Journal of Computational Physics最新文献_第4页

An imbalanced learning-based sampling method for physics-informed neural networks 基于不平衡学习的物理信息神经网络采样方法

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2025-04-17 DOI: 10.1016/j.jcp.2025.114010

Jiaqi Luo , Yahong Yang , Yuan Yuan , Shixin Xu , Wenrui Hao

{"title":"An imbalanced learning-based sampling method for physics-informed neural networks","authors":"Jiaqi Luo , Yahong Yang , Yuan Yuan , Shixin Xu , Wenrui Hao","doi":"10.1016/j.jcp.2025.114010","DOIUrl":"10.1016/j.jcp.2025.114010","url":null,"abstract":"<div><div>This paper introduces Residual-based Smote (RSmote), an innovative local adaptive sampling technique tailored to improve the performance of Physics-Informed Neural Networks (PINNs) through imbalanced learning strategies. Traditional residual-based adaptive sampling methods, while effective in enhancing PINN accuracy, often struggle with efficiency and high memory consumption, particularly in high-dimensional problems. RSmote addresses these challenges by targeting regions with high residuals and employing oversampling techniques from imbalanced learning to refine the sampling process. Our approach is underpinned by a rigorous theoretical analysis that supports the effectiveness of RSmote in managing computational resources more efficiently. Through extensive evaluations, we benchmark RSmote against the state-of-the-art Residual-based Adaptive Distribution (RAD) method across a variety of dimensions and differential equations. The results demonstrate that RSmote not only achieves or exceeds the accuracy of RAD but also significantly reduces memory usage, making it particularly advantageous in high-dimensional scenarios. These contributions position RSmote as a robust and resource-efficient solution for solving complex partial differential equations, especially when computational constraints are a critical consideration.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"534 ","pages":"Article 114010"},"PeriodicalIF":3.8,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143843603","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 mixed-dimensional model for the electrostatic problem on coupled domains 耦合域上静电问题的混合维模型

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2025-04-17 DOI: 10.1016/j.jcp.2025.114015

Beatrice Crippa , Anna Scotti , Andrea Villa

引用次数: 0

Minimum scale and spatial resolution requirement for direct numerical simulations of compressible turbulence 可压缩湍流直接数值模拟的最小尺度和空间分辨率要求

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2025-04-16 DOI: 10.1016/j.jcp.2025.114014

Chensheng Luo , Jian Fang , Le Fang

{"title":"Minimum scale and spatial resolution requirement for direct numerical simulations of compressible turbulence","authors":"Chensheng Luo , Jian Fang , Le Fang","doi":"10.1016/j.jcp.2025.114014","DOIUrl":"10.1016/j.jcp.2025.114014","url":null,"abstract":"<div><div>In the direct numerical simulation (DNS) of compressible turbulence using Navier-Stokes equations, due to the incomplete resolution of shocklets, the classical grid resolution criterion based on the usual Kolmogorov length scale appears insufficient for high-order statistics. The present study discusses the minimum scale of compressible turbulence under the continuum assumption, and establishes new spatial resolution requirements for DNS. We first define the minimum shock scale for one-dimensional Burgers turbulence, and derive a spatial resolution criterion essential for fully resolving the second- and third-order velocity gradient moments. We demonstrate that this shock scale definition is also applicable to one-dimensional Navier-Stokes turbulence, and validate the spatial resolution requirement through numerical simulations of the Shu-Osher problem. The analysis is then extended to multi-dimensional turbulence. Through theoretical analysis and numerical studies, we conclude that the minimum local Kolmogorov scale, <span><math><msub><mrow><mi>η</mi></mrow><mrow><mi>min</mi></mrow></msub></math></span>, describes the smallest structure in turbulence and is determined by the strongest shocklet. Furthermore, we establish a requirement of <span><math><msub><mrow><mi>η</mi></mrow><mrow><mi>min</mi></mrow></msub><mo>/</mo><mi>Δ</mi><mi>x</mi><mo>≳</mo><mn>1.5</mn></math></span> for compressible turbulence, and validate it through DNSs of two-dimensional compressible turbulence with different grid resolutions. The present study provides a reference on spatial resolution requirement for DNS of compressible turbulence.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"534 ","pages":"Article 114014"},"PeriodicalIF":3.8,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143854658","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 hybridizable discontinuous Galerkin method with transmission variables for time-harmonic acoustic problems in heterogeneous media 非均质介质中时谐声学问题的带传输变量的可杂化不连续伽辽金方法

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2025-04-16 DOI: 10.1016/j.jcp.2025.114009

S. Pescuma , G. Gabard , T. Chaumont-Frelet , A. Modave

{"title":"A hybridizable discontinuous Galerkin method with transmission variables for time-harmonic acoustic problems in heterogeneous media","authors":"S. Pescuma , G. Gabard , T. Chaumont-Frelet , A. Modave","doi":"10.1016/j.jcp.2025.114009","DOIUrl":"10.1016/j.jcp.2025.114009","url":null,"abstract":"<div><div>We consider the finite element solution of time-harmonic wave propagation problems in heterogeneous media with hybridizable discontinuous Galerkin (HDG) methods. In the case of homogeneous media, it has been observed that the iterative solution of the linear system can be accelerated by hybridizing with transmission variables instead of numerical traces, as performed in standard approaches. In this work, we extend the HDG method with transmission variables, which is called the CHDG method, to the heterogeneous case with piecewise constant physical coefficients. In particular, we consider formulations with standard upwind and general symmetric fluxes. The CHDG hybridized system can be written as a fixed-point problem, which can be solved with stationary iterative schemes for a class of symmetric fluxes. The standard HDG and CHDG methods are systematically studied with the different numerical fluxes by considering a series of 2D numerical benchmarks. The convergence of standard iterative schemes is always faster with the extended CHDG method than with the standard HDG methods, with upwind and scalar symmetric fluxes.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"534 ","pages":"Article 114009"},"PeriodicalIF":3.8,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143854656","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

Distribution free uncertainty quantification for neuroscience-inspired deep neural operators 基于神经科学的深度神经算子的无分布不确定性量化

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2025-04-16 DOI: 10.1016/j.jcp.2025.114012

Shailesh Garg , Souvik Chakraborty

{"title":"Distribution free uncertainty quantification for neuroscience-inspired deep neural operators","authors":"Shailesh Garg , Souvik Chakraborty","doi":"10.1016/j.jcp.2025.114012","DOIUrl":"10.1016/j.jcp.2025.114012","url":null,"abstract":"<div><div>Energy-efficient deep learning algorithms are essential for a sustainable future and feasible edge computing setups. Spiking neural networks (SNNs), inspired from neuroscience, are a positive step in the direction of achieving the required energy efficiency. However, in a bid to lower the energy requirements, accuracy is marginally sacrificed. Hence, it becomes important to quantify the uncertainties in such models originating from limited and noisy data, surrogate gradients, and non-convex optimization encountered during training. In response to this challenge, we introduce the Conformalized Randomized Prior Operator (CRP-O) framework that leverages Randomized Prior (RP) networks and Split Conformal Prediction (SCP) to quantify uncertainties in both conventional and spiking neural operators. To further enable zero-shot super-resolution, we propose an extension incorporating Gaussian Process Regression. This enhanced super-resolution-enabled CRP-O framework is integrated with the recently developed Variable Spiking Wavelet Neural Operator (VSWNO). To test the performance of the obtained calibrated uncertainty bounds, we discuss four different benchmark examples covering both one-dimensional and two-dimensional partial differential equations. Results demonstrate that the uncertainty bounds produced by the conformalized RP-VSWNO significantly enhance the uncertainty estimates compared to vanilla RP-VSWNO, Quantile WNO (Q-WNO), and Conformalized Quantile WNO (CQ-WNO). These findings underscore the potential of the proposed approach for practical applications.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"534 ","pages":"Article 114012"},"PeriodicalIF":3.8,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143854659","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

Developing and analyzing a DG method for modeling of metasurfaces 开发并分析了一种用于元曲面建模的DG方法

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2025-04-16 DOI: 10.1016/j.jcp.2025.114011

Chanjie Li , Yunqing Huang , Jichun Li

引用次数: 0

Increasingly high-order ALW-MR-WENO schemes for solving hyperbolic conservation laws on tetrahedral grids 求解四面体网格上双曲守恒律的越来越高阶ALW-MR-WENO格式

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2025-04-15 DOI: 10.1016/j.jcp.2025.114007

Yicheng Lin , Jun Zhu

{"title":"Increasingly high-order ALW-MR-WENO schemes for solving hyperbolic conservation laws on tetrahedral grids","authors":"Yicheng Lin , Jun Zhu","doi":"10.1016/j.jcp.2025.114007","DOIUrl":"10.1016/j.jcp.2025.114007","url":null,"abstract":"<div><div>This paper proposes a new fourth-order multi-resolution weighted essentially non-oscillatory scheme (which is termed as the MR-WENO-4 scheme), and the new MR-WENO-3 and MR-WENO-4 schemes with adaptive linear weights (which are termed as the ALW-MR-WENO-3 and ALW-MR-WENO-4 schemes) in the finite volume framework for solving hyperbolic conservation laws on tetrahedral grids. It is the first time to devise three increasingly high-order WENO schemes on tetrahedral grids, since one MR-WENO-4 scheme uses the information defined on four unequal-sized central stencils, and the ALW-MR-WENO-3 and ALW-MR-WENO-4 schemes use the information defined on two unequal-sized central stencils. In comparison to the classical third-order finite volume WENO scheme (Zhang and Shu, 2009 <span><span>[53]</span></span>) that used the sixteen four-cell stencils on tetrahedral grids, the key benefits of these new MR-WENO schemes are their simplicity, efficiency, and compactness in the WENO processes, the arbitrary selection of any positive linear weights without considering the topological structures of the tetrahedral grids, the ideal high-order accuracies in smooth areas, and the non-oscillatory property in the vicinity of strong discontinuities. More importantly, only two linear weights are automatically adjusted to be arbitrarily positive values on condition that one simple restriction is satisfied when designing the high-order ALW-MR-WENO schemes. Finally, some numerical results are proposed to show the good efficiency of these ALW-MR-WENO schemes which save approximately 12%-43% CPU time in comparison to that of the original MR-WENO-3 scheme and the new MR-WENO-4 scheme on tetrahedral grids.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"534 ","pages":"Article 114007"},"PeriodicalIF":3.8,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143838000","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 hierarchical splines-based h-adaptive isogeometric solver for all-electron Kohn–Sham equation 基于分层样条的全电子Kohn-Sham方程h-自适应等几何求解器

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2025-04-14 DOI: 10.1016/j.jcp.2025.114003

Tao Wang , Yang Kuang , Ran Zhang , Guanghui Hu

{"title":"A hierarchical splines-based h-adaptive isogeometric solver for all-electron Kohn–Sham equation","authors":"Tao Wang , Yang Kuang , Ran Zhang , Guanghui Hu","doi":"10.1016/j.jcp.2025.114003","DOIUrl":"10.1016/j.jcp.2025.114003","url":null,"abstract":"<div><div>In this paper, a novel <em>h</em>-adaptive isogeometric solver utilizing high-order hierarchical splines is proposed to solve the all-electron Kohn–Sham equation. In virtue of the smooth nature of Kohn–Sham wavefunctions across the domain, except at the nuclear positions, high-order globally regular basis functions such as B-splines are well suited for achieving high accuracy. To further handle the singularities in the external potential at the nuclear positions, an <em>h</em>-adaptive framework based on the hierarchical splines is presented with a specially designed residual-type error indicator, allowing for different resolutions on the domain. The generalized eigenvalue problem raising from the discretized Kohn–Sham equation is effectively solved by the locally optimal block preconditioned conjugate gradient (LOBPCG) method with an elliptic preconditioner, and it is found that the eigensolver's convergence is not sensitive to the spline basis order. A series of numerical experiments confirm the effectiveness of the <em>h</em>-adaptive framework, with a notable experiment that the numerical accuracy <span><math><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup><mrow><mspace></mspace><mi>Hartree</mi><mo>/</mo><mi>particle</mi></mrow></math></span> in the all-electron simulation of a methane molecule is achieved using only 6355 degrees of freedom, demonstrating the competitiveness of our solver for the all-electron Kohn–Sham equation.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"534 ","pages":"Article 114003"},"PeriodicalIF":3.8,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143843601","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 meshfree Galerkin formulation for nonlinear piezoelectric semiconductors in consideration of flexoelectricity 考虑挠性的非线性压电半导体的无网格伽辽金公式

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2025-04-14 DOI: 10.1016/j.jcp.2025.114013

BingBing Wang , RuoYu Wang , Chunsheng Lu , QiaoYun Zhang , CuiYing Fan , MingHao Zhao , Zengtao Chen , Yue Mei , JianWei Zhang

{"title":"A meshfree Galerkin formulation for nonlinear piezoelectric semiconductors in consideration of flexoelectricity","authors":"BingBing Wang , RuoYu Wang , Chunsheng Lu , QiaoYun Zhang , CuiYing Fan , MingHao Zhao , Zengtao Chen , Yue Mei , JianWei Zhang","doi":"10.1016/j.jcp.2025.114013","DOIUrl":"10.1016/j.jcp.2025.114013","url":null,"abstract":"<div><div>Piezoelectric semiconductors (PSCs) are widely used in a microelectromechanical system, but there is still lack of numerical methods for analyzing the nonlinear multi-field coupling behavior of PSCs in consideration of flexoelectricity. In this study, a meshfree Galerkin formulation is presented for such a nonlinear fourth-order boundary value problem. To satisfy the <em>C</em><sup>1</sup> continuity requirement, the moving least square approximation is employed with a quadratic base. To considering the nonlinear drift-diffusion effect in semiconductors, a nonlinear algorithm with tangent stiffness is proposed, which shows much better convergence than available direct iteration methods with secant stiffness. Further, to simulate electrically isolated PSCs, a Lagrange multiplier method is firstly employed to introduce the electroneutrality condition into the Galerkin weak form. In addition, the consistent integration with nodal smoothed derivatives is used to improve the computational efficiency. Several numerical results validate the proposed formulation and demonstrate the effects of the flexoelectric coefficient, intrinsic length scale parameter and initial carrier concentration.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"534 ","pages":"Article 114013"},"PeriodicalIF":3.8,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143847868","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

Auto-stabilized weak Galerkin finite element methods for Stokes equations on non-convex polytopal meshes 非凸多边形网格上Stokes方程的自稳定弱Galerkin有限元方法

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2025-04-14 DOI: 10.1016/j.jcp.2025.114006

Chunmei Wang , Shangyou Zhang

引用次数: 0