SAM
https://sam.ensam.eu:443
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Thu, 29 Jul 2021 08:24:00 GMT
20210729T08:24:00Z

PGDBased Computational Vademecum for Efficient Design, Optimization and Control
http://hdl.handle.net/10985/10241
PGDBased Computational Vademecum for Efficient Design, Optimization and Control
CHINESTA, Francisco; LEYGUE, Adrien; BORDEU, Felipe; AGUADO, Jose Vicente; CUETO, Elias; GONZALEZ, David; ALFARO, Iciar; AMMAR, Amine; HUERTA, Antonio
In this paper we are addressing a new paradigm in the field of simulationbased engineering sciences (SBES) to face the challenges posed by current ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, some challenging problems remain today intractable. These problems, that are common to many branches of science and engineering, are of different nature. Among them, we can cite those related to highdimensional problems, which do not admit meshbased approaches due to the exponential increase of degrees of freedom. We developed in recent years a novel technique, called Proper Generalized Decomposition (PGD). It is based on the assumption of a separated form of the unknown field and it has demonstrated its capabilities in dealing with highdimensional problems overcoming the strong limitations of classical approaches. But the main opportunity given by this technique is that it allows for a completely new approach for classic problems, not necessarily high dimensional. Many challenging problems can be efficiently cast into a multidimensional framework and this opens new possibilities to solve old and new problems with strategies not envisioned until now. For instance, parameters in a model can be set as additional extracoordinates of the model. In a PGD framework, the resulting model is solved once for life, in order to obtain a general solution that includes all the solutions for every possible value of the parameters, that is, a sort of computational vademecum. Under this rationale, optimization of complex problems, uncertainty quantification, simulationbased control and realtime simulation are now at hand, even in highly complex scenarios, by combining an offline stage in which the general PGD solution, the vademecum, is computed, and an online phase in which, even on deployed, handheld, platforms such as smartphones or tablets, realtime response is obtained as a result of our queries.
Tue, 01 Jan 2013 00:00:00 GMT
http://hdl.handle.net/10985/10241
20130101T00:00:00Z
CHINESTA, Francisco
LEYGUE, Adrien
BORDEU, Felipe
AGUADO, Jose Vicente
CUETO, Elias
GONZALEZ, David
ALFARO, Iciar
AMMAR, Amine
HUERTA, Antonio
In this paper we are addressing a new paradigm in the field of simulationbased engineering sciences (SBES) to face the challenges posed by current ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, some challenging problems remain today intractable. These problems, that are common to many branches of science and engineering, are of different nature. Among them, we can cite those related to highdimensional problems, which do not admit meshbased approaches due to the exponential increase of degrees of freedom. We developed in recent years a novel technique, called Proper Generalized Decomposition (PGD). It is based on the assumption of a separated form of the unknown field and it has demonstrated its capabilities in dealing with highdimensional problems overcoming the strong limitations of classical approaches. But the main opportunity given by this technique is that it allows for a completely new approach for classic problems, not necessarily high dimensional. Many challenging problems can be efficiently cast into a multidimensional framework and this opens new possibilities to solve old and new problems with strategies not envisioned until now. For instance, parameters in a model can be set as additional extracoordinates of the model. In a PGD framework, the resulting model is solved once for life, in order to obtain a general solution that includes all the solutions for every possible value of the parameters, that is, a sort of computational vademecum. Under this rationale, optimization of complex problems, uncertainty quantification, simulationbased control and realtime simulation are now at hand, even in highly complex scenarios, by combining an offline stage in which the general PGD solution, the vademecum, is computed, and an online phase in which, even on deployed, handheld, platforms such as smartphones or tablets, realtime response is obtained as a result of our queries.

Realtime in silico experiments on gene regulatory networks and surgery simulation on handheld devices
http://hdl.handle.net/10985/10254
Realtime 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 realtime 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 GMT
http://hdl.handle.net/10985/10254
20140101T00:00:00Z
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 realtime 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 highresolution numerical strategy based on separated representations
http://hdl.handle.net/10985/6522
Towards a highresolution 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 socalled 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 threedimensional 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 nonhomogeneous boundary conditions and the treatment of problems with a very high number of degrees of freedom.
Tue, 01 Jan 2008 00:00:00 GMT
http://hdl.handle.net/10985/6522
20080101T00:00:00Z
AMMAR, Amine
CUETO, Elias
GONZALEZ, David
CHINESTA, Francisco
Many models in Science and Engineering are defined in spaces (the socalled 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 threedimensional 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 nonhomogeneous boundary conditions and the treatment of problems with a very high number of degrees of freedom.

Reducedorder modeling of soft robots
http://hdl.handle.net/10985/14078
Reducedorder modeling of soft robots
CHENEVIER, Jean; CUETO, Elias; CHINESTA, Francisco; GONZALEZ, David; AGUADO, Jose Vicente
We present a general strategy for the modeling and simulationbased control of soft robots. Although the presented methodology is completely general, we restrict ourselves to the analysis of a model robot made of hyperelastic materials and actuated by cables or tendons. To comply with the stringent realtime constraints imposed by control algorithms, a reducedorder modeling strategy is proposed that allows to minimize the amount of online CPU cost. Instead, an offline training procedure is proposed that allows to determine a sort of response surface that characterizes the response of the robot. Contrarily to existing strategies, the proposed methodology allows for a fully nonlinear modeling of the soft material in a hyperelastic setting as well as a fully nonlinear kinematic description of the movement without any restriction nor simplifying assumption. Examples of different configurations of the robot were analyzed that show the appeal of the method. © 2018 Chenevier et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10985/14078
20180101T00:00:00Z
CHENEVIER, Jean
CUETO, Elias
CHINESTA, Francisco
GONZALEZ, David
AGUADO, Jose Vicente
We present a general strategy for the modeling and simulationbased control of soft robots. Although the presented methodology is completely general, we restrict ourselves to the analysis of a model robot made of hyperelastic materials and actuated by cables or tendons. To comply with the stringent realtime constraints imposed by control algorithms, a reducedorder modeling strategy is proposed that allows to minimize the amount of online CPU cost. Instead, an offline training procedure is proposed that allows to determine a sort of response surface that characterizes the response of the robot. Contrarily to existing strategies, the proposed methodology allows for a fully nonlinear modeling of the soft material in a hyperelastic setting as well as a fully nonlinear kinematic description of the movement without any restriction nor simplifying assumption. Examples of different configurations of the robot were analyzed that show the appeal of the method. © 2018 Chenevier et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Physically sound, selflearning digital twins for sloshing fluids
http://hdl.handle.net/10985/18975
Physically sound, selflearning digital twins for sloshing fluids
MOYA, Beatriz; ALFARO, Iciar; GONZALEZ, David; CHINESTA, Francisco; CUETO, Elías
In this paper, a novel selflearning digital twin strategy is developed for fluid sloshing phenomena. This class of problems is of utmost importance for robotic manipulation of fluids, for instance, or, in general, in simulationassisted decision making. The proposed method infers the (linear or nonlinear) constitutive behavior of the fluid from video sequences of the sloshing phenomena. Realtime prediction of the fluid response is obtained from a reduced order model (ROM) constructed by means of thermodynamicsinformed datadriven learning. From these data, we aim to predict the future response of a twin fluid reacting to the movement of the real container. The constructed system is able to perform accurate forecasts of its future reactions to the movements of the containers. The system is completed with augmented reality techniques, so as to enable comparisons among the predicted result with the actual response of the same liquid and to provide the user with insightful information about the physics taking place.
Wed, 01 Jan 2020 00:00:00 GMT
http://hdl.handle.net/10985/18975
20200101T00:00:00Z
MOYA, Beatriz
ALFARO, Iciar
GONZALEZ, David
CHINESTA, Francisco
CUETO, Elías
In this paper, a novel selflearning digital twin strategy is developed for fluid sloshing phenomena. This class of problems is of utmost importance for robotic manipulation of fluids, for instance, or, in general, in simulationassisted decision making. The proposed method infers the (linear or nonlinear) constitutive behavior of the fluid from video sequences of the sloshing phenomena. Realtime prediction of the fluid response is obtained from a reduced order model (ROM) constructed by means of thermodynamicsinformed datadriven learning. From these data, we aim to predict the future response of a twin fluid reacting to the movement of the real container. The constructed system is able to perform accurate forecasts of its future reactions to the movements of the containers. The system is completed with augmented reality techniques, so as to enable comparisons among the predicted result with the actual response of the same liquid and to provide the user with insightful information about the physics taking place.

Thermodynamically consistent datadriven computational mechanics
http://hdl.handle.net/10985/13822
Thermodynamically consistent datadriven computational mechanics
GONZALEZ, David; CHINESTA, Francisco; CUETO, Elias
In the paradigm of dataintensive science, automated, unsupervised discovering of governing equations for a given physical phenomenon has attracted a lot of attention in several branches of applied sciences. In this work, we propose a method able to avoid the identification of the constitutive equations of complex systems and rather work in a purely numerical manner by employing experimental data. In sharp contrast to most existing techniques, this method does not rely on the assumption on any particular form for the model (other than some fundamental restrictions placed by classical physics such as the second law of thermodynamics, for instance) nor forces the algorithm to find among a predefined set of operators those whose predictions fit best to the available data. Instead, the method is able to identify both the Hamiltonian (conservative) and dissipative parts of the dynamics while satisfying fundamental laws such as energy conservation or positive production of entropy, for instance. The proposed method is tested against some examples of discrete as well as continuum mechanics, whose accurate results demonstrate the validity of the proposed approach.
Tue, 01 Jan 2019 00:00:00 GMT
http://hdl.handle.net/10985/13822
20190101T00:00:00Z
GONZALEZ, David
CHINESTA, Francisco
CUETO, Elias
In the paradigm of dataintensive science, automated, unsupervised discovering of governing equations for a given physical phenomenon has attracted a lot of attention in several branches of applied sciences. In this work, we propose a method able to avoid the identification of the constitutive equations of complex systems and rather work in a purely numerical manner by employing experimental data. In sharp contrast to most existing techniques, this method does not rely on the assumption on any particular form for the model (other than some fundamental restrictions placed by classical physics such as the second law of thermodynamics, for instance) nor forces the algorithm to find among a predefined set of operators those whose predictions fit best to the available data. Instead, the method is able to identify both the Hamiltonian (conservative) and dissipative parts of the dynamics while satisfying fundamental laws such as energy conservation or positive production of entropy, for instance. The proposed method is tested against some examples of discrete as well as continuum mechanics, whose accurate results demonstrate the validity of the proposed approach.

Reduced order modeling for physicallybased augmented reality
http://hdl.handle.net/10985/13809
Reduced order modeling for physicallybased augmented reality
BADIAS, Alberto; ALFARO, Iciar; GONZALEZ, David; CHINESTA, Francisco; CUETO, Elias
In this work we explore the possibilities of reduced order modeling for augmented reality applications. We consider parametric reduced order models based upon separate (affine) parametric dependence so as to speedup the associated data assimilation problems, which involve in a natural manner the minimization of a distance functional. The employ of reduced order methods allows for an important reduction in computational cost, thus allowing to comply with the stringent real time constraints of video streams, i.e., around 30 Hz. Examples are included that show the potential of the proposed technique in different situations.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10985/13809
20180101T00:00:00Z
BADIAS, Alberto
ALFARO, Iciar
GONZALEZ, David
CHINESTA, Francisco
CUETO, Elias
In this work we explore the possibilities of reduced order modeling for augmented reality applications. We consider parametric reduced order models based upon separate (affine) parametric dependence so as to speedup the associated data assimilation problems, which involve in a natural manner the minimization of a distance functional. The employ of reduced order methods allows for an important reduction in computational cost, thus allowing to comply with the stringent real time constraints of video streams, i.e., around 30 Hz. Examples are included that show the potential of the proposed technique in different situations.

Learning datadriven reduced elastic and inelastic models of spotwelded patches
http://hdl.handle.net/10985/20416
Learning datadriven reduced elastic and inelastic models of spotwelded patches
REILLE, Agathe; CHAMPANEY, Victor; DAIM, Fatima; TOURBIER, Yves; HASCOET, Nicolas; GONZALEZ, David; CUETO, Elias; DUVAL, Jean Louis; CHINESTA, Francisco
Solving mechanical problems in large structures with rich localized behaviors remains a challenging issue despite the enormous advances in numerical procedures and computational performance. In particular, these localized behaviors need for extremely fine descriptions, and this has an associated impact in the number of degrees of freedom from one side, and the decrease of the time step employed in usual explicit time integrations, whose stability scales with the size of the smallest element involved in the mesh. In the present work we propose a datadriven technique for learning the rich behavior of a local patch and integrate it into a standard coarser description at the structure level. Thus, localized behaviors impact the global structural response without needing an explicit description of that fine scale behaviors.
Fri, 30 Apr 2021 00:00:00 GMT
http://hdl.handle.net/10985/20416
20210430T00:00:00Z
REILLE, Agathe
CHAMPANEY, Victor
DAIM, Fatima
TOURBIER, Yves
HASCOET, Nicolas
GONZALEZ, David
CUETO, Elias
DUVAL, Jean Louis
CHINESTA, Francisco
Solving mechanical problems in large structures with rich localized behaviors remains a challenging issue despite the enormous advances in numerical procedures and computational performance. In particular, these localized behaviors need for extremely fine descriptions, and this has an associated impact in the number of degrees of freedom from one side, and the decrease of the time step employed in usual explicit time integrations, whose stability scales with the size of the smallest element involved in the mesh. In the present work we propose a datadriven technique for learning the rich behavior of a local patch and integrate it into a standard coarser description at the structure level. Thus, localized behaviors impact the global structural response without needing an explicit description of that fine scale behaviors.

A Multidimensional DataDriven Sparse Identification Technique: The Sparse Proper Generalized Decomposition
http://hdl.handle.net/10985/16676
A Multidimensional DataDriven Sparse Identification Technique: The Sparse Proper Generalized Decomposition
IBAÑEZ, Rubén; ABISSETCHAVANNE, Emmanuelle; AMMAR, Amine; GONZALEZ, David; CUETO, Elias; HUERTA, Antonio; DUVAL, JeanLouis; CHINESTA, Francisco
Sparse model identification by means of data is especially cumbersome if the sought dynamics live in a high dimensional space. This usually involves the need for large amount of data, unfeasible in such a high dimensional settings. This wellknown phenomenon, coined as the curse of dimensionality, is here overcome by means of the use of separate representations. We present a technique based on the same principles of the Proper Generalized Decomposition that enables the identification of complex laws in the lowdata limit. We provide examples on the performance of the technique in up to ten dimensions.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10985/16676
20180101T00:00:00Z
IBAÑEZ, Rubén
ABISSETCHAVANNE, Emmanuelle
AMMAR, Amine
GONZALEZ, David
CUETO, Elias
HUERTA, Antonio
DUVAL, JeanLouis
CHINESTA, Francisco
Sparse model identification by means of data is especially cumbersome if the sought dynamics live in a high dimensional space. This usually involves the need for large amount of data, unfeasible in such a high dimensional settings. This wellknown phenomenon, coined as the curse of dimensionality, is here overcome by means of the use of separate representations. We present a technique based on the same principles of the Proper Generalized Decomposition that enables the identification of complex laws in the lowdata limit. We provide examples on the performance of the technique in up to ten dimensions.

Deep learning of thermodynamicsaware reducedorder models from data
http://hdl.handle.net/10985/20176
Deep learning of thermodynamicsaware reducedorder models from data
HERNANDEZ, Quercus; BADIAS, Alberto; GONZALEZ, David; CHINESTA, Francisco; CUETO, Elias
We present an algorithm to learn the relevant latent variables of a largescale discretized physical system and predict its time evolution using thermodynamicallyconsistent deep neural networks. Our method relies on sparse autoencoders, which reduce the dimensionality of the full order model to a set of sparse latent variables with no prior knowledge of the coded space dimensionality. Then, a second neural network is trained to learn the metriplectic structure of those reduced physical variables and predict its time evolution with a socalled structurepreserving neural network. This databased integrator is guaranteed to conserve the total energy of the system and the entropy inequality, and can be applied to both conservative and dissipative systems. The integrated paths can then be decoded to the original fulldimensional manifold and be compared to the ground truth solution. This method is tested with two examples applied to fluid and solid mechanics.
Fri, 01 Jan 2021 00:00:00 GMT
http://hdl.handle.net/10985/20176
20210101T00:00:00Z
HERNANDEZ, Quercus
BADIAS, Alberto
GONZALEZ, David
CHINESTA, Francisco
CUETO, Elias
We present an algorithm to learn the relevant latent variables of a largescale discretized physical system and predict its time evolution using thermodynamicallyconsistent deep neural networks. Our method relies on sparse autoencoders, which reduce the dimensionality of the full order model to a set of sparse latent variables with no prior knowledge of the coded space dimensionality. Then, a second neural network is trained to learn the metriplectic structure of those reduced physical variables and predict its time evolution with a socalled structurepreserving neural network. This databased integrator is guaranteed to conserve the total energy of the system and the entropy inequality, and can be applied to both conservative and dissipative systems. The integrated paths can then be decoded to the original fulldimensional manifold and be compared to the ground truth solution. This method is tested with two examples applied to fluid and solid mechanics.