Journal of Computational Physics最新文献

{"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}

{"title":"A random forest machine learning in turbulence closure modeling for complex flows and heat transfer based on the non-equilibrium turbulence assumption","authors":"Huakun Huang ,&nbsp;Qingmo Xie ,&nbsp;Tai'an Hu ,&nbsp;Huan Hu ,&nbsp;Peng Yu","doi":"10.1016/j.jcp.2025.113995","DOIUrl":"10.1016/j.jcp.2025.113995","url":null,"abstract":"<div><div>Turbulence models generally require specific corrections or optimization of turbulence constants for predicting the complex flows and heat transfer accurately. However, the high-fidelity methods demand extensive computational costs for solving these complex phenomena. To address this issue, a random forest machine learning driven turbulence model is proposed, based on the non-equilibrium turbulence assumption and in accordance with the traditional turbulence models. The proposed framework adjusts the energy production and dissipation to achieve the non-equilibrium turbulence properties without learning the Reynolds stresses, unlike other machine learning methods. This key feature allows the model to utilize low- and high-fidelity data, broadening its applicability and solving stability. The proposed method is trained on fourteen cases, including the laminar-turbulence transition flows, the jet impingement, the swirling flow, and the reattachment flow. Many unseen cases with different physics are used to evaluate the performance of the above method in terms of prediction accuracy and solving properties. Also, a backward-facing step is estimated for the treatment of high-fidelity data. The results show that the proposed method has the potential to get more accurate results than the reference model not only in the velocity field but also in the heat transfer rate. Additionally, the proposed method consistently produces convergent and robust results, even with changes of geometries and operating conditions.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"533 ","pages":"Article 113995"},"PeriodicalIF":3.8,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143814976","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 quantum lattice algorithm with fourth-order accuracy for the one-dimensional Dirac equation","authors":"Paul J. Dellar","doi":"10.1016/j.jcp.2025.113991","DOIUrl":"10.1016/j.jcp.2025.113991","url":null,"abstract":"<div><div>The discrete time quantum walk is a quantum cellular automaton whose wavefunction comprises pairs of complex numbers assigned to uniformly spaced points on a line. The wavefunction evolves through the application of an alternating sequence of unitary operators: streaming of wavefunction values to adjacent points, and a Hadamard-type unitary matrix to blend pairs of values at individual points. Each operator generates the exact evolution due to part of the Hamiltonian for the one-dimensional Dirac equation over a finite time step. Composing these operators thus creates a discrete approximation to the Dirac equation. However, the composition of two non-commuting operators creates a global splitting error proportional to the length of the time step. The global error can be reduced from first order to second order in the time step by a unitary pre- and post-processing of the initial conditions and final output. The algorithm then becomes equivalent to a symmetric composition, a Strang splitting, between the two operators. This paper describes a fourth-order accurate composition scheme using nine stages, the fewest possible when the lengths of the time steps employed in the different stages are constrained to be integer multiples of some base time step. Each stage is itself a symmetric composition between two operators. This fourth-order scheme produces quantitatively smaller errors for a typical benchmark problem on spatial lattices with 1024 or more points, and shows the expected fourth-order convergence on sufficiently fine lattices. It has greater accuracy, over sufficiently long times, than three better-known fourth-order composition schemes using fewer stages, but with lengths related by irrational coefficients. The truncation error for plane-wave solutions is due to an operator that separates into a resonant part proportional to the Hamiltonian, and a non-resonant part orthogonal to the Hamiltonian. The resonant part commutes with the exact evolution operator, so its error accumulates to grow linearly with time. The orthogonal part produces oscillations that remain bounded over many time steps. The nine-stage integer scheme has the smallest resonant truncation error of the four schemes, despite being the only scheme that can be implemented using local operations. The other schemes implement streaming by irrational fractions of the lattice spacing using discrete Fourier transforms.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"533 ","pages":"Article 113991"},"PeriodicalIF":3.8,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143828204","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 preconditioning method with the Generalized−α time discretization for dynamic crack propagations based on XFEM","authors":"Xingding Chen ,&nbsp;Xiao-Chuan Cai","doi":"10.1016/j.jcp.2025.113992","DOIUrl":"10.1016/j.jcp.2025.113992","url":null,"abstract":"<div><div>In this paper, we consider the efficient simulations of dynamic crack propagations based on the Extended Finite Element Method (XFEM). For the time discretization, the <em>Generalized</em>−<em>α</em> method is adopted to instead of the commonly used Newmark method in engineering, and the non physical numerical oscillations can be reduced in the <em>Generalized</em>−<em>α</em> method by choosing appropriate parameters. Moreover, in order to accelerate the convergence rate of the linear system arising from XFEM, a special crack-tip domain decomposition preconditioning method is developed, in which the computational domain is decomposed into regular subdomains and crack tip subdomains. To construct the Schwarz preconditioners, the subproblems are solved exactly in the crack tip subdomains and inexactly in the regular subdomains by an incomplete LU factorization. When cracks propagate, only the subdomains around the crack tips are updated, and all the other regular subdomains remain unchanged, which can save the computational cost significantly. The numerical experiments verify that the proposed preconditioning algorithm works well for the simulations of dynamic crack propagations.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"533 ","pages":"Article 113992"},"PeriodicalIF":3.8,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143823453","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}