Journal of Computational Physics最新文献_第2页

A framework for learning symbolic turbulence models from indirect observation data via neural networks and feature importance analysis 基于神经网络和特征重要性分析的间接观测数据符号湍流模型学习框架

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2025-05-19 DOI: 10.1016/j.jcp.2025.114068

Chutian Wu , Xin-Lei Zhang , Duo Xu , Guowei He

{"title":"A framework for learning symbolic turbulence models from indirect observation data via neural networks and feature importance analysis","authors":"Chutian Wu , Xin-Lei Zhang , Duo Xu , Guowei He","doi":"10.1016/j.jcp.2025.114068","DOIUrl":"10.1016/j.jcp.2025.114068","url":null,"abstract":"<div><div>Learning symbolic turbulence models from indirect observation data is of significant interest as it not only improves the accuracy of posterior prediction but also provides explicit model formulations with good interpretability. However, it typically resorts to gradient-free evolutionary algorithms, which can be relatively inefficient compared to gradient-based approaches, particularly when the Reynolds-averaged Navier–Stokes (RANS) simulations are involved in the training process. In view of this difficulty, we propose a framework that uses neural networks and the associated feature importance analysis to improve the efficiency of symbolic turbulence modeling. In doing so, the gradient-based method can be used to efficiently learn neural network-based representations of Reynolds stress from indirect data, which is further transformed into simplified mathematical expressions with symbolic regression. Moreover, feature importance analysis is introduced to accelerate the convergence of symbolic regression by excluding insignificant input features. The proposed training strategy is tested in the flow in a square duct, where it correctly learns underlying analytic models from indirect velocity data. Further, the method is applied in the flow over the periodic hills, demonstrating that the feature importance analysis can significantly improve the training efficiency and learn symbolic turbulence models with satisfactory generalizability.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114068"},"PeriodicalIF":3.8,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144116072","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}

引用次数: 0

A structure-preserving discontinuous Galerkin scheme for the Cahn-Hilliard equation including time adaptivity 含时间自适应的Cahn-Hilliard方程的保结构不连续Galerkin格式

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2025-05-19 DOI: 10.1016/j.jcp.2025.114097

Golo A. Wimmer , Ben S. Southworth , Qi Tang

{"title":"A structure-preserving discontinuous Galerkin scheme for the Cahn-Hilliard equation including time adaptivity","authors":"Golo A. Wimmer , Ben S. Southworth , Qi Tang","doi":"10.1016/j.jcp.2025.114097","DOIUrl":"10.1016/j.jcp.2025.114097","url":null,"abstract":"<div><div>We present a novel spatial discretization for the Cahn-Hilliard equation including transport. The method is given by a mixed discretization for the two elliptic operators, with the phase field and chemical potential discretized in discontinuous Galerkin spaces, and two auxiliary flux variables discretized in a divergence-conforming space. This allows for the use of an upwind-stabilized discretization for the transport term, while still ensuring a consistent treatment of structural properties including mass conservation and energy dissipation. Further, we couple the novel spatial discretization to an adaptive time stepping method in view of the Cahn-Hilliard equation’s distinct slow and fast time scale dynamics. The resulting implicit stages are solved with a robust preconditioning strategy, which is derived for our novel spatial discretization based on an existing one for continuous Galerkin based discretizations. Our overall scheme’s accuracy, robustness, efficient time adaptivity as well as structure preservation and stability with respect to advection dominated scenarios are demonstrated in a series of numerical tests.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114097"},"PeriodicalIF":3.8,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144123728","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}

引用次数: 0

Adaptive hp-polynomial based sparse grid collocation algorithms for piecewise smooth functions with kinks 基于自适应hp多项式的带扭结分段光滑函数稀疏网格配置算法

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2025-05-19 DOI: 10.1016/j.jcp.2025.114065

Hendrik Wilka, Jens Lang

{"title":"Adaptive hp-polynomial based sparse grid collocation algorithms for piecewise smooth functions with kinks","authors":"Hendrik Wilka, Jens Lang","doi":"10.1016/j.jcp.2025.114065","DOIUrl":"10.1016/j.jcp.2025.114065","url":null,"abstract":"<div><div>High-dimensional interpolation problems appear in various applications of uncertainty quantification, stochastic optimization and machine learning. Such problems are computationally expensive and request the use of adaptive grid generation strategies like anisotropic sparse grids to mitigate the curse of dimensionality. However, it is well known that the standard dimension-adaptive sparse grid method converges very slowly or even fails in the case of non-smooth functions. For piecewise smooth functions with kinks, we construct two novel <span><math><mrow><mi>h</mi><mi>p</mi></mrow></math></span>-adaptive sparse grid collocation algorithms that combine low-order basis functions with local support in parts of the domain with less regularity and variable-order basis functions elsewhere. Spatial refinement is realized by means of a hierarchical multivariate knot tree which allows the construction of localised hierarchical basis functions with varying order. Hierarchical surplus is used as an error indicator to automatically detect the non-smooth region and adaptively refine the collocation points there. The local polynomial degrees are optionally selected by a greedy approach or a kink detection procedure. Four numerical benchmark examples with different dimensions are discussed and comparison with locally linear, quadratic and highest degree basis functions are given to show the efficiency and accuracy of the proposed methods.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114065"},"PeriodicalIF":3.8,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144146904","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}

引用次数: 0

Structure-preserving nodal DG method for the Euler equations with gravity: well-balanced, entropy stable, and positivity preserving 欧拉方程的保结构节点DG方法：平衡、熵稳定、保正

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2025-05-17 DOI: 10.1016/j.jcp.2025.114095

Yuchang Liu , Wei Guo , Yan Jiang , Mengping Zhang

引用次数: 0

An efficient implicit scheme for the multimaterial Euler equations in Lagrangian coordinates 拉格朗日坐标系下多材料欧拉方程的一种有效隐式格式

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2025-05-17 DOI: 10.1016/j.jcp.2025.114086

Simone Chiocchetti , Giovanni Russo

{"title":"An efficient implicit scheme for the multimaterial Euler equations in Lagrangian coordinates","authors":"Simone Chiocchetti , Giovanni Russo","doi":"10.1016/j.jcp.2025.114086","DOIUrl":"10.1016/j.jcp.2025.114086","url":null,"abstract":"<div><div>Stratified fluids composed of a sequence of alternate layers show interesting macroscopic properties, which may be quite different from those of the individual constituent fluids. On a macroscopic scale, such systems can be considered a sort of fluid metamaterial. In many cases each fluid layer can be described by Euler equations following the stiffened gas equation of state. The computation of detailed numerical solutions of such stratified material poses several challenges, first and foremost the issue of artificial smearing of material parameters across interface boundaries. Lagrangian schemes completely eliminate this issue, but at the cost of rather stringent time step restrictions. In this work we introduce an implicit numerical method for the multimaterial Euler equations in Lagrangian coordinates. The implicit discretization is aimed at bypassing the prohibitive time step restrictions present in flows with stratified media, where one of the materials is particularly dense, or rigid (or both). This is the case for flows of water-air mixtures, air-granular media, or similar high density ratio systems. We will present the novel discretisation approach, which makes extensive use of the remarkable structure of the governing equations in Lagrangian coordinates to find the solution by means of a single implicit discrete wave equation for the pressure field, yielding a symmetric positive definite structure and thus a particularly efficient algorithm. Additionally, we will introduce simple filtering strategies for counteracting the emergence of pressure or density oscillations typically encountered in multimaterial flows, and will present results concerning the robustness, accuracy, and performance of the proposed method, including applications to stratified media with high density and stiffness ratios.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114086"},"PeriodicalIF":3.8,"publicationDate":"2025-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144116071","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}

引用次数: 0

Well-balanced discontinuous Galerkin method with flux globalization for rotating shallow water equations 旋转浅水方程的通量全球化佳平衡不连续伽辽金法

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2025-05-17 DOI: 10.1016/j.jcp.2025.114094

Jiahui Zhang, Yinhua Xia , Yan Xu

{"title":"Well-balanced discontinuous Galerkin method with flux globalization for rotating shallow water equations","authors":"Jiahui Zhang, Yinhua Xia , Yan Xu","doi":"10.1016/j.jcp.2025.114094","DOIUrl":"10.1016/j.jcp.2025.114094","url":null,"abstract":"<div><div>In this paper, we introduce a novel well-balanced discontinuous Galerkin (DG) method for the rotating shallow water equations, which is founded on the flux globalization approach. Our method entails the integration of the source term into the global fluxes, thereby establishing a quasi-conservative formulation of the equations. The well-balanced property is maintained by ensuring the equilibrium at the nodes of the Lagrange DG basis and through a tailored treatment of the numerical flux. Furthermore, we employ linear segment paths between equilibrium variables at the cell interface to preserve the equilibrium state of the scheme. This strategy allows us to handle more complex equilibrium states, including those with spatially global integral quantities, and accommodates discontinuous bottom topography. We conduct a comprehensive series of numerical experiments on shallow water models, including those with and without Coriolis forces. These experiments confirm the high-order accuracy of our DG method and its ability to exactly preserve equilibrium for intricate moving steady states. Additionally, the method successfully propagates small perturbations of the steady state with high-resolution and oscillation-free solutions, even in the presence of challenging bottom topography conditions.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114094"},"PeriodicalIF":3.8,"publicationDate":"2025-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144116073","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}

引用次数: 0

Predicting nonlinear-flow regions in highly heterogeneous porous media using adaptive constitutive laws and neural networks 利用自适应本构律和神经网络预测高度非均质多孔介质中的非线性流动区域

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2025-05-17 DOI: 10.1016/j.jcp.2025.114093

Chiara Giovannini , Alessio Fumagalli , Francesco Saverio Patacchini

{"title":"Predicting nonlinear-flow regions in highly heterogeneous porous media using adaptive constitutive laws and neural networks","authors":"Chiara Giovannini , Alessio Fumagalli , Francesco Saverio Patacchini","doi":"10.1016/j.jcp.2025.114093","DOIUrl":"10.1016/j.jcp.2025.114093","url":null,"abstract":"<div><div>In a porous medium featuring heterogeneous permeabilities, a wide range of fluid velocities may be recorded, so that significant inertial and frictional effects may arise in high-speed regions. In such parts, the link between pressure gradient and velocity is typically made via Darcy’s law, which may fail to account for these effects; instead, the Darcy–Forchheimer law, which introduces a nonlinear term, may be more adequate. Applying the Darcy–Forchheimer law globally in the domain is very costly numerically and, rather, should only be done where strictly necessary. The question of finding a prori the subdomain where to restrict the use of the Darcy–Forchheimer law was recently answered in Fumagalli and Patacchini (2023) by using an adaptive model: given a threshold on the flow’s velocity, the model locally selects the more appropriate law as it is being solved. At the end of the resolution, each mesh cell is flagged as being in the Darcy or Darcy–Forchheimer subdomain. Still, this model is nonlinear itself and thus relatively expensive to run. In this paper, to accelerate the subdivision of the domain into low- and high-speed regions, we instead exploit the adaptive model from Fumagalli and Patacchini (2023) to generate partitioning data given an array of different input parameters, such as boundary conditions and inertial coefficients, and then train neural networks on these data classifying each mesh cell as Darcy or not. Two test cases are studied to illustrate the results, where cost functions, parity plots, precision-recall plots and receiver operating characteristic curves are analyzed.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114093"},"PeriodicalIF":3.8,"publicationDate":"2025-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144123815","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}

引用次数: 0

Fast-slow neural networks for learning singularly perturbed dynamical systems 用于学习奇摄动系统的快慢神经网络

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2025-05-16 DOI: 10.1016/j.jcp.2025.114090

Daniel A. Serino , Allen Alvarez Loya , J.W. Burby , Ioannis G. Kevrekidis , Qi Tang

{"title":"Fast-slow neural networks for learning singularly perturbed dynamical systems","authors":"Daniel A. Serino , Allen Alvarez Loya , J.W. Burby , Ioannis G. Kevrekidis , Qi Tang","doi":"10.1016/j.jcp.2025.114090","DOIUrl":"10.1016/j.jcp.2025.114090","url":null,"abstract":"<div><div>Singularly perturbed dynamical systems play a crucial role in climate dynamics and plasma physics. A powerful and well-known tool to address these systems is the Fenichel normal form, which significantly simplifies fast dynamics near slow manifolds through a transformation. However, this normal form is difficult to realize in conventional numerical algorithms. In this work, we explore an alternative way of realizing it through structure-preserving machine learning. Specifically, a fast-slow neural network (FSNN) is proposed for learning data-driven models of singularly perturbed dynamical systems with dissipative fast timescale dynamics. Our method enforces the existence of a trainable, attracting invariant slow manifold as a hard constraint. Closed-form representation of the slow manifold enables efficient integration on the slow time scale and significantly improves prediction accuracy beyond the training data. We demonstrate the FSNN on examples including the Grad moment system, two-scale Lorenz96 equations, and Abraham-Lorentz dynamics modeling radiation reaction of electrons.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114090"},"PeriodicalIF":3.8,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144106418","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}

引用次数: 0

A dynamic likelihood approach to filtering transport processes: advection-diffusion dynamics 过滤输送过程的动态似然方法：平流-扩散动力学

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2025-05-16 DOI: 10.1016/j.jcp.2025.114089

Johannes Krotz , Juan M. Restrepo , Jorge Ramirez

{"title":"A dynamic likelihood approach to filtering transport processes: advection-diffusion dynamics","authors":"Johannes Krotz , Juan M. Restrepo , Jorge Ramirez","doi":"10.1016/j.jcp.2025.114089","DOIUrl":"10.1016/j.jcp.2025.114089","url":null,"abstract":"<div><div>A Bayesian data assimilation scheme is formulated for advection-dominated advective and diffusive evolutionary problems, based upon the Dynamic Likelihood (DLF) approach to filtering. The DLF was developed specifically for hyperbolic problems –waves–, and in this paper, it is extended via a split step formulation, to handle advection-diffusion problems. In the dynamic likelihood approach, observations and their statistics are used to propagate probabilities along characteristics, evolving the likelihood in time. The estimate posterior thus inherits phase information. For advection-diffusion the advective part of the time evolution is handled on the basis of observations alone, while the diffusive part is informed through the model as well as observations. We expect, and indeed show here, that in advection-dominated problems, the DLF approach produces better estimates than other assimilation approaches, particularly when the observations are sparse and have low uncertainty. The added computational expense of the method is cubic in the total number of observations over time, which is on the same order of magnitude as a standard Kalman filter and can be mitigated by bounding the number of forward propagated observations, discarding the least informative data.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"536 ","pages":"Article 114089"},"PeriodicalIF":3.8,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144090139","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}

引用次数: 0

Unsupervised solution operator learning for mean-field games 平均场博弈的无监督解算子学习

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2025-05-16 DOI: 10.1016/j.jcp.2025.114057

Han Huang , Rongjie Lai

{"title":"Unsupervised solution operator learning for mean-field games","authors":"Han Huang , Rongjie Lai","doi":"10.1016/j.jcp.2025.114057","DOIUrl":"10.1016/j.jcp.2025.114057","url":null,"abstract":"<div><div>Recent advances in deep learning has witnessed many innovative frameworks that solve high dimensional mean-field games (MFG) accurately and efficiently. These methods, however, are restricted to solving single-instance MFG and require extensive computational time per instance, limiting practicality. To overcome this, we develop a novel framework for learning the MFG solution operator. Our model takes MFG instances as input and outputs their solutions with one forward pass. To ensure that the proposed parametrization is well-suited for operator learning, we introduce and prove the notion of sampling consistency for our model, establishing its convergence to a continuous operator in the sampling limit. Our method has two key advantages. First, it is discretization-free, making it particularly suitable for learning operators of high-dimensional MFGs. Secondly, it can be trained without the need for access to superised labels, significantly reducing the overhead associated with creating training datasets in existing operator learning methods. We test our framework on synthetic and realistic datasets with varying complexity and dimensionality to substantiate its robustness. Compared to single-instance neural MFG solvers, our approach reduces the time to solve a MFG problem by more than five orders of magnitude without compromising the quality of computed solutions.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114057"},"PeriodicalIF":3.8,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144106420","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}

引用次数: 0