Esaim-Probability and Statistics最新文献_第4页

Homological- and analytical-preserving serendipity framework for polytopal complexes, with application to the DDR method 多拓扑配合物的同源性和解析性保持偶然性框架及其在DDR方法中的应用

4区数学

Esaim-Probability and Statistics Pub Date : 2023-01-01 DOI: 10.1051/m2an/2022067

Daniele Antonio Di Pietro, Jérôme Droniou

{"title":"Homological- and analytical-preserving serendipity framework for polytopal complexes, with application to the DDR method","authors":"Daniele Antonio Di Pietro, Jérôme Droniou","doi":"10.1051/m2an/2022067","DOIUrl":"https://doi.org/10.1051/m2an/2022067","url":null,"abstract":"In this work we investigate from a broad perspective the reduction of degrees of freedom through serendipity techniques for polytopal methods compatible with Hilbert complexes. We first establish an abstract framework that, given two complexes connected by graded maps, identifies a set of properties enabling the transfer of the homological and analytical properties from one complex to the other. This abstract framework is designed having in mind discrete complexes, with one of them being a reduced version of the other, such as occurring when applying serendipity techniques to numerical methods. We then use this framework as an overarching blueprint to design a serendipity DDR complex. Thanks to the combined use of higher-order reconstructions and serendipity, this complex compares favorably in terms of degrees of freedom (DOF) count to all the other polytopal methods previously introduced and also to finite elements on certain element geometries. The gain resulting from such a reduction in the number of DOFs is numerically evaluated on two model problems: a magnetostatic model, and the Stokes equations.","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136053140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Optimal convergence rates in L² for a first order system least squares finite element method 一阶系统最小二乘有限元法在L2中的最优收敛率

4区数学

Esaim-Probability and Statistics Pub Date : 2023-01-01 DOI: 10.1051/m2an/2022026

Maximilian Bernkopf, Jens Markus Melenk

引用次数: 0

Deep learning-based schemes for singularly perturbed convection-diffusion problems 基于深度学习的奇摄动对流扩散问题求解方法

4区数学

Esaim-Probability and Statistics Pub Date : 2023-01-01 DOI: 10.1051/proc/202373048

Adrien Beguinet, Virginie Ehrlacher, Roberta Flenghi, Maria Fuente, Olga Mula, Agustin Somacal

{"title":"Deep learning-based schemes for singularly perturbed convection-diffusion problems","authors":"Adrien Beguinet, Virginie Ehrlacher, Roberta Flenghi, Maria Fuente, Olga Mula, Agustin Somacal","doi":"10.1051/proc/202373048","DOIUrl":"https://doi.org/10.1051/proc/202373048","url":null,"abstract":"Deep learning-based numerical schemes such as Physically Informed Neural Networks (PINNs) have recently emerged as an alternative to classical numerical schemes for solving Partial Differential Equations (PDEs). They are very appealing at first sight because implementing vanilla versions of PINNs based on strong residual forms is easy, and neural networks offer very high approximation capabilities. However, when the PDE solutions are low regular, an expert insight is required to build deep learning formulations that do not incur in variational crimes. Optimization solvers are also significantly challenged, and can potentially spoil the final quality of the approximated solution due to the convergence to bad local minima, and bad generalization capabilities. In this paper, we present an exhaustive numerical study of the merits and limitations of these schemes when solutions exhibit low-regularity, and compare performance with respect to more benign cases when solutions are very smooth. As a support for our study, we consider singularly perturbed convection-diffusion problems where the regularity of solutions typically degrades as certain multiscale parameters go to zero.","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135058788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Reliable temporal prediction in the Markov stochastic block model 马尔可夫随机块模型的可靠时间预测

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2022-11-30 DOI: 10.1051/ps/2022019

Quentin Duchemin

引用次数: 0

Ergodic behaviour of a multi-type growth-fragmentation process modelling the mycelial network of a filamentous fungus 模拟丝状真菌菌丝网络的多类型生长破碎过程的遍历行为

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2022-10-31 DOI: 10.1051/ps/2022013

M. Tomašević, Vincent Bansaye, A. Véber

{"title":"Ergodic behaviour of a multi-type growth-fragmentation process modelling the mycelial network of a filamentous fungus","authors":"M. Tomašević, Vincent Bansaye, A. Véber","doi":"10.1051/ps/2022013","DOIUrl":"https://doi.org/10.1051/ps/2022013","url":null,"abstract":"In this work, we introduce a stochastic growth-fragmentation model for the expansion of the network of filaments ( mycelium ) of a filamentous fungus. In this model, each individual is described by a discrete type e∈{0,1} indicating whether the individual corresponds to an internal or terminal segment of filament, and a continuous trait x≥0 corresponding to the length of this segment. The length of internal segments cannot grow, while the length of terminal segments increases at a deterministic speed. Both types of individuals/segments branch according to a type-dependent mechanism. After constructing the stochastic bi-type growth-fragmentation process, we analyse the corresponding mean measure. We show that its ergodic behaviour is governed by the maximal eigenelements. In the long run, the total mass of the mean measure increases exponentially fast while the type-dependent density in trait converges to an explicit distribution at some exponential speed. We then obtain a law of large numbers that relates the long term behaviour of the stochastic process to the limiting distribution. The model we consider depends on only 3 parameters and all the quantities needed to describe this asymptotic behaviour are explicit, which paves the way for parameter inference based on data collected in lab experiments.","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":"12 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85709965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

On stochastic orders and total positivity 关于随机序和总正性

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2022-09-16 DOI: 10.1051/ps/2023005

L. Duembgen, Alexandre Mösching

引用次数: 0

Convergence of the empirical measure in expected Wasserstein distance: non asymptotic explicit bounds in Rd 期望Wasserstein距离中经验测度的收敛性:Rd中的非渐近显式界

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2022-09-02 DOI: 10.1051/ps/2023011

N. Fournier

引用次数: 6

Fast calibration of weak FARIMA models 弱FARIMA模型的快速标定

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2022-06-20 DOI: 10.1051/ps/2022021

S. B. Hariz, A. Brouste, Youssef Esstafa, M. Soltane

引用次数: 1

Martingale solutions of the stochastic 2D primitive equations with anisotropic viscosity 具有各向异性黏度的二维随机原始方程的鞅解

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2022-04-20 DOI: 10.1051/ps/2022006

Chengfeng Sun, Hongjun Gao, Hui Liu, Jie-qiong Zhang

引用次数: 1

A probabilistic point of view for the Kolmogorov hypoelliptic equations 柯尔莫哥洛夫半椭圆方程的概率观点

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2021-09-14 DOI: 10.1051/ps/2023007

Pierre Etor'e, Jos'e R. Le'on, C. Prieur

引用次数: 0