><span>https://github.com/hangjianggu/GreensONet</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"539 ","pages":"Article 114244"},"PeriodicalIF":3.8,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144686016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Central-upwind scheme for the phase-transition traffic flow model","authors":"Shaoshuai Chu ,&nbsp;Alexander Kurganov ,&nbsp;Saeed Mohammadian ,&nbsp;Zuduo Zheng","doi":"10.1016/j.jcp.2025.114241","DOIUrl":"10.1016/j.jcp.2025.114241","url":null,"abstract":"<div><div>Phase-transition models are an important family of non-equilibrium continuum traffic flow models, offering properties like replicating complex traffic phenomena, maintaining anisotropy, and promising potentials for accommodating automated vehicles. However, their complex mathematical characteristics such as discontinuous solution domains, pose numerical challenges and limit their exploration in traffic flow theory. This paper focuses on developing a robust and accurate numerical method for phase-transition traffic flow models: We propose a second-order semi-discrete central-upwind scheme specifically designed for phase-transition models. This novel scheme incorporates the projection onto appropriate flow domains, ensuring enhanced handling of discontinuities and maintaining physical consistency and accuracy. We demonstrate the efficacy of the proposed scheme through extensive and challenging numerical tests, showcasing their potential to facilitate further research and application in phase-transition traffic flow modeling. The ability of phase-transition models to embed the “time-gap”—a crucial element in automated traffic control—as a conserved variable aligns seamlessly with the control logic of automated vehicles, presenting significant potential for future applications, and the proposed numerical scheme now substantially facilitates exploring such potentials.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"539 ","pages":"Article 114241"},"PeriodicalIF":3.8,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144680231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"PE-RWP: A deep learning framework for polynomial feature extraction of rogue wave patterns and peregrine waves localization","authors":"Zhe Lin ,&nbsp;Yong Chen","doi":"10.1016/j.jcp.2025.114243","DOIUrl":"10.1016/j.jcp.2025.114243","url":null,"abstract":"<div><div>Rogue wave (RW) patterns are nonlinear wave phenomena universally present in integrable systems. When one or more free internal parameters in the exact RW solutions of integrable systems like the nonlinear Schrödinger (NLS) equation are sufficiently large, the RW exhibit unique geometric patterns fully determined by the zero structure of the Yablonskii-Vorob’ev (Y-V) polynomial hierarchy. In this paper, we propose a deep learning-based “Polynomial Extractor for Rogue Wave Patterns” (PE-RWP). This approach replaces traditional asymptotic analysis of high-order RW solutions under large-parameter conditions, enabling automatic and precise identification of polynomial characteristics within RW patterns. We introduce a generalized polynomial hierarchy with parameters <span><math><msub><mi>γ</mi><mrow><mi>k</mi><mo>,</mo><mi>j</mi></mrow></msub></math></span> that encompasses all Y-V polynomials relevant to RW patterns, serving as the target objective for PE-RWP. The unique dual-branch network architecture (with a regression branch for determining parameter values and a classification branch for identifying corresponding polynomial types) enables PE-RWP to effectively output this generalized polynomial hierarchy and recognize RW patterns subjected to arbitrary scaling and rotational transformations. Furthermore, as an application based on the mathematical theory of RW patterns, we leverage the Y-V polynomials output by PE-RWP to achieve unsupervised localization of Peregrine waves through deep learning methods. Finally, through extensive experimental evaluation, both problems-polynomial extraction and Peregrine wave localization-are effectively solved with high accuracy.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"539 ","pages":"Article 114243"},"PeriodicalIF":3.8,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144686015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"State-observation augmented diffusion model for nonlinear assimilation with unknown dynamics","authors":"Zhuoyuan Li ,&nbsp;Bin Dong ,&nbsp;Pingwen Zhang","doi":"10.1016/j.jcp.2025.114240","DOIUrl":"10.1016/j.jcp.2025.114240","url":null,"abstract":"<div><div>Data assimilation has become a key technique for combining physical models with observational data to estimate state variables. However, classical assimilation algorithms often struggle with the high nonlinearity present in both physical and observational models. To address this challenge, a novel generative model, termed the State-Observation Augmented Diffusion (SOAD) model is proposed for data-driven assimilation. The marginal posterior associated with SOAD has been derived and then proved to match the true posterior distribution under mild assumptions, suggesting its theoretical advantages over previous score-based approaches. Experimental results also indicate that SOAD may offer improved performance compared to existing data-driven methods.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"539 ","pages":"Article 114240"},"PeriodicalIF":3.8,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144662639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Neural chaos: A spectral stochastic neural operator","authors":"Bahador Bahmani ,&nbsp;Ioannis G. Kevrekidis ,&nbsp;Michael D. Shields","doi":"10.1016/j.jcp.2025.114233","DOIUrl":"10.1016/j.jcp.2025.114233","url":null,"abstract":"<div><div>Building surrogate models for operators with uncertainty quantification capabilities is essential for many engineering applications where randomness–such as variability in material properties, boundary conditions, and initial conditions–is unavoidable. Polynomial Chaos Expansion (PCE) is widely recognized as a go-to method for constructing stochastic surrogates in both intrusive and non-intrusive ways, and it has recently been used in the context of operator learning. However, its application becomes challenging for complex or high-dimensional processes, as achieving accuracy requires higher-order polynomials, which can increase computational demand and/or the risk of overfitting. Furthermore, PCE requires specialized treatments to manage random variables that are not independent, and these treatments may be problem-dependent or may fail with increasing complexity. In this work, we adopt the same formalism as the spectral expansion used in PCE; however, we replace the classical polynomial basis functions with neural network (NN) basis functions to leverage their expressivity. To achieve this, we propose an algorithm that identifies NN-parameterized basis functions in a purely data-driven manner, without any prior assumptions about the joint distribution of the random variables involved, whether independent or dependent, or about their marginal distributions. The proposed algorithm identifies each NN-parameterized basis function sequentially, ensuring they are orthogonal with respect to the data distribution. The basis functions are constructed directly on the joint stochastic variables without requiring a tensor product structure or assuming independence of the random variables. This approach may offer greater flexibility for complex stochastic models, while simplifying implementation compared to the tensor product structures typically used in PCE to handle random vectors. This is particularly advantageous given the current state of open-source packages, where building and training neural networks can be done with just a few lines of code and extensive community support. We demonstrate the effectiveness of the proposed scheme through several numerical examples of varying complexity and provide comparisons with classical PCE.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"539 ","pages":"Article 114233"},"PeriodicalIF":3.8,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Comparison of stabilization strategies applied to scale-resolved simulations using the discontinuous Galerkin method","authors":"Amaury Bilocq,&nbsp;Maxime Borbouse,&nbsp;Nayan Levaux,&nbsp;Vincent E. Terrapon,&nbsp;Koen Hillewaert","doi":"10.1016/j.jcp.2025.114238","DOIUrl":"10.1016/j.jcp.2025.114238","url":null,"abstract":"<div><div>This study evaluates several stabilization strategies for the discontinuous Galerkin Spectral Element Method in scale-resolved simulations of compressible turbulence, with emphasis on accuracy, robustness, and computational efficiency. A novel selective entropy-stable approach (DG-ES) is introduced, which activates entropy stabilization only in localized regions to enhance robustness while minimizing dissipation. The performance of DG-ES is benchmarked against artificial viscosity (DG-AV), as well as fully entropy-stable methods based on Gauss–Legendre (ESDG-GL) and Gauss–Lobatto (ESDG-GLL) quadratures, across a range of canonical shock–turbulence interaction test cases. Results show that DG-AV performs well in scenarios involving highly mobile shocks, effectively resolving both shocks and small-scale turbulence, but its accuracy deteriorates in stationary shock configurations. Additionally, DG-AV is highly sensitive to the choice and calibration of its detector. In contrast, entropy-stable methods improve post-shock turbulence accuracy but tend to introduce spurious oscillations near shocks and incur greater computational cost. The ESDG-GL method suffers from entropy projection errors in shocklet-dominated regions, while ESDG-GLL is affected by excess dissipation due to under-integration. DG-ES achieves a favorable balance, accurately capturing turbulence with reduced sensitivity to detector calibration and maintaining competitive efficiency. However, like the ESDG-GL, it requires smaller time steps to ensure stability in the presence of strong shocks, due to the stiffness introduced by the entropy projection.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"539 ","pages":"Article 114238"},"PeriodicalIF":3.8,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Deep generalized Green’s function","authors":"Rixi Peng ,&nbsp;Juncheng Dong ,&nbsp;Jordan Malof ,&nbsp;Willie J. Padilla ,&nbsp;Vahid Tarokh","doi":"10.1016/j.jcp.2025.114235","DOIUrl":"10.1016/j.jcp.2025.114235","url":null,"abstract":"<div><div>The Green’s function has ubiquitous and unparalleled usage for the efficient solving of partial differential equations (PDEs) and analyzing systems governed by PDEs. However, obtaining a closed-form Green’s function for most PDEs on various domains is often impractical. Several approaches attempt to address this issue by approximating the Green’s function with numerical methods, but several challenges remain. We introduce the Deep Generalized Green’s Function (DGGF), a deep-learning approach that overcomes the challenges of problem-specific modeling, long computational times, and large data storage requirements associated with other approaches. Our method efficiently solves PDE problems using an integral solution format. It outperforms direct methods, such as FEM and physics-informed neural networks (PINNs). Additionally, our method alleviates the training burden, scales effectively to various spatial dimensions, and is demonstrated across a range of PDE types and domains. Unlike the direct Gaussian approximation of a Dirac delta function, our method can be used to solve PDEs in higher dimensions. Because our method directly addresses the singularity, it can be used to solve different PDEs without prior knowledge. Unlike BI-GreenNet, which is limited to PDEs with known expressions of the singular part of the Green’s function, our method does not require prior knowledge of the singularity. The results confirm the advantages of DGGFs and the benefits of Generalized Greens Functions as a novel and effective approach to solving PDEs without suffering from singularities.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"539 ","pages":"Article 114235"},"PeriodicalIF":3.8,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Probabilistic data-driven turbulence closure modeling by assimilating statistics","authors":"Sagy R. Ephrati","doi":"10.1016/j.jcp.2025.114234","DOIUrl":"10.1016/j.jcp.2025.114234","url":null,"abstract":"<div><div>A framework for deriving probabilistic data-driven closure models is proposed for coarse-grained numerical simulations of turbulence in statistically stationary state. The approach unites the <em>ideal large-eddy simulation</em> model [8] and data assimilation methods. The method requires <em>a posteriori</em> measured data to define a stochastic large-eddy simulation model, which is combined with a Bayesian statistical correction enforcing user-specified statistics extracted from high-fidelity flow snapshots. Thus, it enables computationally cheap ensemble simulations by combining knowledge of the local integration error and knowledge of desired flow statistics. An example implementation of the modeling framework is given for two-dimensional Rayleigh-Bénard convection at Rayleigh number <span><math><mrow><mi>Ra</mi><mo>=</mo><msup><mn>10</mn><mn>10</mn></msup></mrow></math></span>, incorporating stochastic perturbations and an ensemble Kalman filtering step in a non-intrusive way. Physical flow dynamics are obtained, whilst kinetic energy spectra and heat flux are accurately reproduced in long-time ensemble forecasts on coarse grids for two discretizations. The model is shown to produce accurate results with as few as 20 high-fidelity flow snapshots as input data.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"539 ","pages":"Article 114234"},"PeriodicalIF":3.8,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144757426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multi-plane moment-of-fluid interface reconstruction in 3D","authors":"Jacob Spainhour ,&nbsp;Mikhail Shashkov","doi":"10.1016/j.jcp.2025.114239","DOIUrl":"10.1016/j.jcp.2025.114239","url":null,"abstract":"<div><div>Moment-of-fluid (MOF) methods for interface reconstruction approximate the region occupied by material in each mesh element only through reference to its geometric moments. We present a 3D MOF method that represents the material (POM) in each cell as the convex intersection of the cell and multiple half-spaces, each selected to minimize the least-squares error between computed moments of the approximated material and provided reference moments.</div><div>This optimization problem is highly non-linear and non-convex, making the numerical result very sensitive to the initial guess.To create an effective initial guess in each cell, we construct an ellipsoid from 0th–2nd order reference moments such that its shape corresponds with that of the POM.Within this ellipsoid we inscribe a polyhedron, and initialize the minimization problem with the half-spaces defined by each of its faces.The inscribed polyhedron has minimally 4 faces, and using up to 3rd order moments permits optimization over up to 20 unknown values.We therefore define MOF methods that utilize 4, 5, or 6 half-spaces, correspondingly initialized with the faces of a single inscribed tetrahedron, triangular prism, or hexahedron.Stability of the non-linear optimization is further improved with a prepossessing step that normalizes the reference moments according to the axes of the reference ellipsoid.</div><div>Using this approach, the non-linear least-squares solver reliably converges to a near-global minimum from a single initial guess. We demonstrate accuracy and robustness using single-cell and multi-cell examples over a wide spectrum of geometry. In particular, we demonstrate our ability to exactly reproduce several important and complex features defined by up to four half-spaces, such as corners, filaments, filament tips, and embedded material in the cell.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"539 ","pages":"Article 114239"},"PeriodicalIF":3.8,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}