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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 15 Apr 2024 02:47:41 GMT2024-04-15T02:47:41ZStructure-preserving neural networks
http://hdl.handle.net/10985/19924
Structure-preserving neural networks
HERNÁNDEZ, Quercus; BADÍAS, Alberto; GONZÁLEZ, David; CHINESTA, Francisco; CUETO, Elías
We develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing the metriplectic structure of dissipative Hamiltonian systems in the form of the so-called General Equation for the Non-Equilibrium Reversible-Irreversible Coupling, GENERIC (Öttinger and Grmela (1997) [36]). The method does not need to enforce any kind of balance equation, and thus no previous knowledge on the nature of the system is needed. Conservation of energy and dissipation of entropy in the prediction of previously unseen situations arise as a natural by-product of the structure of the method. Examples of the performance of the method are shown that comprise conservative as well as dissipative systems, discrete as well as continuous ones.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/199242021-01-01T00:00:00ZHERNÁNDEZ, QuercusBADÍAS, AlbertoGONZÁLEZ, DavidCHINESTA, FranciscoCUETO, ElíasWe develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing the metriplectic structure of dissipative Hamiltonian systems in the form of the so-called General Equation for the Non-Equilibrium Reversible-Irreversible Coupling, GENERIC (Öttinger and Grmela (1997) [36]). The method does not need to enforce any kind of balance equation, and thus no previous knowledge on the nature of the system is needed. Conservation of energy and dissipation of entropy in the prediction of previously unseen situations arise as a natural by-product of the structure of the method. Examples of the performance of the method are shown that comprise conservative as well as dissipative systems, discrete as well as continuous ones.Learning non-Markovian physics from data
http://hdl.handle.net/10985/19926
Learning non-Markovian physics from data
GONZÁLEZ, David; CHINESTA, Francisco; CUETO, Elías
We present a method for the data-driven learning of physical phenomena whose evolution in time depends on history terms. It is well known that a Mori-Zwanzig-type projection produces a description of the physical phenomena that depends on history, and also incorporates noise. If the data stream is sampled from the projected Mori-Zwanzig manifold, the description of the phenomenon will always depend on one or more unresolved variables, a priori unknown, and will also incorporate noise. The present work introduces a novel technique able to unveil the presence of such internal variables—although without giving it a precise physical meaning—and to minimize the inherent noise. The method is based upon a refinement of the scale at which the phenomenon is described by means of kernel-PCA techniques. By learning the metriplectic form of the evolution of the physics, the resulting approximation satisfies basic thermodynamic principles such as energy conservation and positive entropy production. Examples are provided that show the potential of the method in both discrete and continuum mechanics.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/199262021-01-01T00:00:00ZGONZÁLEZ, DavidCHINESTA, FranciscoCUETO, ElíasWe present a method for the data-driven learning of physical phenomena whose evolution in time depends on history terms. It is well known that a Mori-Zwanzig-type projection produces a description of the physical phenomena that depends on history, and also incorporates noise. If the data stream is sampled from the projected Mori-Zwanzig manifold, the description of the phenomenon will always depend on one or more unresolved variables, a priori unknown, and will also incorporate noise. The present work introduces a novel technique able to unveil the presence of such internal variables—although without giving it a precise physical meaning—and to minimize the inherent noise. The method is based upon a refinement of the scale at which the phenomenon is described by means of kernel-PCA techniques. By learning the metriplectic form of the evolution of the physics, the resulting approximation satisfies basic thermodynamic principles such as energy conservation and positive entropy production. Examples are provided that show the potential of the method in both discrete and continuum mechanics.Crossing Scales: Data-Driven Determination of the Micro-scale Behavior of Polymers From Non-homogeneous Tests at the Continuum-Scale
http://hdl.handle.net/10985/22235
Crossing Scales: Data-Driven Determination of the Micro-scale Behavior of Polymers From Non-homogeneous Tests at the Continuum-Scale
AMORES, Víctor J.; MONTÁNS, Francisco J.; CUETO, Elías; CHINESTA, Francisco
We propose an efficient method to determine the micro-structural entropic behavior of polymer chains directly from a sufficiently rich non-homogeneous experiment at the continuum scale. The procedure is developed in 2 stages: First, a Macro-Micro-Macro approach; second, a finite element method. Thus, we no longer require the typical stress-strain curves from standard homogeneous tests, but we use instead the applied/reaction forces and the displacement field obtained, for example, from Digital Image Correlation. The approach is based on the P-spline local approximation of the constituents behavior at the micro-scale (a priori unknown). The sought spline vertices determining the polymer behavior are first pushed up from the micro-scale to the integration point of the finite element, and then from the integration point to the element forces. The polymer chain behavior is then obtained immediately by solving a linear system of equations which results from a least squares minimization error, resulting in an inverse problem which crosses material scales. The result is physically interpretable and directly linked to the micro-structure of the material, and the resulting polymer behavior may be employed in any other finite element simulation. We give some demonstrative examples (academic and from actual polymers) in which we demonstrate that we are capable of recovering “unknown” analytical models and spline-based constitutive behavior previously obtained from homogeneous tests.
Sun, 01 May 2022 00:00:00 GMThttp://hdl.handle.net/10985/222352022-05-01T00:00:00ZAMORES, Víctor J.MONTÁNS, Francisco J.CUETO, ElíasCHINESTA, FranciscoWe propose an efficient method to determine the micro-structural entropic behavior of polymer chains directly from a sufficiently rich non-homogeneous experiment at the continuum scale. The procedure is developed in 2 stages: First, a Macro-Micro-Macro approach; second, a finite element method. Thus, we no longer require the typical stress-strain curves from standard homogeneous tests, but we use instead the applied/reaction forces and the displacement field obtained, for example, from Digital Image Correlation. The approach is based on the P-spline local approximation of the constituents behavior at the micro-scale (a priori unknown). The sought spline vertices determining the polymer behavior are first pushed up from the micro-scale to the integration point of the finite element, and then from the integration point to the element forces. The polymer chain behavior is then obtained immediately by solving a linear system of equations which results from a least squares minimization error, resulting in an inverse problem which crosses material scales. The result is physically interpretable and directly linked to the micro-structure of the material, and the resulting polymer behavior may be employed in any other finite element simulation. We give some demonstrative examples (academic and from actual polymers) in which we demonstrate that we are capable of recovering “unknown” analytical models and spline-based constitutive behavior previously obtained from homogeneous tests.Digital twins that learn and correct themselves
http://hdl.handle.net/10985/22208
Digital twins that learn and correct themselves
MOYA, Beatriz; BADÍAS, Alberto; ALFARO, Icíar; CHINESTA, Francisco; CUETO, Elías
Digital twins can be defined as digital representations of physical entities that employ real-time data to enable understanding of the operating conditions of these entities. Here we present a particular type of digital twin that involves a combination of computer vision, scientific machine learning, and augmented reality. This novel digital twin is able, therefore, to see, to interpret what it sees—and, if necessary, to correct the model it is equipped with—and presents the resulting information in the form of augmented reality. The computer vision capabilities allow the twin to receive data continuously. As any other digital twin, it is equipped with one or more models so as to assimilate data. However, if persistent deviations from the predicted values are found, the proposed methodology is able to correct on the fly the existing models, so as to accommodate them to the measured reality. Finally, the suggested methodology is completed with augmented reality capabilities so as to render a completely new type of digital twin. These concepts are tested against a proof-of-concept model consisting on a nonlinear, hyperelastic beam subjected to moving loads whose exact position is to be determined.
Wed, 01 Jun 2022 00:00:00 GMThttp://hdl.handle.net/10985/222082022-06-01T00:00:00ZMOYA, BeatrizBADÍAS, AlbertoALFARO, IcíarCHINESTA, FranciscoCUETO, ElíasDigital twins can be defined as digital representations of physical entities that employ real-time data to enable understanding of the operating conditions of these entities. Here we present a particular type of digital twin that involves a combination of computer vision, scientific machine learning, and augmented reality. This novel digital twin is able, therefore, to see, to interpret what it sees—and, if necessary, to correct the model it is equipped with—and presents the resulting information in the form of augmented reality. The computer vision capabilities allow the twin to receive data continuously. As any other digital twin, it is equipped with one or more models so as to assimilate data. However, if persistent deviations from the predicted values are found, the proposed methodology is able to correct on the fly the existing models, so as to accommodate them to the measured reality. Finally, the suggested methodology is completed with augmented reality capabilities so as to render a completely new type of digital twin. These concepts are tested against a proof-of-concept model consisting on a nonlinear, hyperelastic beam subjected to moving loads whose exact position is to be determined.Structure-preserving neural networks
http://hdl.handle.net/10985/19561
Structure-preserving neural networks
HERNÁNDEZ, Quercus; BADÍAS, Alberto; GONZÁLEZ, David; CHINESTA, Francisco; CUETO, Elías
We develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing the metriplectic structure of dissipative Hamiltonian systems in the form of the so-called General Equation for the Non-Equilibrium Reversible-Irreversible Coupling, GENERIC (Öttinger and Grmela (1997) [36]). The method does not need to enforce any kind of balance equation, and thus no previous knowledge on the nature of the system is needed. Conservation of energy and dissipation of entropy in the prediction of previously unseen situations arise as a natural by-product of the structure of the method. Examples of the performance of the method are shown that comprise conservative as well as dissipative systems, discrete as well as continuous ones.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10985/195612020-01-01T00:00:00ZHERNÁNDEZ, QuercusBADÍAS, AlbertoGONZÁLEZ, DavidCHINESTA, FranciscoCUETO, ElíasWe develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing the metriplectic structure of dissipative Hamiltonian systems in the form of the so-called General Equation for the Non-Equilibrium Reversible-Irreversible Coupling, GENERIC (Öttinger and Grmela (1997) [36]). The method does not need to enforce any kind of balance equation, and thus no previous knowledge on the nature of the system is needed. Conservation of energy and dissipation of entropy in the prediction of previously unseen situations arise as a natural by-product of the structure of the method. Examples of the performance of the method are shown that comprise conservative as well as dissipative systems, discrete as well as continuous ones.Learning non-Markovian physics from data
http://hdl.handle.net/10985/19562
Learning non-Markovian physics from data
GONZÁLEZ, David; CHINESTA, Francisco; CUETO, Elías
We present a method for the data-driven learning of physical phenomena whose evolution in time depends on history terms. It is well known that a Mori-Zwanzig-type projection produces a description of the physical phenomena that depends on history, and also incorporates noise. If the data stream is sampled from the projected Mori-Zwanzig manifold, the description of the phenomenon will always depend on one or more unresolved variables, a priori unknown, and will also incorporate noise. The present work introduces a novel technique able to unveil the presence of such internal variables—although without giving it a precise physical meaning—and to minimize the inherent noise. The method is based upon a refinement of the scale at which the phenomenon is described by means of kernel-PCA techniques. By learning the metriplectic form of the evolution of the physics, the resulting approximation satisfies basic thermodynamic principles such as energy conservation and positive entropy production. Examples are provided that show the potential of the method in both discrete and continuum mechanics.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10985/195622020-01-01T00:00:00ZGONZÁLEZ, DavidCHINESTA, FranciscoCUETO, ElíasWe present a method for the data-driven learning of physical phenomena whose evolution in time depends on history terms. It is well known that a Mori-Zwanzig-type projection produces a description of the physical phenomena that depends on history, and also incorporates noise. If the data stream is sampled from the projected Mori-Zwanzig manifold, the description of the phenomenon will always depend on one or more unresolved variables, a priori unknown, and will also incorporate noise. The present work introduces a novel technique able to unveil the presence of such internal variables—although without giving it a precise physical meaning—and to minimize the inherent noise. The method is based upon a refinement of the scale at which the phenomenon is described by means of kernel-PCA techniques. By learning the metriplectic form of the evolution of the physics, the resulting approximation satisfies basic thermodynamic principles such as energy conservation and positive entropy production. Examples are provided that show the potential of the method in both discrete and continuum mechanics.A Data-Driven Learning Method for Constitutive Modeling: Application to Vascular Hyperelastic Soft Tissues
http://hdl.handle.net/10985/18676
A Data-Driven Learning Method for Constitutive Modeling: Application to Vascular Hyperelastic Soft Tissues
GONZÁLEZ, David; GARCÍA-GONZÁLEZ, Alberto; CHINESTA, Francisco; CUETO, Elías
We address the problem of machine learning of constitutive laws when large experimental deviations are present. This is particularly important in soft living tissue modeling, for instance, where large patient-dependent data is found. We focus on two aspects that complicate the problem, namely, the presence of an important dispersion in the experimental results and the need for a rigorous compliance to thermodynamic settings. To address these difficulties, we propose to use, respectively, Topological Data Analysis techniques and a regression over the so-called General Equation for the Nonequilibrium Reversible-Irreversible Coupling (GENERIC) formalism (M. Grmela and H. Ch. Oettinger, Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys. Rev. E 56, 6620, 1997). This allows us, on one hand, to unveil the true “shape” of the data and, on the other, to guarantee the fulfillment of basic principles such as the conservation of energy and the production of entropy as a consequence of viscous dissipation. Examples are provided over pseudo-experimental and experimental data that demonstrate the feasibility of the proposed approach.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10985/186762020-01-01T00:00:00ZGONZÁLEZ, DavidGARCÍA-GONZÁLEZ, AlbertoCHINESTA, FranciscoCUETO, ElíasWe address the problem of machine learning of constitutive laws when large experimental deviations are present. This is particularly important in soft living tissue modeling, for instance, where large patient-dependent data is found. We focus on two aspects that complicate the problem, namely, the presence of an important dispersion in the experimental results and the need for a rigorous compliance to thermodynamic settings. To address these difficulties, we propose to use, respectively, Topological Data Analysis techniques and a regression over the so-called General Equation for the Nonequilibrium Reversible-Irreversible Coupling (GENERIC) formalism (M. Grmela and H. Ch. Oettinger, Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys. Rev. E 56, 6620, 1997). This allows us, on one hand, to unveil the true “shape” of the data and, on the other, to guarantee the fulfillment of basic principles such as the conservation of energy and the production of entropy as a consequence of viscous dissipation. Examples are provided over pseudo-experimental and experimental data that demonstrate the feasibility of the proposed approach.A separated representation involving multiple time scales within the Proper Generalized Decomposition framework
http://hdl.handle.net/10985/23265
A separated representation involving multiple time scales within the Proper Generalized Decomposition framework
PASQUALE, Angelo; AMMAR, Amine; FALCÓ, Antonio; PEROTTO, Simona; CUETO, Elías; DUVAL, Jean-Louis; CHINESTA, Francisco
Solutions of partial differential equations can exhibit multiple time scales. Standard discretization techniques are constrained to capture the finest scale to accurately predict the response of the system. In this paper, we provide an alternative route to circumvent prohibitive meshes arising from the necessity of capturing fine-scale behaviors. The proposed methodology is based on a time-separated representation within the standard Proper Generalized Decomposition, where the time coordinate is transformed into a multi-dimensional time through new separated coordinates, each representing one scale, while continuity is ensured in the scale coupling. For instance, when considering two different time scales, the governing Partial Differential Equation is commuted into a nonlinear system that iterates between the so-called microtime and macrotime, so that the time coordinate can be viewed as a 2D time. The macroscale effects are taken into account by means of a finite element-based macro-discretization, whereas the microscale effects are handled with unidimensional parent spaces that are replicated throughout the time domain. The resulting separated representation allows us a very fine time discretization without impacting the computational efficiency. The proposed formulation is explored and numerically verified on thermal and elastodynamic problems.
Fri, 26 Nov 2021 00:00:00 GMThttp://hdl.handle.net/10985/232652021-11-26T00:00:00ZPASQUALE, AngeloAMMAR, AmineFALCÓ, AntonioPEROTTO, SimonaCUETO, ElíasDUVAL, Jean-LouisCHINESTA, FranciscoSolutions of partial differential equations can exhibit multiple time scales. Standard discretization techniques are constrained to capture the finest scale to accurately predict the response of the system. In this paper, we provide an alternative route to circumvent prohibitive meshes arising from the necessity of capturing fine-scale behaviors. The proposed methodology is based on a time-separated representation within the standard Proper Generalized Decomposition, where the time coordinate is transformed into a multi-dimensional time through new separated coordinates, each representing one scale, while continuity is ensured in the scale coupling. For instance, when considering two different time scales, the governing Partial Differential Equation is commuted into a nonlinear system that iterates between the so-called microtime and macrotime, so that the time coordinate can be viewed as a 2D time. The macroscale effects are taken into account by means of a finite element-based macro-discretization, whereas the microscale effects are handled with unidimensional parent spaces that are replicated throughout the time domain. The resulting separated representation allows us a very fine time discretization without impacting the computational efficiency. The proposed formulation is explored and numerically verified on thermal and elastodynamic problems.Learning corrections for hyperelastic models from data
http://hdl.handle.net/10985/15682
Learning corrections for hyperelastic models from data
GONZÁLEZ, David; CHINESTA, Francisco; CUETO, Elías
Unveiling physical laws from data is seen as the ultimate sign of human intelligence. While there is a growing interest in this sense around the machine learning community, some recent works have attempted to simply substitute physical laws by data. We believe that getting rid of centuries of scientific knowledge is simply nonsense. There are models whose validity and usefulness is out of any doubt, so try to substitute them by data seems to be a waste of knowledge. While it is true that fitting well-known physical laws to experimental data is sometimes a painful process, a good theory continues to be practical and provide useful insights to interpret the phenomena taking place. That is why we present here a method to construct, based on data, automatic corrections to existing models. Emphasis is put in the correct thermodynamic character of these corrections, so as to avoid violations of first principles such as the laws of thermodynamics. These corrections are sought under the umbrella of the GENERIC framework (Grmela and Oettinger, 1997), a generalization of Hamiltonian mechanics to non-equilibrium thermodynamics. This framework ensures the satisfaction of the first and second laws of thermodynamics, while providing a very appealing context for the proposed automated correction of existing laws. In this work we focus on solid mechanics, particularly large strain (visco-)hyperelasticity.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/156822019-01-01T00:00:00ZGONZÁLEZ, DavidCHINESTA, FranciscoCUETO, ElíasUnveiling physical laws from data is seen as the ultimate sign of human intelligence. While there is a growing interest in this sense around the machine learning community, some recent works have attempted to simply substitute physical laws by data. We believe that getting rid of centuries of scientific knowledge is simply nonsense. There are models whose validity and usefulness is out of any doubt, so try to substitute them by data seems to be a waste of knowledge. While it is true that fitting well-known physical laws to experimental data is sometimes a painful process, a good theory continues to be practical and provide useful insights to interpret the phenomena taking place. That is why we present here a method to construct, based on data, automatic corrections to existing models. Emphasis is put in the correct thermodynamic character of these corrections, so as to avoid violations of first principles such as the laws of thermodynamics. These corrections are sought under the umbrella of the GENERIC framework (Grmela and Oettinger, 1997), a generalization of Hamiltonian mechanics to non-equilibrium thermodynamics. This framework ensures the satisfaction of the first and second laws of thermodynamics, while providing a very appealing context for the proposed automated correction of existing laws. In this work we focus on solid mechanics, particularly large strain (visco-)hyperelasticity.Real‐time interaction of virtual and physical objects in mixed reality applications
http://hdl.handle.net/10985/19295
Real‐time interaction of virtual and physical objects in mixed reality applications
BADÍAS, Alberto; GONZÁLEZ, David; CHINESTA, Francisco; CUETO, Elías; ALFARO, Icíar
We present a real-time method for computing the mechanical interaction between real and virtual objects in an augmented reality environment. Using model order reduction methods we are able to estimate the physical behavior of deformable objects in real time, with the precision of a high-fidelity solver but working at the speed of a video sequence. We merge tools of machine learning, computer vision, and computer graphics in a single application to describe the behavior of deformable virtual objects allowing the user to interact with them in a natural way. Three examples are provided to test the performance of the method.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10985/192952020-01-01T00:00:00ZBADÍAS, AlbertoGONZÁLEZ, DavidCHINESTA, FranciscoCUETO, ElíasALFARO, IcíarWe present a real-time method for computing the mechanical interaction between real and virtual objects in an augmented reality environment. Using model order reduction methods we are able to estimate the physical behavior of deformable objects in real time, with the precision of a high-fidelity solver but working at the speed of a video sequence. We merge tools of machine learning, computer vision, and computer graphics in a single application to describe the behavior of deformable virtual objects allowing the user to interact with them in a natural way. Three examples are provided to test the performance of the method.