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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Wed, 29 Mar 2023 11:19:00 GMT2023-03-29T11:19:00ZStructure-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.Physically sound, self-learning digital twins for sloshing fluids
http://hdl.handle.net/10985/18975
Physically sound, self-learning digital twins for sloshing fluids
MOYA, Beatriz; ALFARO, Iciar; GONZALEZ, David; CHINESTA, Francisco; CUETO, Elías
In this paper, a novel self-learning 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 simulation-assisted decision making. The proposed method infers the (linear or non-linear) constitutive behavior of the fluid from video sequences of the sloshing phenomena. Real-time prediction of the fluid response is obtained from a reduced order model (ROM) constructed by means of thermodynamics-informed data-driven 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 GMThttp://hdl.handle.net/10985/189752020-01-01T00:00:00ZMOYA, BeatrizALFARO, IciarGONZALEZ, DavidCHINESTA, FranciscoCUETO, ElíasIn this paper, a novel self-learning 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 simulation-assisted decision making. The proposed method infers the (linear or non-linear) constitutive behavior of the fluid from video sequences of the sloshing phenomena. Real-time prediction of the fluid response is obtained from a reduced order model (ROM) constructed by means of thermodynamics-informed data-driven 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.Natural Element Method for the Simulation of Structures and Processes
http://hdl.handle.net/10985/18738
Natural Element Method for the Simulation of Structures and Processes
CHINESTA, Francisco; CESCOTTO, Serge; CUETO, Elías; LORONG, Philippe
Computational mechanics is the discipline concerned with the use of computational methods to study phenomena governed by the principles of mechanics. Before the emergence of computational science (also called scientific computing) as a "third way" besides theoretical and experimental sciences, computational mechanics was widely considered to be a sub-discipline of applied mechanics. It is now considered to be a sub-discipline within computational science. 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.(4th cover, excerpt from publisher's website)
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/187382013-01-01T00:00:00ZCHINESTA, FranciscoCESCOTTO, SergeCUETO, ElíasLORONG, PhilippeComputational mechanics is the discipline concerned with the use of computational methods to study phenomena governed by the principles of mechanics. Before the emergence of computational science (also called scientific computing) as a "third way" besides theoretical and experimental sciences, computational mechanics was widely considered to be a sub-discipline of applied mechanics. It is now considered to be a sub-discipline within computational science. 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.(4th cover, excerpt from publisher's website)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.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; ALFARO, Iciar; CHINESTA, Francisco; CUETO, Elías
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, DavidALFARO, IciarCHINESTA, FranciscoCUETO, ElíasWe 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.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.