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Multiscale Model. Simul.最新文献

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A Low-Rank Approximated Multiscale Method for Pdes With Random Coefficients 带随机系数偏微分方程的低秩近似多尺度方法
Multiscale Model. Simul. Pub Date : 2020-12-08 DOI: 10.1137/19m1288565
Na Ou, G. Lin, Lijian Jiang
{"title":"A Low-Rank Approximated Multiscale Method for Pdes With Random Coefficients","authors":"Na Ou, G. Lin, Lijian Jiang","doi":"10.1137/19m1288565","DOIUrl":"https://doi.org/10.1137/19m1288565","url":null,"abstract":"This work presents a stochastic multiscale model reduction approach to solve PDEs with random coefficients. An ensemble-based low-rank approximation method is proposed to approximate multiscale bas...","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126003896","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: 5
Modeling and Computation of Kubo Conductivity for Two-Dimensional Incommensurate Bilayers 二维不相称双层Kubo电导率的建模与计算
Multiscale Model. Simul. Pub Date : 2020-12-03 DOI: 10.1137/19m1273499
S. Etter, Daniel Massatt, M. Luskin, C. Ortner
{"title":"Modeling and Computation of Kubo Conductivity for Two-Dimensional Incommensurate Bilayers","authors":"S. Etter, Daniel Massatt, M. Luskin, C. Ortner","doi":"10.1137/19m1273499","DOIUrl":"https://doi.org/10.1137/19m1273499","url":null,"abstract":"This paper presents a unified approach to the modeling and computation of the Kubo conductivity of incommensurate bilayer heterostructures at finite temperature. First, we derive an expression for ...","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128253463","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
Wide-band butterfly network: stable and efficient inversion via multi-frequency neural networks 宽带蝴蝶网络:通过多频神经网络实现稳定高效的反演
Multiscale Model. Simul. Pub Date : 2020-11-24 DOI: 10.1137/20m1383276
Matthew Li, L. Demanet, Leonardo Zepeda-N'unez
{"title":"Wide-band butterfly network: stable and efficient inversion via multi-frequency neural networks","authors":"Matthew Li, L. Demanet, Leonardo Zepeda-N'unez","doi":"10.1137/20m1383276","DOIUrl":"https://doi.org/10.1137/20m1383276","url":null,"abstract":"We introduce an end-to-end deep learning architecture called the wide-band butterfly network (WideBNet) for approximating the inverse scattering map from wide-band scattering data. This architecture incorporates tools from computational harmonic analysis, such as the butterfly factorization, and traditional multi-scale methods, such as the Cooley-Tukey FFT algorithm, to drastically reduce the number of trainable parameters to match the inherent complexity of the problem. As a result WideBNet is efficient: it requires fewer training points than off-the-shelf architectures, and has stable training dynamics, thus it can rely on standard weight initialization strategies. The architecture automatically adapts to the dimensions of the data with only a few hyper-parameters that the user must specify. WideBNet is able to produce images that are competitive with optimization-based approaches, but at a fraction of the cost, and we also demonstrate numerically that it learns to super-resolve scatterers in the full aperture scattering setup.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130572968","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
Approximate Optimal Controls via Instanton Expansion for Low Temperature Free Energy Computation 基于瞬子展开的低温自由能近似最优控制
Multiscale Model. Simul. Pub Date : 2020-11-22 DOI: 10.1137/20m1385809
Gr'egoire Ferr'e, T. Grafke
{"title":"Approximate Optimal Controls via Instanton Expansion for Low Temperature Free Energy Computation","authors":"Gr'egoire Ferr'e, T. Grafke","doi":"10.1137/20m1385809","DOIUrl":"https://doi.org/10.1137/20m1385809","url":null,"abstract":"The computation of free energies is a common issue in statistical physics. A natural technique to compute such high dimensional integrals is to resort to Monte Carlo simulations. However these techniques generally suffer from a high variance in the low temperature regime, because the expectation is dominated by high values corresponding to rare system trajectories. A standard way to reduce the variance of the estimator is to modify the drift of the dynamics with a control enhancing the probability of rare event, leading to so-called importance sampling estimators. In theory, the optimal control leads to a zero-variance estimator; it is however defined implicitly and computing it is of the same difficulty as the original problem. We propose here a general strategy to build approximate optimal controls, with the first goal to reduce the variance of free energy Monte Carlo estimators. Our construction builds upon low noise asymptotics by expanding the optimal control around the instanton, which is the path describing most likely fluctuations at low temperature. This technique not only helps reducing variance, but it is also interesting as a theoretical tool since it differs from usual small temperature expansions (WKB ansatz). As a complementary consequence of our expansion, we provide a perturbative formula for computing the free energy in the small temperature regime, which refines the now standard Freidlin-Wentzell asymptotics. We compute this expansion explicitly for lower orders, and explain how our strategy can be extended to an arbitrary order of accuracy. We support our findings with illustrative numerical examples.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130596781","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: 6
On Asymptotic Preserving schemes for a class of Stochastic Differential Equations in averaging and diffusion approximation regimes 一类随机微分方程在平均和扩散近似下的渐近保持格式
Multiscale Model. Simul. Pub Date : 2020-11-04 DOI: 10.1137/20m1379836
Charles-Edouard Br'ehier, Shmuel Rakotonirina-Ricquebourg
{"title":"On Asymptotic Preserving schemes for a class of Stochastic Differential Equations in averaging and diffusion approximation regimes","authors":"Charles-Edouard Br'ehier, Shmuel Rakotonirina-Ricquebourg","doi":"10.1137/20m1379836","DOIUrl":"https://doi.org/10.1137/20m1379836","url":null,"abstract":"We introduce and study a notion of Asymptotic Preserving schemes, related to convergence in distribution, for a class of slow-fast Stochastic Differential Equations. In some examples , crude schemes fail to capture the correct limiting equation resulting from averaging and diffusion approximation procedures. We propose examples of Asymptotic Preserving schemes: when the timescale separation vanishes, one obtains a limiting scheme, which is shown to be consistent in distribution with the limiting Stochastic Differential Equation. Numerical experiments illustrate the importance of the proposed Asymptotic Preserving schemes for several examples. In addition, in the averaging regime, error estimates are obtained and the proposed scheme is proved to be uniformly accurate.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131837645","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: 8
Transition path theory for Langevin dynamics on manifold: optimal control and data-driven solver 流形上朗之万动力学的过渡路径理论:最优控制和数据驱动求解器
Multiscale Model. Simul. Pub Date : 2020-10-20 DOI: 10.1137/21M1437883
Yuan Gao, Tiejun Li, Xiaoguang Li, Jianguo Liu
{"title":"Transition path theory for Langevin dynamics on manifold: optimal control and data-driven solver","authors":"Yuan Gao, Tiejun Li, Xiaoguang Li, Jianguo Liu","doi":"10.1137/21M1437883","DOIUrl":"https://doi.org/10.1137/21M1437883","url":null,"abstract":"We present a data-driven point of view for the rare events, which represent conformational transitions in biochemical reactions modeled by over-damped Langevin dynamics on manifolds in high dimensions. Given the point clouds sampled from an unknown reaction dynamics, we construct a discrete Markov process based on an approximated Voronoi tesselation which incorporates both the equilibrium and the manifold information. We reinterpret the transition state theory and transition path theory from the optimal control viewpoint. The controlled random walk on point clouds is utilized to simulate the transition path, which becomes an almost sure event instead of a rare event in the original reaction dynamics. Some numerical examples on sphere and torus are conducted to illustrate the data-driven solver for transition path theory on point clouds. The resulting dominated transition path highly coincides with the mean transition path obtained via the controlled Monte Carlo simulations.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130279701","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: 18
Multiscale Modeling of Glioma Invasion: From Receptor Binding to Flux-Limited Macroscopic PDEs 胶质瘤侵袭的多尺度建模:从受体结合到通量有限的宏观PDEs
Multiscale Model. Simul. Pub Date : 2020-10-07 DOI: 10.1137/21m1412104
Anne Dietrich, N. Kolbe, Nikolaos Sfakianakis, C. Surulescu
{"title":"Multiscale Modeling of Glioma Invasion: From Receptor Binding to Flux-Limited Macroscopic PDEs","authors":"Anne Dietrich, N. Kolbe, Nikolaos Sfakianakis, C. Surulescu","doi":"10.1137/21m1412104","DOIUrl":"https://doi.org/10.1137/21m1412104","url":null,"abstract":"We propose a novel approach to modeling cell migration in an anisotropic environment with biochemical heterogeneity and interspecies interactions, using as a paradigm glioma invasion in brain tissue under the influence of hypoxia-triggered angiogenesis. The multiscale procedure links single-cell and mesoscopic dynamics with population level behavior, leading on the macroscopic scale to flux-limited glioma diffusion and multiple taxis. We verify the non-negativity of regular solutions (provided they exist) to the obtained macroscopic PDE-ODE system and perform numerical simulations to illustrate the solution behavior under several scenarios.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123725758","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: 10
Mixed finite element approximation of periodic Hamilton-Jacobi-Bellman problems with application to numerical homogenization 周期Hamilton-Jacobi-Bellman问题的混合有限元逼近及其在数值均匀化中的应用
Multiscale Model. Simul. Pub Date : 2020-10-04 DOI: 10.1137/20M1371397
D. Gallistl, Timo Sprekeler, E. Süli
{"title":"Mixed finite element approximation of periodic Hamilton-Jacobi-Bellman problems with application to numerical homogenization","authors":"D. Gallistl, Timo Sprekeler, E. Süli","doi":"10.1137/20M1371397","DOIUrl":"https://doi.org/10.1137/20M1371397","url":null,"abstract":"In the first part of the paper, we propose and rigorously analyze a mixed finite element method for the approximation of the periodic strong solution to the fully nonlinear second-order Hamilton--Jacobi--Bellman equation with coefficients satisfying the Cordes condition. These problems arise as the corrector problems in the homogenization of Hamilton--Jacobi--Bellman equations. The second part of the paper focuses on the numerical homogenization of such equations, more precisely on the numerical approximation of the effective Hamiltonian. Numerical experiments demonstrate the approximation scheme for the effective Hamiltonian and the numerical solution of the homogenized problem.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"218 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126106838","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: 10
Optimal Convergence Rates for Elliptic Homogenization Problems in Nondivergence-Form: Analysis and Numerical Illustrations 非发散型椭圆均匀化问题的最优收敛速率:分析与数值实例
Multiscale Model. Simul. Pub Date : 2020-09-23 DOI: 10.1137/20M137121X
Timo Sprekeler, H. Tran
{"title":"Optimal Convergence Rates for Elliptic Homogenization Problems in Nondivergence-Form: Analysis and Numerical Illustrations","authors":"Timo Sprekeler, H. Tran","doi":"10.1137/20M137121X","DOIUrl":"https://doi.org/10.1137/20M137121X","url":null,"abstract":"We study optimal convergence rates in the periodic homogenization of linear elliptic equations of the form $-A(x/varepsilon):D^2 u^{varepsilon} = f$ subject to a homogeneous Dirichlet boundary condition. We show that the optimal rate for the convergence of $u^{varepsilon}$ to the solution of the corresponding homogenized problem in the $W^{1,p}$-norm is $mathcal{O}(varepsilon)$. We further obtain optimal gradient and Hessian bounds with correction terms taken into account in the $L^p$-norm. We then provide an explicit $c$-bad diffusion matrix and use it to perform various numerical experiments, which demonstrate the optimality of the obtained rates.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117339837","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: 10
Multiscale Control of Generic Second Order Traffic Models by Driver-Assist Vehicles 驾驶辅助车辆通用二阶交通模型的多尺度控制
Multiscale Model. Simul. Pub Date : 2020-08-17 DOI: 10.1137/20M1360128
F. A. Chiarello, B. Piccoli, A. Tosin
{"title":"Multiscale Control of Generic Second Order Traffic Models by Driver-Assist Vehicles","authors":"F. A. Chiarello, B. Piccoli, A. Tosin","doi":"10.1137/20M1360128","DOIUrl":"https://doi.org/10.1137/20M1360128","url":null,"abstract":"We study the derivation of generic high order macroscopic traffic models from a follow-the-leader particle description via a kinetic approach. First, we recover a third order traffic model as the hydrodynamic limit of an Enskog-type kinetic equation. Next, we introduce in the vehicle interactions a binary control modelling the automatic feedback provided by driver-assist vehicles and we upscale such a new particle description by means of another Enskog-based hydrodynamic limit. The resulting macroscopic model is now a Generic Second Order Model (GSOM), which contains in turn a control term inherited from the microscopic interactions. We show that such a control may be chosen so as to optimise global traffic trends, such as the vehicle flux or the road congestion, constrained by the GSOM dynamics. By means of numerical simulations, we investigate the effect of this control hierarchy in some specific case studies, which exemplify the multiscale path from the vehicle-wise implementation of a driver-assist control to its optimal hydrodynamic design.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"240 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122996827","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: 4
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