Esaim-Probability and Statistics最新文献_第5页

Impact of physical model error on state estimation for neutronics applications 物理模型误差对中子应用状态估计的影响

4区数学

Esaim-Probability and Statistics Pub Date : 2023-01-01 DOI: 10.1051/proc/202373158

Yonah Conjungo Taumhas, David Labeurthre, Francois Madiot, Olga Mula, Tommaso Taddei

引用次数: 0

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":null,"pages":null},"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

Approximation of the invariant distribution for a class of ergodic SDEs with one-sided Lipschitz continuous drift coefficient using an explicit tamed Euler scheme 一类具有单侧Lipschitz连续漂移系数的遍历SDEs的不变分布的显式正则欧拉格式逼近

4区数学

Esaim-Probability and Statistics Pub Date : 2023-01-01 DOI: 10.1051/ps/2023017

Charles-Edouard Bréhier

{"title":"Approximation of the invariant distribution for a class of ergodic SDEs with one-sided Lipschitz continuous drift coefficient using an explicit tamed Euler scheme","authors":"Charles-Edouard Bréhier","doi":"10.1051/ps/2023017","DOIUrl":"https://doi.org/10.1051/ps/2023017","url":null,"abstract":"We study the behavior in a large time regime of an explicit tamed Euler-Maruyama scheme applied to a class of ergodic Ito stochastic differential equations with one-sided Lipschitz continuous drift coefficient and bounded globally Lipschitz diffusion coefficient. Our first main contribution is to prove moments for the numerical scheme, which, on the one hand, are uniform with respect to the time-step size, and which, on the other hand, may not be uniform but have at most polynomial growth with respect to time. Our second main contribution is to apply this result to obtain weak error estimates to quantify the error to approximate averages with respect to the invariant distribution of the continuous-time process, as a function of the time-step size and of the time horizon. The explicit tamed Euler scheme is shown to be computationally effective for the approximation of the invariant distribution: even if the moment bounds and error estimates are not proved to be uniform with respect to time, the obtained polynomial growth results in a marginal increase in the upper bound of the computational cost. To the best of our knowledge, this is the first result in the literature concerning the approximation of the invariant distribution for stochastic differential equations with non-globally Lipschitz coefficients using an explicit tamed Euler-Maruyama scheme.","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135784438","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: 5

On the asymptotic behaviour of superexponential Levy processes 超指数Levy过程的渐近性

4区数学

Esaim-Probability and Statistics Pub Date : 2023-01-01 DOI: 10.1051/ps/2023015

Patrik Albin, Mattias Sunden

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":null,"pages":null},"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":null,"pages":null},"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 optimal uniform approximation of Lévy processes on Banach spaces with finite variation processes 有限变分过程Banach空间上lsamvy过程的最优一致逼近

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2022-10-30 DOI: 10.1051/ps/2022011

Rafal Marcin Lochowski, Witold Marek Bednorz, Rafał Martynek

引用次数: 1

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