Journal of Computational Physics最新文献

{"title":"Multi-head physics-informed neural networks for learning functional priors and uncertainty quantification","authors":"Zongren Zou,&nbsp;George Em Karniadakis","doi":"10.1016/j.jcp.2025.113947","DOIUrl":"10.1016/j.jcp.2025.113947","url":null,"abstract":"<div><div>In numerous applications, the integration of prior knowledge and historical information is essential, particularly for tasks requiring the solution of ordinary or partial differential equations (ODEs/PDEs) in data-sparse or noisy environments. For instance, achieving accurate solutions to time-dependent PDEs with limited initial condition measurements necessitates an effective strategy for embedding prior knowledge. Hard-parameter sharing architectures in neural networks (NNs) have demonstrated success in both traditional and scientific machine learning domains, facilitating the learning of informative representations.</div><div>In this study, we introduce a novel, yet efficient, method to enhance physics-informed neural networks (PINNs) by incorporating a multi-head structure that enables the learning of functional priors from both empirical data and governing physical laws. This prior information can then be used to address data sparsity and high-level noise in solving ODE/PDE problems with uncertainty quantification (UQ). The approach, termed Multi-Head PINN (MH-PINN), consists of a shared <em>body</em> NN and multiple <em>head</em> NNs, each corresponding to an individual PINN instance. Our framework for functional prior learning is carried out in two stages: (1) training the MH-PINNs to develop a shared body NN alongside multiple head NNs, and (2) employing these trained head NNs to estimate a prior distribution through a normalizing flow-based density estimator.</div><div>The learned functional prior can then be applied as a regularization mechanism in deterministic contexts or as an informative prior within a Bayesian inference framework, aiding in the resolution of subsequent ODE/PDE tasks. We evaluate the efficacy of MH-PINNs across five benchmark problems, including a high-dimensional parametric PDE, all characterized by data sparsity or substantial noise levels. Our findings reveal that MH-PINNs deliver accurate solutions and robust UQ, demonstrating adaptability across a range of complex and challenging scenarios.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113947"},"PeriodicalIF":3.8,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686399","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 Bayesian extension to FEMU for identification of spatially varying stochastic elastic properties from digital image and volume correlation measurements","authors":"Armand Touminet ,&nbsp;Sabine Cantournet ,&nbsp;Victor Fabre ,&nbsp;Pierre Kerfriden","doi":"10.1016/j.jcp.2025.113946","DOIUrl":"10.1016/j.jcp.2025.113946","url":null,"abstract":"<div><div>We present a Bayesian framework for the identification of stochastic and spatially varying elastic parameters using noisy displacement observations obtained with DIC or DVC trials. Our method is a generalization of identification procedures such as FEMU or I-DIC to materials with spatially varying properties and stochastic mesostructures, where the elasticity tensor is modelled as a parametric non-Gaussian random field. Both the elastic parameters and the parameters of the random field model are identified jointly from the displacement measurement. We formulate the approach as a hierarchical Bayesian PDE-constrained inverse problem and MAP estimates are obtained through gradient based optimization. We resort to an adjoint based formulation and leverage automatic differentiation to derive the parameter sensitivities. We show how modelling unknown parameters with Gaussian Random Fields leads to a natural Bayesian regularization and leverage the use of Whittle-Matérn priors. Covariance parameter estimation is discussed, and we propose an empirical Bayes approach to avoid numerical shortcomings related to a standard hierarchical model. A set of numerical examples is presented to assess the performance of the proposed method, based on synthetic data generated through Matérn Random fields. In particular, we show how data noise is naturally modelled by the Bayesian formulation and impacts spatial covariance of identified parameters.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113946"},"PeriodicalIF":3.8,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A mesh-constrained discrete point method for incompressible flows with moving boundaries","authors":"Takeharu Matsuda ,&nbsp;Satoshi Ii","doi":"10.1016/j.jcp.2025.113945","DOIUrl":"10.1016/j.jcp.2025.113945","url":null,"abstract":"<div><div>Particle-based methods are a practical tool in computational fluid dynamics, and novel types of methods have been proposed. However, widely developed Lagrangian-type formulations suffer from the nonuniform distribution of particles, which is enhanced over time and result in problems in computational efficiency and parallel computations. To mitigate these problems, a mesh-constrained discrete point (MCD) method was developed for stationary boundary problems (Matsuda et al., 2022). Although the MCD method is a meshless method that uses moving least-squares approximation, the arrangement of particles (or discrete points (DPs)) is specialized so that their positions are constrained in a background mesh to obtain a closely uniform distribution. This achieves a reasonable approximation for spatial derivatives with compact stencils without encountering any ill-posed condition and leads to good performance in terms of computational efficiency. In this study, a novel meshless method based on the MCD method for incompressible flows with moving boundaries is proposed. To ensure the mesh constraint of each DP in moving boundary problems, a novel updating algorithm for the DP arrangement is developed so that the position of DPs is not only rearranged but the DPs are also reassigned the role of being on the boundary or not. The proposed method achieved reasonable results in numerical experiments for well-known moving boundary problems.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"532 ","pages":"Article 113945"},"PeriodicalIF":3.8,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143696115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Moment-preserving Monte-Carlo Coulomb collision method for particle codes","authors":"Justin Ray Angus,&nbsp;Yichen Fu,&nbsp;Vasily Geyko,&nbsp;Dave Grote,&nbsp;David Larson","doi":"10.1016/j.jcp.2025.113927","DOIUrl":"10.1016/j.jcp.2025.113927","url":null,"abstract":"<div><div>Binary-pairing Monte-Carlo methods are widely used in particle-in-cell codes to capture effects of small angle Coulomb collisions. These methods preserve momentum and energy exactly when the simulation particles have equal weights. However, when the interacting particles are of varying weight, these physical conservation laws are only preserved on average. Here, we 1) extend these methods to weighted particles such that the scattering physics is correct on average, and 2) describe a new method for adjusting the particle velocities post scatter to restore exact conservation of momentum and energy. The efficacy of the model is illustrated with various test problems.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113927"},"PeriodicalIF":3.8,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686396","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":"Structure-preserving parametric finite element methods for simulating axisymmetric solid-state dewetting problems with anisotropic surface energies","authors":"Meng Li,&nbsp;Chunjie Zhou","doi":"10.1016/j.jcp.2025.113944","DOIUrl":"10.1016/j.jcp.2025.113944","url":null,"abstract":"<div><div>Solid-state dewetting (SSD), a widespread phenomenon in solid-solid-vapor system, could be used to describe the accumulation of solid thin films on the substrate. In this work, we consider the sharp-interface model for axisymmetric SSD with anisotropic surface energy. By introducing two types of surface energy matrices from the anisotropy functions, we aim to design two structure-preserving algorithms for the axisymmetric SSD. The newly designed schemes are applicable to a broader range of anisotropy functions, and we can theoretically prove their volume conservation and energy stability. In addition, based on a novel weak formulation for the axisymmetric SSD, we further build another two numerical schemes that have good mesh properties. Finally, numerous numerical tests are reported to showcase the accuracy and efficiency of the numerical methods.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113944"},"PeriodicalIF":3.8,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686402","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 fully-decoupled second-order-in-time and unconditionally energy stable scheme for the Cahn-Hilliard-Navier-Stokes equations with variable density","authors":"Jinpeng Zhang ,&nbsp;Li Luo ,&nbsp;Xiaoping Wang","doi":"10.1016/j.jcp.2025.113943","DOIUrl":"10.1016/j.jcp.2025.113943","url":null,"abstract":"<div><div>In this paper, we develop a second-order, fully decoupled, and energy-stable numerical scheme for the Cahn-Hilliard-Navier-Stokes model for two phase flow with variable density and viscosity. We propose a new decoupling Constant Scalar Auxiliary Variable (D-CSAV) method which is easy to generalize to schemes with high order accuracy in time. The method is designed using the “zero-energy-contribution” property while maintaining conservative time discretization for the “non-zero-energy-contribution” terms. A new set of scalar auxiliary variables is introduced to develop second-order-in-time, unconditionally energy stable, and decoupling-type numerical schemes. We also introduce a stabilization parameter <em>α</em> to improve the stability of the scheme by slowing down the dynamics of the scalar auxiliary variables. Our algorithm simplifies to solving three independent linear elliptic systems per time step, two of them with constant coefficients. The update of all scalar auxiliary variables is explicit and decoupled from solving the phase field variable and velocity field. We rigorously prove unconditional energy stability of the scheme and perform extensive benchmark simulations to demonstrate accuracy and efficiency of the method.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"532 ","pages":"Article 113943"},"PeriodicalIF":3.8,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143696116","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":"High-order inverse Lax-Wendroff procedure for compressible fluid-structure interaction problems","authors":"Zepeng Liu ,&nbsp;Yan Jiang ,&nbsp;Chi-Wang Shu ,&nbsp;Mengping Zhang","doi":"10.1016/j.jcp.2025.113942","DOIUrl":"10.1016/j.jcp.2025.113942","url":null,"abstract":"<div><div>In this study, we propose a global high-order approach for fluid-structure interaction (FSI) problems involving compressible inviscid flows and deformable elastic solids. A partitioned coupling strategy is employed to solve the fluid and solid equations. The compressible Euler equations in the fluid domain are solved using a high-order finite difference weighted essentially non-oscillatory (WENO) method on fixed Cartesian Eulerian grids. In the solid domain, the linear elastodynamic equations are discretized via the Lagrangian discontinuous Galerkin (DG) finite element method on unstructured meshes. To handle the moving interface between the fluid and solid domains, we develop a high-order treatment derived from the inverse Lax-Wendroff (ILW) boundary scheme. This approach avoids the need for mesh generation and sub-iterations at each time step, simplifying implementation. Furthermore, the specialized interface treatment ensures stability in challenging cases, such as those involving light solids coupled with heavy fluids. Stability analysis for linear systems further demonstrates the robustness of the method. We validate the proposed approach through numerical tests on one- and two-dimensional problems. The results demonstrate that our method could achieve third-order accuracy for smooth solutions, handle shock induced FSI problems without oscillation, and remain stable across a wide range of material parameters.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113942"},"PeriodicalIF":3.8,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686397","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 accurate immersed boundary method using radial-basis functions for incompressible flows","authors":"Hamayun Farooq ,&nbsp;Imran Akhtar ,&nbsp;Arman Hemmati ,&nbsp;Muhammad Saif Ullah Khalid","doi":"10.1016/j.jcp.2025.113928","DOIUrl":"10.1016/j.jcp.2025.113928","url":null,"abstract":"<div><div>In this work, we introduce a parallel computational solver based on the sharp-interface immersed boundary method for simulating three-dimensional incompressible flows over stationary and moving boundaries. Despite the robustness and ease of implementation of conventional body-conformal grid methods, they are limited to relatively simple immersed geometries, leading to challenges in grid generation and quality. Our approach employs a multi-dimensional ghost-cell methodology and radial basis functions interpolation/splines to achieve accurate boundary condition and superior efficiency. We utilize unstructured triangular elements for geometric surface discretization and non-uniform Cartesian grids for constructing flow domains around the immersed boundaries. Furthermore, full parallelization using domain decomposition ensures scalability on distributed memory platforms, facilitated through message-passing interface libraries. Additionally, we introduce a flow smoothing strategy to mitigate spurious pressure oscillations near immersed bodies. Through simulations of two- and three-dimensional fluid-structure interaction problems, we demonstrate the effectiveness, accuracy, and efficiency of our computational solver.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113928"},"PeriodicalIF":3.8,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Non-isothermal filtration problem: Two-temperature computational model","authors":"Maksim I. Ivanov,&nbsp;Igor A. Kremer,&nbsp;Yuri M. Laevsky","doi":"10.1016/j.jcp.2025.113941","DOIUrl":"10.1016/j.jcp.2025.113941","url":null,"abstract":"<div><div>The article proposes a new computational model of non-isothermal filtration of a two-phase incompressible fluid. From the point of view of applications, we are talking about the displacement of oil by water when hot water enters from an injection well. The specificity of the proposed model is its two-temperature formulation. The two-temperature formulation is understood as thermal heterogeneity, in which at each point of the domain under consideration the temperatures of the two-phase fluid and porous blocks are determined, and the thermal interaction between the two continua is indicated. The mathematical model is presented in a mixed formulation in the form of a system of first-order equations in terms of four scalar functions (liquid pressure, water saturation, liquid and porous medium temperatures) and three vector functions (total liquid velocity and heat conductive fluxes of the liquid and porous medium). The spatial approximation is based on a combination of mixed FEM and centered FVM. The time approximation consists of using an explicit-implicit scheme with upwinding. In particular, IMPES-type method is used for the filtration equations, and the energy equations explicitly consider convective transfer with the choice of time step according to the CFL condition. For heat exchange between the fluid and the porous medium, both explicit and implicit approximations are used. It is shown that the stability condition of the explicit scheme is significantly weaker than the CFL conditions for convective flows in the mass and energy conservation laws at an accuracy coinciding with the accuracy of the implicit scheme. Also, the two-temperature model made it possible to study the role of heat conductive transfer in a liquid.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113941"},"PeriodicalIF":3.8,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686534","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":"Constructing stable, high-order finite-difference operators on point clouds over complex geometries","authors":"Jason Hicken,&nbsp;Ge Yan ,&nbsp;Sharanjeet Kaur","doi":"10.1016/j.jcp.2025.113940","DOIUrl":"10.1016/j.jcp.2025.113940","url":null,"abstract":"<div><div>High-order difference operators with the summation-by-parts (SBP) property can be used to build stable discretizations of hyperbolic conservation laws; however, most high-order SBP operators require a conforming, high-order mesh for the domain of interest. To circumvent this requirement, we present an algorithm for building high-order, diagonal-norm, first-derivative SBP operators on point clouds over level-set geometries. The algorithm is <em>not</em> mesh-free, since it uses a Cartesian cut-cell mesh to define the sparsity pattern of the operators and to provide intermediate quadrature rules; however, the mesh is generated automatically and can be discarded once the SBP operators have been constructed. Using this temporary mesh, we construct local, cell-based SBP difference operators that are assembled into global SBP operators. We identify conditions for the existence of a positive-definite diagonal mass matrix, and we compute the diagonal norm by solving a sparse system of linear inequalities using an interior-point algorithm. We also describe an artificial dissipation operator that complements the first-derivative operators when solving hyperbolic problems, although the dissipation is not required for stability. The numerical results confirm the conditions under which a diagonal norm exists and study the distribution of the norm's entries. In addition, the results verify the accuracy and stability of the point-cloud SBP operators using the linear advection equation.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"532 ","pages":"Article 113940"},"PeriodicalIF":3.8,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143697991","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}