Journal of Computational Physics最新文献

{"title":"Score-based neural ordinary differential equations for computing mean field control problems","authors":"Mo Zhou ,&nbsp;Stanley Osher ,&nbsp;Wuchen Li","doi":"10.1016/j.jcp.2025.114369","DOIUrl":"10.1016/j.jcp.2025.114369","url":null,"abstract":"<div><div>Classical neural ordinary differential equations (ODEs) are powerful tools for approximating the log-density functions in high-dimensional spaces along trajectories, where neural networks parameterize the velocity fields. We specify a system of neural differential equations representing first- and second-order score functions along trajectories based on deep neural networks. We reformulate the mean field control (MFC) problem with individual noises into an unconstrained optimization problem framed by the proposed neural ODE system. Additionally, we introduce a novel regularization term to enforce characteristics of viscous Hamilton–Jacobi–Bellman (HJB) equations to be satisfied based on the evolution of the second-order score function. Examples include regularized Wasserstein proximal operators (RWPOs), probability flow matching of Fokker–Planck (FP) equations, and linear quadratic (LQ) MFC problems, which demonstrate the effectiveness and accuracy of the proposed method.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114369"},"PeriodicalIF":3.8,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097575","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":"Monte Carlo physics-informed neural networks for multiscale heat conduction via phonon Boltzmann transport equation","authors":"Qingyi Lin ,&nbsp;Chuang Zhang ,&nbsp;Xuhui Meng ,&nbsp;Zhaoli Guo","doi":"10.1016/j.jcp.2025.114364","DOIUrl":"10.1016/j.jcp.2025.114364","url":null,"abstract":"<div><div>The phonon Boltzmann transport equation (BTE) is widely used for the description of multiscale heat conduction (from nm to <span><math><mi>μ</mi></math></span>m or mm) in solid materials. Developing numerical approaches to solve this equation is challenging since it is a 7-dimensional integral-differential equation. In this work, we propose the Monte Carlo physics-informed neural networks (MC-PINNs), which provide an effective way to combat the <em>“curse of dimensionality”</em> in solving the phonon Boltzmann transport equation for modeling multiscale heat conduction in solid materials. In MC-PINNs, we utilize a deep neural network to approximate the solution to the BTE and encode the BTE as well as the corresponding boundary/initial conditions using automatic differentiation. In addition, we propose a novel two-step sampling approach to address the issues of inefficiency and inaccuracy in the widely used sampling methods in PINNs. In particular, we first randomly sample a certain number of points in the temporal-spatial space (Step I) and then draw another number of points randomly in the solid angular space (Step II). The training points at each step are constructed based on the data drawn from the above two steps using the tensor product. The two-step sampling strategy enables the MC-PINNs (1) to model the heat conduction from ballistic to diffusive regimes, and (2) to be more memory efficient compared to the conventional numerical solvers or existing PINNs for BTE. A series of numerical examples, including quasi-one-dimensional (quasi-1D) steady/unsteady heat conduction in a film, and the heat conduction in quasi-two-dimensional (quasi-2D) and three-dimensional (3D) domains, are conducted to justify the effectiveness of the MC-PINNs for heat conduction spanning diffusive and ballistic regimes. Finally, we perform a comparison on the computational time and the memory usage between the MC-PINNs and one of the state-of-the-art numerical methods to demonstrate the potential of MC-PINNs for large-scale problems in real-world applications.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114364"},"PeriodicalIF":3.8,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097566","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":"The direct discontinuous Galerkin method with explicit-implicit-null time discretizations for the compressible Navier-Stokes equations","authors":"Yumiao Li ,&nbsp;Tiegang Liu ,&nbsp;Kui Cao ,&nbsp;Weixiong Yuan ,&nbsp;Yin Yang","doi":"10.1016/j.jcp.2025.114362","DOIUrl":"10.1016/j.jcp.2025.114362","url":null,"abstract":"<div><div>In this paper, we discuss the direct discontinuous Galerkin (DDG) method combined with two specific high-order explicit-implicit-null (EIN) time discretizations for solving the compressible Navier-Stokes (CNS) equations. This paper presents the EIN method whose basic idea is to add and subtract an identical Laplacian operator on the right-hand side of the considered equations, and then apply the implicit-explicit (IMEX) time-marching method to the equivalent equations. More specifically, the added term is treated implicitly while the rest of the terms are treated explicitly. The EIN method is designed to eliminate the severe time step restriction associated with explicit methods, without requiring any nonlinear iterative solver. Based on the Fourier method, we analyze the stability of the EIN-DDG schemes for the one-dimensional CNS equations, and further validate numerically that the stability criteria can be extended to the two-dimensional case. The numerical results demonstrate that our schemes achieve both stability and optimal orders of accuracy under a relaxed time-step restriction, provided that an appropriate coefficient is used for the Laplacian operator. Furthermore, the computational efficiency of different time discretizations, such as the strong stability-preserving Runge-Kutta (SSP-RK) and EIN methods, is evaluated and compared, demonstrating the advantages of the proposed schemes.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114362"},"PeriodicalIF":3.8,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097569","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":"Adaptive subcell shock capturing for discontinuous galerkin methods in high speed flows I. Two-dimensional mixed meshes","authors":"Taegeon Kim ,&nbsp;Juhyun Kim ,&nbsp;Hojun You ,&nbsp;Chongam Kim","doi":"10.1016/j.jcp.2025.114361","DOIUrl":"10.1016/j.jcp.2025.114361","url":null,"abstract":"<div><div>We propose a novel subcell shock capturing for the discontinuous Galerkin (DG) method to simulate high-speed flows involving strong physical discontinuities. High-order simulations of hypersonic flows have remained challenging, primarily due to the susceptibility of high-order methods to numerical oscillations near strong physical discontinuities. While the posteriori subcell limiting demonstrated some desirable features to hypersonic flow simulations, we observe that it also suffers from Gibbs-Wilbraham (GW) oscillations when the subcell finite volume method (FVM) solutions are used to reconstruct a high-order solution, leading to the loss of accuracy and robustness, especially in steady-state simulations. To address this issue, we firstly design a novel detection process for GW oscillations at reconstruction step. Analyzing the nature of reconstructed polynomials exhibiting GW oscillations, we obtain the conditions to design the indicators for boundary and interior oscillations, from which a process to detect reconstruction oscillations is formulated. We then retain the subcell FVM solutions if reconstruction oscillations are persistent at reconstruction step. At the interface boundary of DG cell and FVM cell, the flux coupling between DG solutions and subcell FVM solutions is realized by evaluating the numerical fluxes on subcell boundary points using the direct reconstruction method (DRM). As a result, the DG-FVM solver facilitates the simultaneous update of the subcell FVM solutions and neighboring DG solutions at each time step. Extensive high-order simulations of high-speed flows up to a free stream Mach number of 20, including hypersonic thermochemical equilibrium flows and hypersonic shock-shock interactions, are conducted to assess and verify the performance of the proposed subcell shock-capturing strategy, called adaptive subcell limiting process (ASLP). The numerical results demonstrate the outstanding accuracy and robustness in capturing physical discontinuities across a wide range of high-speed flows, even on curved-mixed meshes. Moreover, the proposed method shows improved convergence of aerodynamic coefficients by effectively damping temporal oscillations induced by shock waves.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114361"},"PeriodicalIF":3.8,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097571","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":"Non-Markovian intelligent dissipative particle dynamics integrated with machine learning for enhancing coarse-grained simulations","authors":"Shuyuan Zhang ,&nbsp;Ting Ye ,&nbsp;Baocai Jing ,&nbsp;Huiqi Yin ,&nbsp;Dingyi Pan","doi":"10.1016/j.jcp.2025.114356","DOIUrl":"10.1016/j.jcp.2025.114356","url":null,"abstract":"<div><div>We propose a machine learning-based coarse-grained method that integrates molecular dynamics (MD) with dissipative particle dynamics (DPD) to address the limitations of the Markovian approximation in systems where particle motion and fluctuating forces exhibit overlapping time scales. Our approach, termed non-Markovian intelligent dissipative particle dynamics (NM-IDPD), utilizes MD data to train a neural network capable of predicting both conservative and dissipative forces within the DPD framework, effectively accounting for non-Markovian effects. We have also incorporated a pressure constraint mechanism into the neural network to accurately capture the system pressure, which is a challenging issue for most traditional coarse-grained methods. Through applications to star polymers, methane, and water systems, NM-IDPD has demonstrated good performance in replicating both the static and dynamic properties of simulated systems across various time scales. This advancement offers a promising avenue for material dynamics simulation, enhancing the accuracy and efficiency of computational modeling in complex systems.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114356"},"PeriodicalIF":3.8,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145057315","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":"FENN: Feature-enhanced neural network for solving partial differential equations involving fluid mechanics","authors":"Jiahao Song ,&nbsp;Wenbo Cao ,&nbsp;Weiwei Zhang","doi":"10.1016/j.jcp.2025.114370","DOIUrl":"10.1016/j.jcp.2025.114370","url":null,"abstract":"<div><div>Physics-informed neural networks (PINNs) have shown remarkable prospects in solving forward and inverse problems involving partial differential equations (PDEs). However, PINNs still face the challenge of high computational cost in solving strongly nonlinear PDEs involving fluid dynamics. In this study, inspired by the input design in surrogate modeling, we propose a feature-enhanced neural network. By introducing geometric features including distance and angle or physical features including the solution of the potential flow equation in the inputs of PINNs, FENN can learn the flow more easily, resulting in better performance in terms of both accuracy and efficiency. We establish the feature networks in advance to avoid the invalid PDE loss in FENN caused by neglecting the partial derivatives of the features with respect to space-time coordinates. Through five numerical experiments involving forward, inverse, and parametric problems, we verify that FENN generally reduces the computational cost of PINNs and advanced algorithm by approximately four times and two times, respectively. In addition, it is demonstrated by the numerical experiments that the proposed method can reduce the number of observed data for the inverse problem and successfully solve the parametric problem where PINNs fail.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114370"},"PeriodicalIF":3.8,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097586","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":"FAMAW-PINN: A physics-informed neural network integrating adaptive loss weighting with firefly-inspired adaptive point movement","authors":"Yi Wang,&nbsp;Xingyu Qiu,&nbsp;Qiuyan Pei,&nbsp;Junhui Wang,&nbsp;Peng Zhang,&nbsp;Xin Bai","doi":"10.1016/j.jcp.2025.114363","DOIUrl":"10.1016/j.jcp.2025.114363","url":null,"abstract":"<div><div>The Physics-Informed Neural Network (PINN) uses automatic differentiation to embed the governing partial differential equation (PDE) into the neural network’s loss function as physical constraints, providing a powerful approach for solving forward and inverse PDE problems. During training, physical loss calculation relies on predefined spatiotemporal collocation points. However, when solving equations with steep gradients or singularities, conventional fixed or randomly distributed training points often fail to capture critical solution structures, reducing PINN’s prediction accuracy. Inspired by firefly phototaxis, this paper proposes a bio-inspired dynamic training point movement strategy named firefly adaptive collocation point movement (FAM). Its core mechanism uses the neural network’s residual or gradient as the \"brightness\" signal (analogous to firefly perception) to drive training points toward high-residual or high-gradient regions in the computational domain, thereby capturing key physical features. To further enhance PINN’s performance, we integrate FAM with an adaptive loss weighting technique (AW), forming a new adaptive strategy termed FAMAW. This strategy dynamically balances the migration of training points and the weighting of loss terms. Numerical experiments and comparisons with established methods demonstrate the significant superiority of FAMAW-PINN and its marked improvement in solution accuracy.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114363"},"PeriodicalIF":3.8,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145047965","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":"Species weighting scheme in direct simulation Monte Carlo applied to jet plume simulations","authors":"V. Charton ,&nbsp;E. Yamaoka ,&nbsp;T. Morimoto ,&nbsp;K. Kinefuchi","doi":"10.1016/j.jcp.2025.114354","DOIUrl":"10.1016/j.jcp.2025.114354","url":null,"abstract":"<div><div>In the conventional Direct Simulation Monte Carlo (DSMC) method, large density variation among the flow species involves an enormous quantity of numerical particles representing the denser species to enable the simulation of the trace ones. In this work, a Species Weighting Scheme method is used to define different ratios between numerical and physical particles depending on the species they represent, and simulate both major and trace species accurately while reducing the computational time and the memory cost. Collision momentum, energy conservation, and flow transport properties, are verified by comparing them with conventional DSMC on one cell, Couette and Fourier flow simulations. The novelty of this study is to evaluate the influence of the species weight settings and the use of enhanced pair collision selection methods using academic and more complex cases involving nozzle free jet expansion and jet impingement into a conical surface. The Species Weighting Scheme shows excellent agreement with conventional DSMC for a major to trace species numerical particle ratio of 10 and deviation below this threshold. Furthermore, using enhanced pair collision selection allowed us to obtain accurate results even for low ratios down to 2 or 1, leading to a significant computational time reduction by a factor of 7.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114354"},"PeriodicalIF":3.8,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097567","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":"Time-integration of Gaussian variational approximation for the magnetic Schrödinger equation","authors":"Malik Scheifinger ,&nbsp;Kurt Busch ,&nbsp;Marlis Hochbruck ,&nbsp;Caroline Lasser","doi":"10.1016/j.jcp.2025.114349","DOIUrl":"10.1016/j.jcp.2025.114349","url":null,"abstract":"<div><div>In the present paper we consider the semiclassical magnetic Schrödinger equation, which describes the dynamics of charged particles under the influence of an electro-magnetic field. The solution of the time-dependent Schrödinger equation is approximated by a single Gaussian wave packet via the time-dependent Dirac–Frenkel variational principle. For the approximation we use ordinary differential equations of motion for the parameters of the variational solution and extend the second-order Boris algorithm for classical mechanics to the quantum mechanical case. In addition, we propose a modified version of the classical fourth-order Runge–Kutta method. Numerical experiments explore parameter convergence and geometric properties. Moreover, we benchmark against the analytical solution of the Penning trap.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114349"},"PeriodicalIF":3.8,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145045131","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":"Boundary integral formulations for flexural wave scattering in thin plates","authors":"Peter Nekrasov ,&nbsp;Zhaosen Su ,&nbsp;Travis Askham ,&nbsp;Jeremy G. Hoskins","doi":"10.1016/j.jcp.2025.114355","DOIUrl":"10.1016/j.jcp.2025.114355","url":null,"abstract":"<div><div>In this paper, we develop second kind integral formulations for flexural wave scattering problems involving the clamped, supported, and free plate boundary conditions. While the clamped plate problem can be solved with layer potentials developed for the biharmonic equation, the free plate problem is more difficult due to the order and complexity of the boundary conditions. In this work, we describe a representation for the free plate problem that uses the Hilbert transform to cancel singularities of certain layer potentials, ultimately leading to a Fredholm integral equation of the second kind. Additionally, for the supported plate problem, we improve on an existing representation to obtain a second kind integral equation formulation. With these representations it is possible to solve flexural wave scattering problems with high-order-accurate methods, examine the far field patterns of scattering objects, and solve large problems involving multiple scatterers.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114355"},"PeriodicalIF":3.8,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145047966","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}