Multiscale Model. Simul.最新文献_第2页

On the Multiscale Landau-Lifshitz-Gilbert Equation: Two-Scale Convergence and Stability Analysis 关于多尺度Landau-Lifshitz-Gilbert方程:两尺度收敛性和稳定性分析

Multiscale Model. Simul. Pub Date : 2022-06-30 DOI: 10.1137/21m1438177

Jingrun Chen, Rui Du, Zetao Ma, Z. Sun, Lei Zhang

引用次数: 1

AMS-Net: Adaptive Multiscale Sparse Neural Network with Interpretable Basis Expansion for Multiphase Flow Problems 基于可解释基展开的多相流问题自适应多尺度稀疏神经网络

Multiscale Model. Simul. Pub Date : 2022-06-23 DOI: 10.1137/21m1405289

Yating Wang, W. Leung, Guang Lin

{"title":"AMS-Net: Adaptive Multiscale Sparse Neural Network with Interpretable Basis Expansion for Multiphase Flow Problems","authors":"Yating Wang, W. Leung, Guang Lin","doi":"10.1137/21m1405289","DOIUrl":"https://doi.org/10.1137/21m1405289","url":null,"abstract":"In this work, we propose an adaptive sparse learning algorithm that can be applied to learn the physical processes and obtain a sparse representation of the solution given a large snapshot space. Assume that there is a rich class of precomputed basis functions that can be used to approximate the quantity of interest. We then design a neural network architecture to learn the coefficients of solutions in the spaces which are spanned by these basis functions. The information of the basis functions are incorporated in the loss function, which minimizes the differences between the downscaled reduced order solutions and reference solutions at multiple time steps. The network contains multiple submodules and the solutions at different time steps can be learned simultaneously. We propose some strategies in the learning framework to identify important degrees of freedom. To find a sparse solution representation, a soft thresholding operator is applied to enforce the sparsity of the output coefficient vectors of the neural network. To avoid over-simplification and enrich the approximation space, some degrees of freedom can be added back to the system through a greedy algorithm. In both scenarios, that is, removing and adding degrees of freedom, the corresponding network connections are pruned or reactivated guided by the magnitude of the solution coefficients obtained from the network outputs. The proposed adaptive learning process is applied to some toy case examples to demonstrate that it can achieve a good basis selection and accurate approximation. More numerical tests are performed on two-phase multiscale flow problems to show the capability and interpretability of the proposed method on complicated applications.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122079018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Online multiscale model reduction for nonlinear stochastic PDEs with multiplicative noise 带有乘性噪声的非线性随机偏微分方程的在线多尺度模型约简

Multiscale Model. Simul. Pub Date : 2022-04-25 DOI: 10.48550/arXiv.2204.11712

Lijian Jiang, Mengnan Li, Meng Zhao

{"title":"Online multiscale model reduction for nonlinear stochastic PDEs with multiplicative noise","authors":"Lijian Jiang, Mengnan Li, Meng Zhao","doi":"10.48550/arXiv.2204.11712","DOIUrl":"https://doi.org/10.48550/arXiv.2204.11712","url":null,"abstract":"In this paper, an online multiscale model reduction method is presented for stochastic partial differential equations (SPDEs) with multiplicative noise, where the diffusion coefficient is spatially multiscale and the noise perturbation nonlinearly depends on the diffusion dynamics. It is necessary to efficiently compute all possible trajectories of the stochastic dynamics for quantifying model's uncertainty and statistic moments. The multiscale diffusion and nonlinearity may cause the computation intractable. To overcome the multiscale difficulty, a constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) is used to localize the computation and obtain an effective coarse model. However, the nonlinear terms are still defined on a fine scale space after the Galerkin projection of CEM-GMsFEM is applied to the nonlinear SPDEs. This significantly impacts on the simulation efficiency by CEM-GMsFEM. To this end, a stochastic online discrete empirical interpolation method (DEIM) is proposed to treat the stochastic nonlinearity. The stochastic online DEIM incorporates offline snapshots and online snapshots. The offline snapshots consist of the nonlinear terms at the approximate mean of the stochastic dynamics and are used to construct an offline reduced model. The online snapshots contain some information of the current new trajectory and are used to correct the offline reduced model in an increment manner. The stochastic online DEIM substantially reduces the dimension of the nonlinear dynamics and enhances the prediction accuracy for the reduced model. Thus, the online multiscale model reduction is constructed by using CEM-GMsFEM and the stochastic online DEIM. A priori error analysis is carried out for the nonlinear SPDEs. We present a few numerical examples with diffusion in heterogeneous porous media and show the effectiveness of the proposed model reduction.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126996579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Enriched Nonconforming Multiscale Finite Element Method for Stokes Flows in Heterogeneous Media Based on High-order Weighting Functions 基于高阶加权函数的非均匀介质中斯托克斯流动的非协调多尺度有限元方法

Multiscale Model. Simul. Pub Date : 2022-03-01 DOI: 10.1137/21m141926x

Q. Feng, G. Allaire, P. Omnes

引用次数: 0

Efficiency of Micro-Macro Models for Reactive Two-Mineral Systems 反应性双矿物体系微观-宏观模型的有效性

Multiscale Model. Simul. Pub Date : 2022-03-01 DOI: 10.1137/20m1380648

Stephan Gärttner, P. Frolkovic, P. Knabner, N. Ray

引用次数: 4

Hamiltonian Dysthe Equation for Three-Dimensional Deep-Water Gravity Waves 三维深水重力波的哈密顿方程

Multiscale Model. Simul. Pub Date : 2022-03-01 DOI: 10.1137/21m1432788

P. Guyenne, Adilbek Kairzhan, C. Sulem

引用次数: 2

The Consistency and the Monte Carlo Method for Semiconductor Boltzmann Equations with Multivalley 多谷半导体玻尔兹曼方程的一致性及蒙特卡罗方法

Multiscale Model. Simul. Pub Date : 2022-02-28 DOI: 10.1137/19m128750x

Jiachuan Cao, Li-qun Cao

引用次数: 0

Multiscale Elliptic PDE Upscaling and Function Approximation via Subsampled Data 基于次采样数据的多尺度椭圆PDE上尺度与函数逼近

Multiscale Model. Simul. Pub Date : 2022-02-24 DOI: 10.1137/20m1372214

Yifan Chen, T. Hou

{"title":"Multiscale Elliptic PDE Upscaling and Function Approximation via Subsampled Data","authors":"Yifan Chen, T. Hou","doi":"10.1137/20m1372214","DOIUrl":"https://doi.org/10.1137/20m1372214","url":null,"abstract":". There is an intimate connection between numerical upscaling of multiscale PDEs and scattered data approximation of heterogeneous functions: the coarse variables selected for deriving an upscaled equation (in the former) correspond to the sampled information used for approximation (in the latter). As such, both problems can be thought of as recovering a target function based on some coarse data that are either artificially chosen by an upscaling algorithm or determined by some physical measurement process. The purpose of this paper is then to study, under such a setup and for a specific elliptic problem, how the lengthscale of the coarse data, which we refer to as the subsampled lengthscale, influences the accuracy of recovery, given limited computational budgets. Our analysis and experiments identify that reducing the subsampling lengthscale may improve the accuracy, implying a guiding criterion for coarse-graining or data acquisition in this computationally constrained scenario, especially leading to direct insights for the implementation of the Gamblets method in the numerical homogenization literature. Moreover, reducing the lengthscale to zero may lead to a blow-up of approximation error if the target function does not have enough regularity, suggesting the need for a stronger prior assumption on the target function to be approximated. We introduce a singular weight function to deal with it, both theoretically and numerically. This work sheds light on the interplay of the lengthscale of coarse data, the computational costs, the regularity of the target function, and the accuracy of approximations and numerical simulations.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124909075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Uniformly Accurate Nested Picard Iterative Integrators for the Nonlinear Dirac Equation in the Nonrelativistic Regime 非相对论状态下非线性Dirac方程的一致精确嵌套Picard迭代积分器

Multiscale Model. Simul. Pub Date : 2022-02-22 DOI: 10.1137/20m133573x

Yongyong Cai, Yan Wang

引用次数: 2

Multiscale Modeling of Sorption Kinetics 吸附动力学的多尺度模拟

Multiscale Model. Simul. Pub Date : 2022-02-05 DOI: 10.1137/21m1463872

Clarissa Astuto, A. Raudino, G. Russo

引用次数: 4