{"title":"Workshop on Compressible Multiphase Flows Derivation, closure laws, thermodynamics","authors":"P. Helluy, J. Hérard, N. Seguin","doi":"10.1051/proc/201966000","DOIUrl":"https://doi.org/10.1051/proc/201966000","url":null,"abstract":"","PeriodicalId":53260,"journal":{"name":"ESAIM Proceedings and Surveys","volume":"121 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89384482","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}
Cyril Bénézet, J. Bonnefoy, J. Chassagneux, Shuoqing Deng, Camilo A. Garcia Trillos, L. Lenôtre
In this work, we present a numerical method based on a sparse grid approximation to compute the loss distribution of the balance sheet of a financial or an insurance company. We first describe, in a stylised way, the assets and liabilities dynamics that are used for the numerical estimation of the balance sheet distribution. For the pricing and hedging model, we chose a classical Black & choles model with a stochastic interest rate following a Hull & White model. The risk management model describing the evolution of the parameters of the pricing and hedging model is a Gaussian model. The new numerical method is compared with the traditional nested simulation approach. We review the convergence of both methods to estimate the risk indicators under consideration. Finally, we provide numerical results showing that the sparse grid approach is extremely competitive for models with moderate dimension.
{"title":"A sparse grid approach to balance sheet risk measurement","authors":"Cyril Bénézet, J. Bonnefoy, J. Chassagneux, Shuoqing Deng, Camilo A. Garcia Trillos, L. Lenôtre","doi":"10.1051/PROC/201965236","DOIUrl":"https://doi.org/10.1051/PROC/201965236","url":null,"abstract":"In this work, we present a numerical method based on a sparse grid approximation to compute the loss distribution of the balance sheet of a financial or an insurance company. We first describe, in a stylised way, the assets and liabilities dynamics that are used for the numerical estimation of the balance sheet distribution. For the pricing and hedging model, we chose a classical Black & choles model with a stochastic interest rate following a Hull & White model. The risk management model describing the evolution of the parameters of the pricing and hedging model is a Gaussian model. The new numerical method is compared with the traditional nested simulation approach. We review the convergence of both methods to estimate the risk indicators under consideration. Finally, we provide numerical results showing that the sparse grid approach is extremely competitive for models with moderate dimension.","PeriodicalId":53260,"journal":{"name":"ESAIM Proceedings and Surveys","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82434059","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}
Pub Date : 2018-10-17DOI: 10.1051/PROC/201862186201
A. Barlukova, S. Honoré, F. Hubert
Microtubule-targeted agents (MTAs), widely used in chemotherapy, are molecules that are able to block cancer cell migration and division. Their effect on microtubule (MT) dynamic instability is measured by their influence on observable parameters of MT dynamics such as growth speed, time-based catastrophe frequency, time-based rescue fre- quency, etc. In this paper, we propose a new mathematical model that is able to reproduce MT dynamics with an appropriate estimation of the main observable parameters. Using the experimental data on paclitaxel effect in presence of EB proteins, we fitted param- eters of the model from several drug concentrations. It enable us to understand which non-observable model parameters are able to reproduce the effect of MTAs and thus to highlight a new potential mechanism of action associated with MTAs effect in presence of EB protein.
{"title":"Mathematical Modeling of Effect Of Microtubule-Targeted Agents On Microtubule Dynamic Instability","authors":"A. Barlukova, S. Honoré, F. Hubert","doi":"10.1051/PROC/201862186201","DOIUrl":"https://doi.org/10.1051/PROC/201862186201","url":null,"abstract":"Microtubule-targeted agents (MTAs), widely used in chemotherapy, are molecules that are able to block cancer cell migration and division. Their effect on microtubule (MT) dynamic instability is measured by their influence on observable parameters of MT dynamics such as growth speed, time-based catastrophe frequency, time-based rescue fre- quency, etc. In this paper, we propose a new mathematical model that is able to reproduce MT dynamics with an appropriate estimation of the main observable parameters. Using the experimental data on paclitaxel effect in presence of EB proteins, we fitted param- eters of the model from several drug concentrations. It enable us to understand which non-observable model parameters are able to reproduce the effect of MTAs and thus to highlight a new potential mechanism of action associated with MTAs effect in presence of EB protein.","PeriodicalId":53260,"journal":{"name":"ESAIM Proceedings and Surveys","volume":"29 1","pages":"1-16"},"PeriodicalIF":0.0,"publicationDate":"2018-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84879940","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}
Ludovic Goudenège, Adam Larat, J. Llobell, M. Massot, David Mercier, O. Thomine, Aymeric Vi'e FR3487, Bacchus, Coffee, EM2C, Cealeti, Coria
This paper exposes a novel exploratory formalism, the end goal of which is the numerical simulation of the dynamics of a cloud of particles weakly or strongly coupled with a turbulent fluid. Given the large panel of expertise of the list of authors, the content of this paper scans a wide range of connex notions, from the physics of turbulence to the rigorous definition of stochastic processes. Our approach is to develop reduced-order models for the dynamics of both carrying and carried phases which remain consistant within this formalism, and to set up a numerical process to validate these models. The novelties of this paper lie in the gathering of a large panel of mathematical and physical definitions and results within a common framework and an agreed vocabulary (sections 1 and 2), and in some preliminary results and achievements within this context, section 3. While the first three sections have been simplified to the context of a gas field providing that the disperse phase only retrieves energy through drag, the fourth section opens this study to the more complex situation when the disperse phase interacts with the continuous phase as well, in an energy conservative manner. This will allow us to expose the perspectives of the project and to conclude.
{"title":"Statistical and probabilistic modeling of a cloud of particles coupled with a turbulent fluid","authors":"Ludovic Goudenège, Adam Larat, J. Llobell, M. Massot, David Mercier, O. Thomine, Aymeric Vi'e FR3487, Bacchus, Coffee, EM2C, Cealeti, Coria","doi":"10.1051/proc/201965401","DOIUrl":"https://doi.org/10.1051/proc/201965401","url":null,"abstract":"This paper exposes a novel exploratory formalism, the end goal of which is the numerical simulation of the dynamics of a cloud of particles weakly or strongly coupled with a turbulent fluid. Given the large panel of expertise of the list of authors, the content of this paper scans a wide range of connex notions, from the physics of turbulence to the rigorous definition of stochastic processes. Our approach is to develop reduced-order models for the dynamics of both carrying and carried phases which remain consistant within this formalism, and to set up a numerical process to validate these models. The novelties of this paper lie in the gathering of a large panel of mathematical and physical definitions and results within a common framework and an agreed vocabulary (sections 1 and 2), and in some preliminary results and achievements within this context, section 3. While the first three sections have been simplified to the context of a gas field providing that the disperse phase only retrieves energy through drag, the fourth section opens this study to the more complex situation when the disperse phase interacts with the continuous phase as well, in an energy conservative manner. This will allow us to expose the perspectives of the project and to conclude.","PeriodicalId":53260,"journal":{"name":"ESAIM Proceedings and Surveys","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83021480","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}
We introduce a new streamline derivative projection-based closure modeling strategy for the numerical stabilization of Proper Orthogonal Decomposition-Reduced Order Models (POD-ROM). As a first preliminary step, the proposed model is analyzed and tested for advection-dominated advection-diffusion-reaction equations. In this framework, the numerical analysis for the Finite Element (FE) discretization of the proposed new POD-ROM is presented, by mainly deriving the corresponding error estimates. Numerical tests for advection-dominated regime show the effciency of the proposed method, as well the increased accuracy over the standard POD-ROM that discovers its well-known limitations very soon in the numerical settings considered, i.e. for low diffusion coeffcients.
{"title":"A streamline derivative POD-ROM for advection-diffusion-reaction equations","authors":"S. Rubino","doi":"10.1051/PROC/201864121","DOIUrl":"https://doi.org/10.1051/PROC/201864121","url":null,"abstract":"We introduce a new streamline derivative projection-based closure modeling strategy for the numerical stabilization of Proper Orthogonal Decomposition-Reduced Order Models (POD-ROM). As a first preliminary step, the proposed model is analyzed and tested for advection-dominated advection-diffusion-reaction equations. In this framework, the numerical analysis for the Finite Element (FE) discretization of the proposed new POD-ROM is presented, by mainly deriving the corresponding error estimates. Numerical tests for advection-dominated regime show the effciency of the proposed method, as well the increased accuracy over the standard POD-ROM that discovers its well-known limitations very soon in the numerical settings considered, i.e. for low diffusion coeffcients.","PeriodicalId":53260,"journal":{"name":"ESAIM Proceedings and Surveys","volume":"13 1","pages":"121-136"},"PeriodicalIF":0.0,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84457041","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}
In this paper, we prove that the weak error between a stochastic differential equation with nonlinearity in the sense of McKean given by moments and its approximation by the Euler discretization with time-step h of a system of N interacting particles is 𝒪(N-1+h). We provide numerical experiments confirming this behaviour and showing that it extends to more general mean-field interaction and study the efficiency of the antithetic sampling technique on the same examples.
{"title":"Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean","authors":"Oumaima Bencheikh, B. Jourdain","doi":"10.1051/PROC/201965219","DOIUrl":"https://doi.org/10.1051/PROC/201965219","url":null,"abstract":"In this paper, we prove that the weak error between a stochastic differential equation with nonlinearity in the sense of McKean given by moments and its approximation by the Euler discretization with time-step h of a system of N interacting particles is 𝒪(N-1+h). We provide numerical experiments confirming this behaviour and showing that it extends to more general mean-field interaction and study the efficiency of the antithetic sampling technique on the same examples.","PeriodicalId":53260,"journal":{"name":"ESAIM Proceedings and Surveys","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78855954","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}
Simple models for size structured cell populations undergoing growth and division produce a class of functional ordinary differential equations, called pantograph equations, that describe the long time asymptotics of the cell number density. Pantograph equations arise in a number of applications outside this model and, as a result, have been studied heavily over the last five decades. In this paper we review and survey the role of the pantograph equation in the context of cell division. In addition, for a simple case we present a method of solution based on the Mellin transform and establish uniqueness directly from the transform equation.
{"title":"Cell Division And The Pantograph Equation","authors":"B. Brunt, A. Zaidi, T. Lynch","doi":"10.1051/PROC/201862158","DOIUrl":"https://doi.org/10.1051/PROC/201862158","url":null,"abstract":"Simple models for size structured cell populations undergoing growth and division produce a class of functional ordinary differential equations, called pantograph equations, that describe the long time asymptotics of the cell number density. Pantograph equations arise in a number of applications outside this model and, as a result, have been studied heavily over the last five decades. In this paper we review and survey the role of the pantograph equation in the context of cell division. In addition, for a simple case we present a method of solution based on the Mellin transform and establish uniqueness directly from the transform equation.","PeriodicalId":53260,"journal":{"name":"ESAIM Proceedings and Surveys","volume":"15 1","pages":"158-167"},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84968946","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}
Julien Bigot, V. Grandgirard, G. Latu, J. Méhaut, L. F. Millani, C. Passeron, S. Masnada, J. Richard, B. Videau
Modeling turbulent transport is a major goal in order to predict confinement performance in a tokamak plasma. The gyrokinetic framework considers a computational domain in five dimensions to look at kinetic issues in a plasma; this leads to huge computational needs. Therefore, optimization of the code is an especially important aspect, especially since coprocessors and complex manycore architectures are foreseen as building blocks for Exascale systems. This project aims to evaluate the applicability of two auto-tuning approaches with the BOAST and StarPU tools on the gysela code in order to circumvent performance portability issues. A specific computation intensive kernel is considered in order to evaluate the benefit of these methods. StarPU enables to match the performance and even sometimes outperform the hand-optimized version of the code while leaving scheduling choices to an automated process. BOAST on the other hand reveals to be well suited to get a gain in terms of execution time on four architectures. Speedups in-between 1.9 and 5.7 are obtained on a cornerstone computation intensive kernel.
{"title":"Building and Auto-Tuning Computing Kernels: Experimenting with BOAST and StarPU in the GYSELA Code","authors":"Julien Bigot, V. Grandgirard, G. Latu, J. Méhaut, L. F. Millani, C. Passeron, S. Masnada, J. Richard, B. Videau","doi":"10.1051/PROC/201863152","DOIUrl":"https://doi.org/10.1051/PROC/201863152","url":null,"abstract":"Modeling turbulent transport is a major goal in order to predict confinement performance in a tokamak plasma. The gyrokinetic framework considers a computational domain in five dimensions to look at kinetic issues in a plasma; this leads to huge computational needs. Therefore, optimization of the code is an especially important aspect, especially since coprocessors and complex manycore architectures are foreseen as building blocks for Exascale systems. This project aims to evaluate the applicability of two auto-tuning approaches with the BOAST and StarPU tools on the gysela code in order to circumvent performance portability issues. A specific computation intensive kernel is considered in order to evaluate the benefit of these methods. StarPU enables to match the performance and even sometimes outperform the hand-optimized version of the code while leaving scheduling choices to an automated process. BOAST on the other hand reveals to be well suited to get a gain in terms of execution time on four architectures. Speedups in-between 1.9 and 5.7 are obtained on a cornerstone computation intensive kernel.","PeriodicalId":53260,"journal":{"name":"ESAIM Proceedings and Surveys","volume":"25 1 1","pages":"152-178"},"PeriodicalIF":0.0,"publicationDate":"2018-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89903406","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}
Laurence Beaude, Thibaud Beltzung, K. Brenner, S. Lopez, R. Masson, F. Smaï, Jean-Frédéric Thebault, F. Xing
To answer the need for an efficient and robust geothermal simulation tool going beyond existing code capabilities in terms of geological and physical complexity, we have started to develop a parallel geothermal simulator based on unstructured meshes. The model takes into account complex geology including fault networks acting as major heat and mass transfer corridors and complex physics coupling the mass and energy conservations to the thermodynamical equilibrium between the gas and liquid phases. The objective of this Cemracs project is to focus on well modeling which is a key missing ingredient in our current simulator in order to perform realistic geothermal studies both in terms of monitoring and in terms of history matching. The well is discretized by a set of edges of the mesh in order to represent efficiently slanted or multi-branch wells on unstructured meshes. The connection with the 3D matrix and the 2D fault network at each node of the well is accounted for using Peaceman's approach. The non-isothermal flow model inside the well is based on the usual single unknown approach assuming the hydrostatic and thermodynamical equilibrium inside the well. The parallelization of the well model is implemented in such a way that the assembly of the Jacobian at each Newton step and the computation of the pressure drops inside the well can be done locally on each process without MPI communications.
{"title":"Parallel geothermal numerical model with faults and multi-branch wells","authors":"Laurence Beaude, Thibaud Beltzung, K. Brenner, S. Lopez, R. Masson, F. Smaï, Jean-Frédéric Thebault, F. Xing","doi":"10.1051/PROC/201863109","DOIUrl":"https://doi.org/10.1051/PROC/201863109","url":null,"abstract":"To answer the need for an efficient and robust geothermal simulation tool going beyond existing code capabilities in terms of geological and physical complexity, we have started to develop a parallel geothermal simulator based on unstructured meshes. The model takes into account complex geology including fault networks acting as major heat and mass transfer corridors and complex physics coupling the mass and energy conservations to the thermodynamical equilibrium between the gas and liquid phases. The objective of this Cemracs project is to focus on well modeling which is a key missing ingredient in our current simulator in order to perform realistic geothermal studies both in terms of monitoring and in terms of history matching. The well is discretized by a set of edges of the mesh in order to represent efficiently slanted or multi-branch wells on unstructured meshes. The connection with the 3D matrix and the 2D fault network at each node of the well is accounted for using Peaceman's approach. The non-isothermal flow model inside the well is based on the usual single unknown approach assuming the hydrostatic and thermodynamical equilibrium inside the well. The parallelization of the well model is implemented in such a way that the assembly of the Jacobian at each Newton step and the computation of the pressure drops inside the well can be done locally on each process without MPI communications.","PeriodicalId":53260,"journal":{"name":"ESAIM Proceedings and Surveys","volume":"104 1","pages":"109-134"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85869527","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}
Andrea Angiuli, Christy V. Graves, Houzhi Li, J. Chassagneux, Franccois Delarue, R. Carmona
This project investigates numerical methods for solving fully coupled forward-backward stochastic differential equations (FBSDEs) of McKean-Vlasov type. Having numerical solvers for such mean field FBSDEs is of interest because of the potential application of these equations to optimization problems over a large population, say for instance mean field games (MFG) and optimal mean field control problems. Theory for this kind of problems has met with great success since the early works on mean field games by Lasry and Lions, see [29], and by Huang, Caines, and Malhamé, see [26]. Generally speaking, the purpose is to understand the continuum limit of optimizers or of equilibria (say in Nash sense) as the number of underlying players tends to infinity. When approached from the probabilistic viewpoint, solutions to these control problems (or games) can be described by coupled mean field FBSDEs, meaning that the coefficients depend upon the own marginal laws of the solution. In this note, we detail two methods for solving such FBSDEs which we implement and apply to five benchmark problems. The first method uses a tree structure to represent the pathwise laws of the solution, whereas the second method uses a grid discretization to represent the time marginal laws of the solutions. Both are based on a Picard scheme; importantly, we combine each of them with a generic continuation method that permits to extend the time horizon (or equivalently the coupling strength between the two equations) for which the Picard iteration converges.
{"title":"Cemracs 2017: numerical probabilistic approach to MFG","authors":"Andrea Angiuli, Christy V. Graves, Houzhi Li, J. Chassagneux, Franccois Delarue, R. Carmona","doi":"10.1051/PROC/201965084","DOIUrl":"https://doi.org/10.1051/PROC/201965084","url":null,"abstract":"This project investigates numerical methods for solving fully coupled forward-backward stochastic differential equations (FBSDEs) of McKean-Vlasov type. Having numerical solvers for such mean field FBSDEs is of interest because of the potential application of these equations to optimization problems over a large population, say for instance mean field games (MFG) and optimal mean field control problems. Theory for this kind of problems has met with great success since the early works on mean field games by Lasry and Lions, see [29], and by Huang, Caines, and Malhamé, see [26]. Generally speaking, the purpose is to understand the continuum limit of optimizers or of equilibria (say in Nash sense) as the number of underlying players tends to infinity. When approached from the probabilistic viewpoint, solutions to these control problems (or games) can be described by coupled mean field FBSDEs, meaning that the coefficients depend upon the own marginal laws of the solution. In this note, we detail two methods for solving such FBSDEs which we implement and apply to five benchmark problems. The first method uses a tree structure to represent the pathwise laws of the solution, whereas the second method uses a grid discretization to represent the time marginal laws of the solutions. Both are based on a Picard scheme; importantly, we combine each of them with a generic continuation method that permits to extend the time horizon (or equivalently the coupling strength between the two equations) for which the Picard iteration converges.","PeriodicalId":53260,"journal":{"name":"ESAIM Proceedings and Surveys","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78711095","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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