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Fri, 04 Oct 2024 17:17:18 GMT
20241004T17:17:18Z

PGDBased Computational Vademecum for Efficient Design, Optimization and Control
http://hdl.handle.net/10985/10241
PGDBased Computational Vademecum for Efficient Design, Optimization and Control
LEYGUE, Adrien; BORDEU, Felipe; AGUADO, Jose Vicente; CUETO, Elias; GONZALEZ, David; HUERTA, Antonio; ALFARO, Icíar; AMMAR, Amine; CHINESTA SORIA, Francisco
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
LEYGUE, Adrien
BORDEU, Felipe
AGUADO, Jose Vicente
CUETO, Elias
GONZALEZ, David
HUERTA, Antonio
ALFARO, Icíar
AMMAR, Amine
CHINESTA SORIA, Francisco
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.

Reduced order modeling for physicallybased augmented reality
http://hdl.handle.net/10985/13809
Reduced order modeling for physicallybased augmented reality
BADIAS, Alberto; GONZALEZ, David; CUETO, Elias; ALFARO, Icíar; CHINESTA SORIA, Francisco
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
GONZALEZ, David
CUETO, Elias
ALFARO, Icíar
CHINESTA SORIA, Francisco
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 SORIA, 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, 01 Jan 2021 00:00:00 GMT
http://hdl.handle.net/10985/20416
20210101T00:00:00Z
REILLE, Agathe
CHAMPANEY, Victor
DAIM, Fatima
TOURBIER, Yves
HASCOET, Nicolas
GONZALEZ, David
CUETO, Elias
DUVAL, Jean Louis
CHINESTA SORIA, 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.

MORPHDSLAM: Model Order Reduction for PhysicsBased Deformable SLAM
http://hdl.handle.net/10985/23641
MORPHDSLAM: Model Order Reduction for PhysicsBased Deformable SLAM
BADIAS, Alberto; GONZALEZ, David; CUETO, Elias; ALFARO, Icíar; CHINESTA SORIA, Francisco
We propose a new methodology to estimate the 3D displacement field of deformable objects from video sequences using standard monocular cameras. We solve in real time the complete (possibly visco)hyperelasticity problem to properly describe the strain and stress fields that are consistent with the displacements captured by the images, constrained by real physics. We do not impose any adhoc prior or energy minimization in the external surface, since the real and complete mechanics problem is solved. This means that we can also estimate the internal state of the objects, even in occluded areas, just by observing the external surface and the knowledge of material properties and geometry. Solving this problem in real time using a realistic constitutive law, usually nonlinear, is out of reach for current systems. To overcome this difficulty, we solve offline a parametrized problem that considers each source of variability in the problem as a new parameter and, consequently, as a new dimension in the formulation. Model Order Reduction methods allow us to reduce the dimensionality of the problem, and therefore, its computational cost, while preserving the visualization of the solution in the highdimensionality space. This allows an accurate estimation of the object deformations, improving also the robustness in the 3D points estimation.
Tue, 01 Nov 2022 00:00:00 GMT
http://hdl.handle.net/10985/23641
20221101T00:00:00Z
BADIAS, Alberto
GONZALEZ, David
CUETO, Elias
ALFARO, Icíar
CHINESTA SORIA, Francisco
We propose a new methodology to estimate the 3D displacement field of deformable objects from video sequences using standard monocular cameras. We solve in real time the complete (possibly visco)hyperelasticity problem to properly describe the strain and stress fields that are consistent with the displacements captured by the images, constrained by real physics. We do not impose any adhoc prior or energy minimization in the external surface, since the real and complete mechanics problem is solved. This means that we can also estimate the internal state of the objects, even in occluded areas, just by observing the external surface and the knowledge of material properties and geometry. Solving this problem in real time using a realistic constitutive law, usually nonlinear, is out of reach for current systems. To overcome this difficulty, we solve offline a parametrized problem that considers each source of variability in the problem as a new parameter and, consequently, as a new dimension in the formulation. Model Order Reduction methods allow us to reduce the dimensionality of the problem, and therefore, its computational cost, while preserving the visualization of the solution in the highdimensionality space. This allows an accurate estimation of the object deformations, improving also the robustness in the 3D points estimation.

Towards a highresolution numerical strategy based on separated representations
http://hdl.handle.net/10985/6522
Towards a highresolution numerical strategy based on separated representations
CUETO, Elias; GONZALEZ, David; AMMAR, Amine; CHINESTA SORIA, 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
CUETO, Elias
GONZALEZ, David
AMMAR, Amine
CHINESTA SORIA, 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.

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, Ruben; GONZALEZ, David; CUETO, Elias; HUERTA, Antonio; DUVAL, JeanLouis; ABISSETCHAVANNE, Emmanuelle; AMMAR, Amine; CHINESTA SORIA, 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, Ruben
GONZALEZ, David
CUETO, Elias
HUERTA, Antonio
DUVAL, JeanLouis
ABISSETCHAVANNE, Emmanuelle
AMMAR, Amine
CHINESTA SORIA, 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.

Thermodynamically consistent datadriven computational mechanics
http://hdl.handle.net/10985/13822
Thermodynamically consistent datadriven computational mechanics
GONZALEZ, David; CUETO, Elias; CHINESTA SORIA, Francisco
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
CUETO, Elias
CHINESTA SORIA, Francisco
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.

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
GONZALEZ, David; BORDEU, Felipe; LEYGUE, Adrien; CUETO, Elias; ALFARO, Icíar; AMMAR, Amine; CHINESTA SORIA, 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
GONZALEZ, David
BORDEU, Felipe
LEYGUE, Adrien
CUETO, Elias
ALFARO, Icíar
AMMAR, Amine
CHINESTA SORIA, 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.

Reducedorder modeling of soft robots
http://hdl.handle.net/10985/14078
Reducedorder modeling of soft robots
CHENEVIER, Jean; CUETO, Elias; GONZALEZ, David; AGUADO, Jose Vicente; CHINESTA SORIA, Francisco
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
GONZALEZ, David
AGUADO, Jose Vicente
CHINESTA SORIA, Francisco
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.

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; CUETO, Elias; CHINESTA SORIA, Francisco
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
CUETO, Elias
CHINESTA SORIA, Francisco
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.