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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 18 Oct 2021 20:52:00 GMT2021-10-18T20:52:00ZReduction of the chemical master equation for gene regulatory networks using proper generalized decompositions
http://hdl.handle.net/10985/8467
Reduction of the chemical master equation for gene regulatory networks using proper generalized decompositions
AMMAR, Amine; CUETO, Elias; CHINESTA, Francisco
The numerical solution of the chemical master equation (CME) governing gene regulatory networks and cell signaling processes remains a challenging task owing to its complexity, exponentially growing with the number of species involved. Although most of the existing techniques rely on the use of Monte Carlo-like techniques, we present here a new technique based on the approximation of the unknown variable (the probability of having a particular chemical state) in terms of a finite sum of separable functions. In this framework, the complexity of the CME grows only linearly with the number of state space dimensions. This technique generalizes the so-called Hartree approximation, by using terms as needed in the finite sums decomposition for ensuring convergence. But noteworthy, the ease of the approximation allows for an easy treatment of unknown parameters (as is frequently the case when modeling gene regulatory networks, for instance). These unknown parameters can be considered as new space dimensions. In this way, the proposed method provides solutions for any value of the unknown parameters (within some interval of arbitrary size) in one execution of the program.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/84672012-01-01T00:00:00ZAMMAR, AmineCUETO, EliasCHINESTA, FranciscoThe numerical solution of the chemical master equation (CME) governing gene regulatory networks and cell signaling processes remains a challenging task owing to its complexity, exponentially growing with the number of species involved. Although most of the existing techniques rely on the use of Monte Carlo-like techniques, we present here a new technique based on the approximation of the unknown variable (the probability of having a particular chemical state) in terms of a finite sum of separable functions. In this framework, the complexity of the CME grows only linearly with the number of state space dimensions. This technique generalizes the so-called Hartree approximation, by using terms as needed in the finite sums decomposition for ensuring convergence. But noteworthy, the ease of the approximation allows for an easy treatment of unknown parameters (as is frequently the case when modeling gene regulatory networks, for instance). These unknown parameters can be considered as new space dimensions. In this way, the proposed method provides solutions for any value of the unknown parameters (within some interval of arbitrary size) in one execution of the program.Natural Element Method for the Simulation of Structures and Processes
http://hdl.handle.net/10985/9957
Natural Element Method for the Simulation of Structures and Processes
CHINESTA, Francisco; CESCOTTO, Serge; CUETO, Elias; LORONG, Philippe
The Natural Element Method (NEM) is halfway between meshless methods and the finite element method. This book presents a recent state of the art on the foundations and applications of the meshless natural element method in computational mechanics, including structural mechanics and material-forming processes involving solids and Newtonian and non-Newtonian fluids. The purpose of this text is to describe the natural element technique in its context, i.e. compared to the finite element-type techniques, which have proved reliable for many years, but also compared to other techniques with and without meshes. Both advantages and disadvantages of the technique have been listed. It has been written with a teaching purpose in mind, to be used by both professionals and students at Master's level.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/99572011-01-01T00:00:00ZCHINESTA, FranciscoCESCOTTO, SergeCUETO, EliasLORONG, PhilippeThe Natural Element Method (NEM) is halfway between meshless methods and the finite element method. This book presents a recent state of the art on the foundations and applications of the meshless natural element method in computational mechanics, including structural mechanics and material-forming processes involving solids and Newtonian and non-Newtonian fluids. The purpose of this text is to describe the natural element technique in its context, i.e. compared to the finite element-type techniques, which have proved reliable for many years, but also compared to other techniques with and without meshes. Both advantages and disadvantages of the technique have been listed. It has been written with a teaching purpose in mind, to be used by both professionals and students at Master's level.Separated representation of incremental elastoplastic simulations
http://hdl.handle.net/10985/9514
Separated representation of incremental elastoplastic simulations
NASRI, Mohamed Aziz; AGUADO, Jose Vicente; AMMAR, Amine; CUETO, Elias; CHINESTA, Francisco; MOREL, Franck; ROBERT, Camille; EL AREM, Saber
Forming processes usually involve irreversible plastic transformations. The calculation in that case becomes cumbersome when large parts and processes are considered. Recently Model Order Reduction techniques opened new perspectives for an accurate and fast simulation of mechanical systems, however nonlinear history-dependent behaviors remain still today challenging scenarios for the application of these techniques. In this work we are proposing a quite simple non intrusive strategy able to address such behaviors by coupling a separated representation with a POD-based reduced basis within an incremental elastoplastic formulation.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/95142015-01-01T00:00:00ZNASRI, Mohamed AzizAGUADO, Jose VicenteAMMAR, AmineCUETO, EliasCHINESTA, FranciscoMOREL, FranckROBERT, CamilleEL AREM, SaberForming processes usually involve irreversible plastic transformations. The calculation in that case becomes cumbersome when large parts and processes are considered. Recently Model Order Reduction techniques opened new perspectives for an accurate and fast simulation of mechanical systems, however nonlinear history-dependent behaviors remain still today challenging scenarios for the application of these techniques. In this work we are proposing a quite simple non intrusive strategy able to address such behaviors by coupling a separated representation with a POD-based reduced basis within an incremental elastoplastic formulation.Parametric solutions involving geometry: A step towards efficient shape optimization
http://hdl.handle.net/10985/10244
Parametric solutions involving geometry: A step towards efficient shape optimization
AMMAR, Amine; HUERTA, Antonio; CHINESTA, Francisco; CUETO, Elias; LEYGUE, Adrien
Optimization of manufacturing processes or structures involves the optimal choice of many parameters (process parameters, material parameters or geometrical parameters). Usual strategies proceed by defining a trial choice of those parameters and then solving the resulting model. Then, an appropriate cost function is evaluated and its optimality checked. While the optimum is not reached, the process parameters should be updated by using an appropriate optimization procedure, and then the model must be solved again for the updated process parameters. Thus, a direct numerical solution is needed for each choice of the process parameters, with the subsequent impact on the computing time. In this work we focus on shape optimization that involves the appropriate choice of some parameters defining the problem geometry. The main objective of this work is to describe an original approach for computing an off-line parametric solution. That is, a solution able to include information for different parameter values and also allowing to compute readily the sensitivities. The curse of dimensionality is circumvented by invoking the Proper Generalized Decomposition (PGD) introduced in former works, which is applied here to compute geometrically parametrized solutions.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/102442014-01-01T00:00:00ZAMMAR, AmineHUERTA, AntonioCHINESTA, FranciscoCUETO, EliasLEYGUE, AdrienOptimization of manufacturing processes or structures involves the optimal choice of many parameters (process parameters, material parameters or geometrical parameters). Usual strategies proceed by defining a trial choice of those parameters and then solving the resulting model. Then, an appropriate cost function is evaluated and its optimality checked. While the optimum is not reached, the process parameters should be updated by using an appropriate optimization procedure, and then the model must be solved again for the updated process parameters. Thus, a direct numerical solution is needed for each choice of the process parameters, with the subsequent impact on the computing time. In this work we focus on shape optimization that involves the appropriate choice of some parameters defining the problem geometry. The main objective of this work is to describe an original approach for computing an off-line parametric solution. That is, a solution able to include information for different parameter values and also allowing to compute readily the sensitivities. The curse of dimensionality is circumvented by invoking the Proper Generalized Decomposition (PGD) introduced in former works, which is applied here to compute geometrically parametrized solutions.Real-time in silico experiments on gene regulatory networks and surgery simulation on handheld devices
http://hdl.handle.net/10985/10254
Real-time in silico experiments on gene regulatory networks and surgery simulation on handheld devices
ALFARO, Iciar; GONZALEZ, David; BORDEU, Felipe; LEYGUE, Adrien; AMMAR, Amine; CUETO, Elias; CHINESTA, Francisco
Simulation of all phenomena taking place in a surgical procedure is a formidable task that involves, when possible, the use of supercomputing facilities over long time periods. However, decision taking in the operating room needs for fast methods that provide an accurate response in real time. To this end, Model Order Reduction (MOR) techniques have emerged recently in the field of Computational Surgery to help alleviate this burden. In this paper, we review the basics of classical MOR and explain how a technique recently developed by the authors and coined as Proper Generalized Decomposition could make real-time feedback available with the use of simple devices like smartphones or tablets. Examples are given on the performance of the technique for problems at different scales of the surgical procedure, form gene regulatory networks to macroscopic soft tissue deformation and cutting.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/102542014-01-01T00:00:00ZALFARO, IciarGONZALEZ, DavidBORDEU, FelipeLEYGUE, AdrienAMMAR, AmineCUETO, EliasCHINESTA, FranciscoSimulation of all phenomena taking place in a surgical procedure is a formidable task that involves, when possible, the use of supercomputing facilities over long time periods. However, decision taking in the operating room needs for fast methods that provide an accurate response in real time. To this end, Model Order Reduction (MOR) techniques have emerged recently in the field of Computational Surgery to help alleviate this burden. In this paper, we review the basics of classical MOR and explain how a technique recently developed by the authors and coined as Proper Generalized Decomposition could make real-time feedback available with the use of simple devices like smartphones or tablets. Examples are given on the performance of the technique for problems at different scales of the surgical procedure, form gene regulatory networks to macroscopic soft tissue deformation and cutting.Towards a high-resolution numerical strategy based on separated representations
http://hdl.handle.net/10985/6522
Towards a high-resolution numerical strategy based on separated representations
AMMAR, Amine; CUETO, Elias; GONZALEZ, David; CHINESTA, Francisco
Many models in Science and Engineering are defined in spaces (the so-called conformation spaces) of high dimensionality. In kinetic theory, for instance, the micro scale of a fluid evolves in a space whose number of dimensions is much higher than the usual physical space (two or three). Models defined in such a framework suffer from the curse of dimensionality, since the complexity of the problem growths exponentially with the number of dimensions. This curse of dimensionality makes this class of problems nearly intractable if we perform a standard discretization, say, with finite element methods, for instance. Problems defined in two or three-dimensional spaces, but densely discretized along each spatial dimension are also hardly tractable by finite element methods. In this paper we present some recent results concerning a method based on the method of separation of variables, originally developed in [1]. We focus on an efficient imposition of essential non-homogeneous boundary conditions and the treatment of problems with a very high number of degrees of freedom.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10985/65222008-01-01T00:00:00ZAMMAR, AmineCUETO, EliasGONZALEZ, DavidCHINESTA, FranciscoMany models in Science and Engineering are defined in spaces (the so-called conformation spaces) of high dimensionality. In kinetic theory, for instance, the micro scale of a fluid evolves in a space whose number of dimensions is much higher than the usual physical space (two or three). Models defined in such a framework suffer from the curse of dimensionality, since the complexity of the problem growths exponentially with the number of dimensions. This curse of dimensionality makes this class of problems nearly intractable if we perform a standard discretization, say, with finite element methods, for instance. Problems defined in two or three-dimensional spaces, but densely discretized along each spatial dimension are also hardly tractable by finite element methods. In this paper we present some recent results concerning a method based on the method of separation of variables, originally developed in [1]. We focus on an efficient imposition of essential non-homogeneous boundary conditions and the treatment of problems with a very high number of degrees of freedom.Wavelet-based multiscale proper generalized decomposition
http://hdl.handle.net/10985/13282
Wavelet-based multiscale proper generalized decomposition
ANGEL, Leon; BARASINSKI, Anais; ABISSET-CHAVANNE, Emmanuelle; CUETO, Elias; CHINESTA, Francisco
Separated representations at the heart of Proper Generalized Decomposition are constructed incrementally by minimizing the problem residual. However, the modes involved in the resulting decomposition do not exhibit a clear multi-scale character. In order to recover a multi-scale description of the solution within a separated representation framework, we study the use of wavelets for approximating the functions involved in the separated representation of the solution. We will prove that such an approach allows separating the different scales as well as taking profit from its multi-resolution behavior for defining adaptive strategies.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/132822018-01-01T00:00:00ZANGEL, LeonBARASINSKI, AnaisABISSET-CHAVANNE, EmmanuelleCUETO, EliasCHINESTA, FranciscoSeparated representations at the heart of Proper Generalized Decomposition are constructed incrementally by minimizing the problem residual. However, the modes involved in the resulting decomposition do not exhibit a clear multi-scale character. In order to recover a multi-scale description of the solution within a separated representation framework, we study the use of wavelets for approximating the functions involved in the separated representation of the solution. We will prove that such an approach allows separating the different scales as well as taking profit from its multi-resolution behavior for defining adaptive strategies.Efficient Stabilization of Advection Terms Involved in Separated Representations of Boltzmann and Fokker-Planck Equations
http://hdl.handle.net/10985/10237
Efficient Stabilization of Advection Terms Involved in Separated Representations of Boltzmann and Fokker-Planck Equations
CHINESTA, Francisco; ABISSET-CHAVANNE, Emmanuelle; AMMAR, Amine; CUETO, Elias
The fine description of complex fluids can be carried out by describing the evolution of each individual constituent (e.g. each particle, each macromolecule, etc.). This procedure, despite its conceptual simplicity, involves many numerical issues, the most challenging one being that related to the computing time required to update the system configuration by describing all the interactions between the different individuals. Coarse grained approaches allow alleviating the just referred issue: the system is described by a distribution function providing the fraction of entities that at certain time and position have a particular conformation. Thus, mesoscale models involve many different coordinates, standard space and time, and different conformational coordinates whose number and nature depend on the particular system considered. Balance equation describing the evolution of such distribution function consists of an advection-diffusion partial differential equation defined in a high dimensional space. Standard mesh-based discretization techniques fail at solving high-dimensional models because of the curse of dimensionality. Recently the authors proposed an alternative route based on the use of separated representations. However, until now these approaches were unable to address the case of advection dominated models due to stabilization issues. In this paper this issue is revisited and efficient procedures for stabilizing the advection operators involved in the Boltzmann and Fokker-Planck equation within the PGD framework are proposed.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/102372015-01-01T00:00:00ZCHINESTA, FranciscoABISSET-CHAVANNE, EmmanuelleAMMAR, AmineCUETO, EliasThe fine description of complex fluids can be carried out by describing the evolution of each individual constituent (e.g. each particle, each macromolecule, etc.). This procedure, despite its conceptual simplicity, involves many numerical issues, the most challenging one being that related to the computing time required to update the system configuration by describing all the interactions between the different individuals. Coarse grained approaches allow alleviating the just referred issue: the system is described by a distribution function providing the fraction of entities that at certain time and position have a particular conformation. Thus, mesoscale models involve many different coordinates, standard space and time, and different conformational coordinates whose number and nature depend on the particular system considered. Balance equation describing the evolution of such distribution function consists of an advection-diffusion partial differential equation defined in a high dimensional space. Standard mesh-based discretization techniques fail at solving high-dimensional models because of the curse of dimensionality. Recently the authors proposed an alternative route based on the use of separated representations. However, until now these approaches were unable to address the case of advection dominated models due to stabilization issues. In this paper this issue is revisited and efficient procedures for stabilizing the advection operators involved in the Boltzmann and Fokker-Planck equation within the PGD framework are proposed.On the physical interpretation of fractional diffusion
http://hdl.handle.net/10985/13278
On the physical interpretation of fractional diffusion
NADAL, Enrique; ABISSET-CHAVANNE, Emmanuelle; CUETO, Elias; CHINESTA, Francisco
Even if the diffusion equation has been widely used in physics and engineering, and its physical content is well understood, some variants of it escape fully physical understanding. In particular, anormal diffusion appears in the so-called fractional diffusion equation, whose main particularity is its non-local behavior, whose physical interpretation represents the main part of the present work.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/132782018-01-01T00:00:00ZNADAL, EnriqueABISSET-CHAVANNE, EmmanuelleCUETO, EliasCHINESTA, FranciscoEven if the diffusion equation has been widely used in physics and engineering, and its physical content is well understood, some variants of it escape fully physical understanding. In particular, anormal diffusion appears in the so-called fractional diffusion equation, whose main particularity is its non-local behavior, whose physical interpretation represents the main part of the present work.Kinetic Theory Modeling and Efficient Numerical Simulation of Gene Regulatory Networks Based on Qualitative Descriptions
http://hdl.handle.net/10985/9964
Kinetic Theory Modeling and Efficient Numerical Simulation of Gene Regulatory Networks Based on Qualitative Descriptions
CHINESTA, Francisco; MAGNIN, Morgan; ROUX, Olivier; AMMAR, Amine; CUETO, Elias
In this work, we begin by considering the qualitative modeling of biological regulatory systems using process hitting, from which we define its probabilistic counterpart by considering the chemical master equation within a kinetic theory framework. The last equation is efficiently solved by considering a separated representation within the proper generalized decomposition framework that allows circumventing the so-called curse of dimensionality. Finally, model parameters can be added as extra-coordinates in order to obtain a parametric solution of the model.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/99642015-01-01T00:00:00ZCHINESTA, FranciscoMAGNIN, MorganROUX, OlivierAMMAR, AmineCUETO, EliasIn this work, we begin by considering the qualitative modeling of biological regulatory systems using process hitting, from which we define its probabilistic counterpart by considering the chemical master equation within a kinetic theory framework. The last equation is efficiently solved by considering a separated representation within the proper generalized decomposition framework that allows circumventing the so-called curse of dimensionality. Finally, model parameters can be added as extra-coordinates in order to obtain a parametric solution of the model.