Journal of Computational Physics最新文献

{"title":"A flexible GMRES solver with reduced order model enhanced synthetic acceleration preconditioner for parametric radiative transfer equation","authors":"Zhichao Peng","doi":"10.1016/j.jcp.2025.114004","DOIUrl":"10.1016/j.jcp.2025.114004","url":null,"abstract":"<div><div>Parametric radiative transfer equation (RTE) occurs in multi-query applications such as uncertainty quantification, inverse problems, and sensitivity analysis, which require solving RTE multiple times for a range of parameters. Consequently, efficient iterative solvers are highly desired.</div><div>Classical Synthetic Acceleration (SA) preconditioners for RTE build on low order approximations to an ideal kinetic correction equation such as its diffusion limit in Diffusion Synthetic Acceleration (DSA). Their performance depends on the effectiveness of the underlying low order approximation. In addition, they do not leverage low rank structures with respect to the parameters of the parametric problem.</div><div>To address these issues, we proposed a ROM-enhanced SA strategy, called ROMSAD, under the Source Iteration framework in Peng (2024). In this paper, we further extend the ROMSAD preconditioner to flexible general minimal residual method (FGMRES). The main new advancement is twofold. First, after identifying the ideal kinetic correction equation within the FGMRES framework, we reformulate it into an equivalent form, allowing us to develop an iterative procedure to construct a ROM for this ideal correction equation without directly solving it. Second, we introduce a greedy algorithm to build the underlying ROM for the ROMSAD preconditioner more efficiently.</div><div>Our numerical examples demonstrate that FGMRES with the ROMSAD preconditioner (FGMRES-ROMSAD) is more efficient than GMRES with the right DSA preconditioner. Furthermore, when the underlying ROM in ROMSAD is not highly accurate, FGMRES-ROMSAD exhibits greater robustness compared to Source Iteration accelerated by ROMSAD.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"534 ","pages":"Article 114004"},"PeriodicalIF":3.8,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143838001","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":"Multiscale extended finite element method (MS-XFEM): Analysis of fractured geological formations under compression","authors":"Fanxiang Xu ,&nbsp;Hadi Hajibeygi ,&nbsp;Lambertus J. Sluys","doi":"10.1016/j.jcp.2025.113998","DOIUrl":"10.1016/j.jcp.2025.113998","url":null,"abstract":"<div><div>The activation of fracture networks poses significant risks and raises safety concerns for projects involving such geological structures. Consequently, an accurate and efficient simulation strategy is essential for modeling highly fractured subsurface formations. While the extended finite element method (XFEM), coupled with the penalty method, effectively models slip-stick conditions along fracture surfaces and fracture propagation under compression, its efficiency declines when handling dense fracture networks. To address this challenge, a multiscale XFEM (MS-XFEM) approach is developed and presented. MS-XFEM approximates fine-scale displacement field by interpolating solutions on a coarser-scale mesh using algebraically constructed basis functions. All extra degrees of freedom (DOFs) are incorporated within the basis functions matrix, rendering the coarse-scale system a standard finite element-based system. In each propagation step, basis functions are algebraically and locally updated to capture fracture propagation. Through four proof-of-concept test cases, the accuracy and efficiency of MS-XFEM in simulating fractured geological formations are demonstrated, emphasizing its potential for real-world applications.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"533 ","pages":"Article 113998"},"PeriodicalIF":3.8,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143834672","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":"GoRINNs: Godunov-Riemann informed neural networks for learning hyperbolic conservation laws","authors":"Dimitrios G. Patsatzis ,&nbsp;Mario di Bernardo ,&nbsp;Lucia Russo ,&nbsp;Constantinos Siettos","doi":"10.1016/j.jcp.2025.114002","DOIUrl":"10.1016/j.jcp.2025.114002","url":null,"abstract":"<div><div>We introduce Godunov-Riemann Informed Neural Networks (GoRINNs), a hybrid framework that combines shallow neural networks with high-resolution finite volume (FV) Godunov-type schemes to solve inverse problems in nonlinear conservation laws. In contrast to other proposed - based on deep neural networks - schemes, that learn numerical fluxes of conservative FV methods or model parameters, GoRINNs directly learn physical flux functions using <em>numerical analysis- informed</em> shallow neural networks, preserving conservation laws while reducing computational complexity. Using second-order accurate schemes with flux limiters and approximate Riemann solvers (satisfying the Rankine-Hugoniot condition), GoRINNs demonstrate high accuracy across benchmark problems such as Burgers', Shallow Water, Lighthill-Whitham-Richards, and Payne-Whitham traffic flow models, showcasing a robust and interpretable approach to integrating machine learning with classical numerical methods. An uncertainty quantification was also conducted by evaluating training performance variability across multiple realizations, each with different randomly sampled datasets and initial parameter values.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"534 ","pages":"Article 114002"},"PeriodicalIF":3.8,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143854655","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":"Data-driven stochastic closure modeling via conditional diffusion model and neural operator","authors":"Xinghao Dong,&nbsp;Chuanqi Chen,&nbsp;Jin-Long Wu","doi":"10.1016/j.jcp.2025.114005","DOIUrl":"10.1016/j.jcp.2025.114005","url":null,"abstract":"<div><div>Closure models are widely used in simulating complex multiscale dynamical systems such as turbulence and the earth system, for which direct numerical simulation that resolves all scales is often too expensive. For those systems without a clear scale separation, deterministic and local closure models usually lack enough generalization capability, which limits their performance in many real-world applications. In this work, we propose a data-driven modeling framework for constructing stochastic and non-local closure models via conditional diffusion model and neural operator. Specifically, the Fourier neural operator is incorporated into a score-based diffusion model, which serves as a data-driven stochastic closure model for complex dynamical systems governed by partial differential equations (PDEs). We also demonstrate how accelerated sampling methods can improve the efficiency of the data-driven stochastic closure model. The results show that the proposed methodology provides a systematic approach via generative machine learning techniques to construct data-driven stochastic closure models for multiscale dynamical systems with continuous spatiotemporal fields.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"534 ","pages":"Article 114005"},"PeriodicalIF":3.8,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143843602","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":"Petrov-Galerkin model reduction for thermochemical nonequilibrium gas mixtures","authors":"Ivan Zanardi,&nbsp;Alberto Padovan,&nbsp;Daniel J. Bodony,&nbsp;Marco Panesi","doi":"10.1016/j.jcp.2025.113999","DOIUrl":"10.1016/j.jcp.2025.113999","url":null,"abstract":"<div><div>State-specific thermochemical collisional models are crucial to accurately describe the physics of systems involving nonequilibrium plasmas, but they are also computationally expensive and impractical for large-scale, multi-dimensional simulations. Historically, computational cost has been mitigated by using empirical and physics-based arguments to reduce the complexity of the governing equations. However, the resulting models are often inaccurate and they fail to capture the important features of the original physics. Additionally, the construction of these models is often impractical, as it requires extensive user supervision and time-consuming parameter tuning. In this paper, we address these issues through an easily implementable and computationally efficient model reduction pipeline based on the Petrov-Galerkin projection of the nonlinear kinetic equations onto a low-dimensional subspace. Our approach is justified by the observation that kinetic systems in thermal nonequilibrium tend to exhibit low-rank dynamics that rapidly drive the state towards a low-dimensional subspace that can be exploited for reduced-order modeling. Furthermore, despite the nonlinear nature of the governing equations, we observe that the dynamics of these systems evolve on subspaces that can be accurately identified using the linearized equations about thermochemical equilibrium steady states, and we shall see that this allows us to significantly reduce the cost associated with the construction of the model. The approach is demonstrated on two distinct thermochemical systems: a rovibrational collisional model for the O₂-O system, and a vibrational collisional model for the combined O₂-O and O₂-O₂ systems. Our method achieves high accuracy, with relative errors of less than 1% for macroscopic quantities (i.e., moments) and 10% for microscopic quantities (i.e., energy levels population), while also delivering excellent compression rates and speedups, outperforming existing state-of-the-art techniques.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"533 ","pages":"Article 113999"},"PeriodicalIF":3.8,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143823454","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":"A family of provable Lp stable and boundedness preserving high order Runge-Kutta discrete exterior calculus discretization for conservative phase field method","authors":"Minmiao Wang","doi":"10.1016/j.jcp.2025.114000","DOIUrl":"10.1016/j.jcp.2025.114000","url":null,"abstract":"<div><div>Conservative phase field (PF) equation and its axisymmetric version are expressed under the discrete exterior calculus (DEC) framework. The boundedness proof <span><span>[1]</span></span> of conservative PF method in the DEC framework is extended to its axisymmetric version. A sufficient condition for boundedness of conservative PF method and its axisymmetric version with Runge-Kutta (RK) time integration scheme has been proved. By this sufficient condition, the boundedness proof of the method for Euler forward time integration scheme has been extended to high order RK time integration schemes, such as Heun's method, classical third order RK method and a five stages fourth order RK method, which is independent of spatial discretization method, i.e. not limited to the DEC framework. The conservation and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> stability for <span><math><mn>1</mn><mo>≤</mo><mi>p</mi><mo>≤</mo><mo>∞</mo></math></span> of conservative PF method and its axisymmetric version are also proved in the DEC framework. Several two phase advection simulations on 2D Riemannian manifolds and its axisymmetric version for interface capturing are presented, which verify the proved properties of phase field, i.e. conservation, <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> stability and boundedness.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"533 ","pages":"Article 114000"},"PeriodicalIF":3.8,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143825557","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":"Adjoint lattice kinetic scheme for topology optimization in fluid problems","authors":"Yuta Tanabe ,&nbsp;Kentaro Yaji ,&nbsp;Kuniharu Ushijima","doi":"10.1016/j.jcp.2025.114001","DOIUrl":"10.1016/j.jcp.2025.114001","url":null,"abstract":"<div><div>This paper proposes a topology optimization method for non-thermal and thermal fluid problems using the Lattice Kinetic Scheme (LKS). LKS, which is derived from the Lattice Boltzmann Method (LBM), requires only macroscopic values, such as fluid velocity and pressure, whereas LBM requires velocity distribution functions, thereby reducing memory requirements. The proposed method computes design sensitivities based on the adjoint variable method, and the adjoint equation is solved in the same manner as LKS; thus, we refer to it as the <em>Adjoint Lattice Kinetic Scheme</em> (ALKS). A key contribution of this method is the proposed approximate treatment of boundary conditions for the adjoint equation, which is challenging to apply directly due to the characteristics of LKS boundary conditions. We demonstrate numerical examples for steady and unsteady problems involving non-thermal and thermal fluids, and the results are physically meaningful and consistent with previous research, exhibiting similar trends in parameter dependencies, such as the Reynolds number. Furthermore, the proposed method reduces memory usage by up to 75% compared to the conventional LBM in an unsteady thermal fluid problem.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"533 ","pages":"Article 114001"},"PeriodicalIF":3.8,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143828660","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":"Tensor decomposition-based neural operator with dynamic mode decomposition for parameterized time-dependent problems","authors":"Yuanhong Chen ,&nbsp;Yifan Lin ,&nbsp;Xiang Sun ,&nbsp;Chunxin Yuan ,&nbsp;Zhen Gao","doi":"10.1016/j.jcp.2025.113996","DOIUrl":"10.1016/j.jcp.2025.113996","url":null,"abstract":"<div><div>Deep operator networks (DeepONets), as a powerful tool to approximate nonlinear mappings between different function spaces, have gained significant attention recently for applications in modeling parameterized partial differential equations. However, limited by the poor extrapolation ability of purely data-driven neural operators, these models tend to fail in predicting solutions with high accuracy outside the training time interval. To address this issue, a novel operator learning framework, TDMD-DeepONet, is proposed in this work, based on tensor train decomposition (TTD) and dynamic mode decomposition (DMD). We first demonstrate the mathematical agreement of the representation of TTD and DeepONet. Then the TTD is performed on a higher-order tensor consisting of given spatial-temporal snapshots collected under a set of parameter values to generate the parameter-, space- and time-dependent cores. DMD is then utilized to model the evolution of the time-dependent core, which is combined with the space-dependent cores to represent the trunk net. Similar to DeepONet, the branch net employs a neural network, with the parameters as inputs and outputs merged with the trunk net for prediction. Furthermore, the feature-enhanced TDMD-DeepONet (ETDMD-DeepONet) is proposed to improve the accuracy, in which an additional linear layer is incorporated into the branch network compared with TDMD-DeepONet. The input to the linear layer is obtained by projecting the initial conditions onto the trunk network. The proposed methods' good performance is demonstrated through several classical examples, in which the results demonstrate that the new methods are more accurate in forecasting solutions than the standard DeepONet.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"533 ","pages":"Article 113996"},"PeriodicalIF":3.8,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143823455","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":"New efficient data-driven reduced order models for oscillatory dynamics","authors":"Filippo Terragni ,&nbsp;Jose M. Vega","doi":"10.1016/j.jcp.2025.113997","DOIUrl":"10.1016/j.jcp.2025.113997","url":null,"abstract":"<div><div>A new methodology is presented to construct data-driven reduced order models able to efficiently approximate periodic attractors of dynamical systems depending on one or more parameters. In an offline stage, some sets of temporally equidistant snapshots are computed for a limited number of parameter values. Such computation is performed using a standard numerical solver when the problem is governed by a low-dimensional system of ordinary differential equations. If, instead, the underlying dynamical system is high-dimensional (i.e., governed by partial differential equations), the snapshots are computed relying on a physics-based reduced order model obtained via proper orthogonal decomposition plus Galerkin projection. The snapshot sets are then treated using a recent, very robust data processing method, the higher order dynamic mode decomposition, which permits describing the periodic attractors as synchronized expansions in terms of spatial modes and associated temporal frequencies. Modes and frequencies are effectively interpolated at new parameter values, different from those involved in the offline stage. The online operation of the resulting data-driven reduced order model is very fast, since it requires carrying out only a small number of algebraic computations. The performance of the new method is tested for two representative dynamical systems, namely the three-dimensional Lorenz system and a high-dimensional system describing the electron transport in a semiconductor superlattice.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"533 ","pages":"Article 113997"},"PeriodicalIF":3.8,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143828771","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":"Sequential data assimilation for PDEs using shape-morphing solutions","authors":"Zachary T. Hilliard,&nbsp;Mohammad Farazmand","doi":"10.1016/j.jcp.2025.113994","DOIUrl":"10.1016/j.jcp.2025.113994","url":null,"abstract":"<div><div>Shape-morphing solutions (also known as evolutional deep neural networks, reduced-order nonlinear solutions, and neural Galerkin schemes) are a new class of methods for approximating the solution of time-dependent partial differential equations (PDEs). Here, we introduce a sequential data assimilation method for incorporating observational data in a shape-morphing solution (SMS). Our method takes the form of a predictor-corrector scheme, where the observations are used to correct the SMS parameters using Newton-like iterations. Between observation points, the SMS equations—a set of ordinary differential equations— are used to evolve the solution forward in time. We prove that, under certain conditions, the data assimilated SMS (DA-SMS) converges uniformly towards the true state of the system. We demonstrate the efficacy of DA-SMS on three examples: the nonlinear Schrödinger equation, the Kuramoto–Sivashinsky equation, and a two-dimensional advection-diffusion equation. Our numerical results suggest that DA-SMS converges with relatively sparse observations and a single iteration of the Newton-like method.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"533 ","pages":"Article 113994"},"PeriodicalIF":3.8,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143814977","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}