This review presents some recent works on the construction of closure relations for moment systems extracted from a kinetic equation. A rough construction of those closures and the main properties of the resulting systems are described. Especially, based on the underlying kinetic equation, the main properties desired for such moment systems are the realizability, i.e. the positivity of an underlying kinetic solution, global strong hyperbolicity and entropy dissipation.
{"title":"Some recent advances on the method of moments in kinetic theory","authors":"Teddy Pichard","doi":"10.1051/proc/202375086","DOIUrl":"https://doi.org/10.1051/proc/202375086","url":null,"abstract":"This review presents some recent works on the construction of closure relations for moment systems extracted from a kinetic equation. A rough construction of those closures and the main properties of the resulting systems are described. Especially, based on the underlying kinetic equation, the main properties desired for such moment systems are the realizability, i.e. the positivity of an underlying kinetic solution, global strong hyperbolicity and entropy dissipation.","PeriodicalId":505884,"journal":{"name":"ESAIM: Proceedings and Surveys","volume":" 47","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139196250","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}
Max Fathi, Pierre Le Bris, A. Menegaki, Pierre Monmarche, Julien Reygner, Milica Tomasevic
This article presents a selection of recent results in the mathematical study of physical systems described by a large number of particles, with various types of interactions (mean-field, moderate, nearest-neighbor). Limit theorems are obtained concerning either the large-scale or the long-time behavior of these systems. These results rely on the use of a large range of mathematical tools, arising from both probability theory and the analysis of partial differential equations, and thereby illustrate fruitful interactions between these two disciplines.
{"title":"Recent progress on limit theorems for large stochastic particle systems","authors":"Max Fathi, Pierre Le Bris, A. Menegaki, Pierre Monmarche, Julien Reygner, Milica Tomasevic","doi":"10.1051/proc/202375002","DOIUrl":"https://doi.org/10.1051/proc/202375002","url":null,"abstract":"This article presents a selection of recent results in the mathematical study of physical systems described by a large number of particles, with various types of interactions (mean-field, moderate, nearest-neighbor). Limit theorems are obtained concerning either the large-scale or the long-time behavior of these systems. These results rely on the use of a large range of mathematical tools, arising from both probability theory and the analysis of partial differential equations, and thereby illustrate fruitful interactions between these two disciplines.","PeriodicalId":505884,"journal":{"name":"ESAIM: Proceedings and Surveys","volume":"69 5-6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139190804","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}
This paper reviews the different existing Contact Dynamics schemes for the simulation of granular media, for which the discrete incremental problem is based on the resolution of convex problems. This type of discretization has the great advantage of allowing the use of standard convex optimization algorithms. In the case of frictional contacts, we consider schemes based on a convex relaxation of the constraint as well as a fixed point scheme. The model and the computations leading to the discrete problems are detailed in the case of convex, regular but not necessarily spherical particles. We prove, using basic tools of convex analysis, that the discrete optimization problem can be seen as a minimization problem of a global discrete energy for the system, in which the velocity to be considered is an average of the pre- and post-impact velocities. A numerical study on an academic test case is conducted, illustrating for the first time the convergence with order 1 in the time step of the different schemes. We also discuss the influence of the convex relaxation of the constraint on the behavior of the system. We show in particular that, although it induces numerical dilatation, it does not significantly modify the macrosopic behavior of a column collapse en 2d. The numerical tests are performed using the code SCoPI.
{"title":"On convex numerical schemes for inelastic contacts with friction","authors":"Helene Bloch, Aline Lefebvre-Lepot","doi":"10.1051/proc/202375024","DOIUrl":"https://doi.org/10.1051/proc/202375024","url":null,"abstract":"This paper reviews the different existing Contact Dynamics schemes for the simulation of granular media, for which the discrete incremental problem is based on the resolution of convex problems. This type of discretization has the great advantage of allowing the use of standard convex optimization algorithms. In the case of frictional contacts, we consider schemes based on a convex relaxation of the constraint as well as a fixed point scheme. The model and the computations leading to the discrete problems are detailed in the case of convex, regular but not necessarily spherical particles. We prove, using basic tools of convex analysis, that the discrete optimization problem can be seen as a minimization problem of a global discrete energy for the system, in which the velocity to be considered is an average of the pre- and post-impact velocities. A numerical study on an academic test case is conducted, illustrating for the first time the convergence with order 1 in the time step of the different schemes. We also discuss the influence of the convex relaxation of the constraint on the behavior of the system. We show in particular that, although it induces numerical dilatation, it does not significantly modify the macrosopic behavior of a column collapse en 2d. The numerical tests are performed using the code SCoPI.","PeriodicalId":505884,"journal":{"name":"ESAIM: Proceedings and Surveys","volume":"60 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139191821","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}
Electromagnetic simulations on large domains require a huge memory consumption. Domain decomposition methods, based on Trefftz methods, could be an answer to this issue. In this paper, we associate to heterogeneous three-dimensional Maxwell equations one variational formulation which can be obtained either by upwind fluxes or Riemann traces. We associate to this variational formulation an iterative Trefftz Krylov solver. The poor conditioning due to the use of plane wave basis functions is bypassed thanks to a compression strategy. Moreover, the developed iterative solver is accelerated thanks to a left preconditioner. The considered numerical cases illustrate the performance of this basis reduction, which leads to the consideration of an industrial case of more than 750 millions of degrees of freedom.
{"title":"Ultra-weak variational formulation for heterogeneous Maxwell problem in the context of high performance computing","authors":"S. Pernet, Margot Sirdey, S. Tordeux","doi":"10.1051/proc/202375096","DOIUrl":"https://doi.org/10.1051/proc/202375096","url":null,"abstract":"Electromagnetic simulations on large domains require a huge memory consumption. Domain decomposition methods, based on Trefftz methods, could be an answer to this issue. In this paper, we associate to heterogeneous three-dimensional Maxwell equations one variational formulation which can be obtained either by upwind fluxes or Riemann traces. We associate to this variational formulation an iterative Trefftz Krylov solver. The poor conditioning due to the use of plane wave basis functions is bypassed thanks to a compression strategy. Moreover, the developed iterative solver is accelerated thanks to a left preconditioner. The considered numerical cases illustrate the performance of this basis reduction, which leads to the consideration of an industrial case of more than 750 millions of degrees of freedom.","PeriodicalId":505884,"journal":{"name":"ESAIM: Proceedings and Surveys","volume":"28 1-3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139188325","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}
This article summarizes some recent works and associated challenges in the field of Bayesian statistics that were presented during the Journées MAS 2020. The goal of the session was to give an overview of the many aspects of Bayesian statistics investigated by young researchers of the community.
本文总结了在 "Journées MAS 2020 "期间发表的贝叶斯统计领域的一些最新研究成果和相关挑战。该会议的目的是概述贝叶斯统计领域年轻研究人员所研究的诸多方面。
{"title":"Bayes in action in deep learning and dictionary learning","authors":"Julyan Arbel, Hong-Phuong Dang, Clément Elvira, Cédric Herzet, Zacharie Naulet, M. Vladimirova","doi":"10.1051/proc/202374090","DOIUrl":"https://doi.org/10.1051/proc/202374090","url":null,"abstract":"This article summarizes some recent works and associated challenges in the field of Bayesian statistics that were presented during the Journées MAS 2020. The goal of the session was to give an overview of the many aspects of Bayesian statistics investigated by young researchers of the community.","PeriodicalId":505884,"journal":{"name":"ESAIM: Proceedings and Surveys","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139294285","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}
M. Capitaine, S. Coste, F. Gabriel, P. Maillard, C. Mailler
We collect recent results on random matrices and random graphs. The topics covered are: fluctuations of the empirical measure of random matrices, finite-size effects of algorithms involving random matrices, characteristic polynomial of sparse matrices and Voronoi tesselations of split trees.
{"title":"Random matrices and random graphs","authors":"M. Capitaine, S. Coste, F. Gabriel, P. Maillard, C. Mailler","doi":"10.1051/proc/202374137","DOIUrl":"https://doi.org/10.1051/proc/202374137","url":null,"abstract":"We collect recent results on random matrices and random graphs. The topics covered are: fluctuations of the empirical measure of random matrices, finite-size effects of algorithms involving random matrices, characteristic polynomial of sparse matrices and Voronoi tesselations of split trees.","PeriodicalId":505884,"journal":{"name":"ESAIM: Proceedings and Surveys","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139300951","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}
Between 1980 and 2020, extreme weather and climate change events have caused, in Europe, up to 520 billion euros in economic losses, according to a 2022 report released by the European Environment Agency. Many weather extreme events such as heatwaves, droughts, tropical cyclones and cold spells will change in frequency and/or intensity due to the ongoing anthropogenic climate change, driving our planet to unprecedented threats. From a theoretical point of view, such extreme events are difficult to characterize because they are rare and they do occur at specific spatiotemporal scales of the dynamics, not necessarily the largest or the smallest of the climate system. Their study requires a framework capable of tracking their probability of occurrence, predictability and persistence. In this manuscript I will describe how dynamical systems theory helps in building numerical and theoretical tools for weather extreme events, using recurrences of patterns termed analogues. These tools can be used to study whether climate change do already affect the dynamics of extremes. Three recent examples will be analysed in details, namely the Argentinian heatwave, the Greek cold spell and the windstorm Malik, all occurred in January 2022.
{"title":"Dynamical systems approaches to the study of climate with applications to 2022 extreme weather events","authors":"Davide Faranda","doi":"10.1051/proc/202374051","DOIUrl":"https://doi.org/10.1051/proc/202374051","url":null,"abstract":"Between 1980 and 2020, extreme weather and climate change events have caused, in Europe, up to 520 billion euros in economic losses, according to a 2022 report released by the European Environment Agency. Many weather extreme events such as heatwaves, droughts, tropical cyclones and cold spells will change in frequency and/or intensity due to the ongoing anthropogenic climate change, driving our planet to unprecedented threats. From a theoretical point of view, such extreme events are difficult to characterize because they are rare and they do occur at specific spatiotemporal scales of the dynamics, not necessarily the largest or the smallest of the climate system. Their study requires a framework capable of tracking their probability of occurrence, predictability and persistence. In this manuscript I will describe how dynamical systems theory helps in building numerical and theoretical tools for weather extreme events, using recurrences of patterns termed analogues. These tools can be used to study whether climate change do already affect the dynamics of extremes. Three recent examples will be analysed in details, namely the Argentinian heatwave, the Greek cold spell and the windstorm Malik, all occurred in January 2022.","PeriodicalId":505884,"journal":{"name":"ESAIM: Proceedings and Surveys","volume":"83 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139292897","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}
Sophie Dabo-Niang, Julien Ah-Pine, Pamela Llop, A. Yao
This paper presents some recent results on regression and classification in Functional Data Analysis setting. The first work decated to Multiple kernel SVM for classifying functional data in Sobolev spaces focus on optimization of the information from each derivatives of the original functions, the second work devoted to An input/output-based aggregation rule for functional data classification when the last is interested with the problem of regression if the functional data lives in a finite dimensionnal submanifold.
{"title":"Some results on statistics and functional data analysis","authors":"Sophie Dabo-Niang, Julien Ah-Pine, Pamela Llop, A. Yao","doi":"10.1051/proc/202374002","DOIUrl":"https://doi.org/10.1051/proc/202374002","url":null,"abstract":"This paper presents some recent results on regression and classification in Functional Data Analysis setting. The first work decated to Multiple kernel SVM for classifying functional data in Sobolev spaces focus on optimization of the information from each derivatives of the original functions, the second work devoted to An input/output-based aggregation rule for functional data classification when the last is interested with the problem of regression if the functional data lives in a finite dimensionnal submanifold.","PeriodicalId":505884,"journal":{"name":"ESAIM: Proceedings and Surveys","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139303027","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}
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