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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.Hybrid constitutive modeling: data-driven learning of corrections to plasticity models
http://hdl.handle.net/10985/17438
Hybrid constitutive modeling: data-driven learning of corrections to plasticity models
IBÁÑEZ, Rubén; ABISSET-CHAVANNE, Emmanuelle; GONZÁLEZ, David; DUVAL, Jean Louis; CUETO, Elias; CHINESTA, Francisco
In recent times a growing interest has arose on the development of data-driven techniques to avoid the employ of phenomenological constitutive models. While it is true that, in general, data do not fit perfectly to existing models, and present deviations from the most popular ones, we believe that this does not justify (or, at least, not always) to abandon completely all the acquired knowledge on the constitutive characterization of materials. Instead, what we propose here is, by means of machine learning techniques, to develop correction to those popular models so as to minimize the errors in constitutive modeling.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/174382019-01-01T00:00:00ZIBÁÑEZ, RubénABISSET-CHAVANNE, EmmanuelleGONZÁLEZ, DavidDUVAL, Jean LouisCUETO, EliasCHINESTA, FranciscoIn recent times a growing interest has arose on the development of data-driven techniques to avoid the employ of phenomenological constitutive models. While it is true that, in general, data do not fit perfectly to existing models, and present deviations from the most popular ones, we believe that this does not justify (or, at least, not always) to abandon completely all the acquired knowledge on the constitutive characterization of materials. Instead, what we propose here is, by means of machine learning techniques, to develop correction to those popular models so as to minimize the errors in constitutive modeling.Data-driven GENERIC modeling of poroviscoelastic materials
http://hdl.handle.net/10985/18480
Data-driven GENERIC modeling of poroviscoelastic materials
GHNATIOS, Chady; ALFARO, Iciar; GONZÁLEZ, David; CHINESTA, Francisco; CUETO, Elías G.
Biphasic soft materials are challenging to model by nature. Ongoing efforts are targeting their effective modeling and simulation. This work uses experimental atomic force nanoindentation of thick hydrogels to identify the indentation forces are a function of the indentation depth. Later on, the atomic force microscopy results are used in a GENERIC general equation for non-equilibrium reversible-irreversible coupling (GENERIC) formalism to identify the best model conserving basic thermodynamic laws. The data-driven GENERIC analysis identifies the material behavior with high fidelity for both data fitting and prediction.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/184802019-01-01T00:00:00ZGHNATIOS, ChadyALFARO, IciarGONZÁLEZ, DavidCHINESTA, FranciscoCUETO, Elías G.Biphasic soft materials are challenging to model by nature. Ongoing efforts are targeting their effective modeling and simulation. This work uses experimental atomic force nanoindentation of thick hydrogels to identify the indentation forces are a function of the indentation depth. Later on, the atomic force microscopy results are used in a GENERIC general equation for non-equilibrium reversible-irreversible coupling (GENERIC) formalism to identify the best model conserving basic thermodynamic laws. The data-driven GENERIC analysis identifies the material behavior with high fidelity for both data fitting and prediction.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.kPCA-Based Parametric Solutions Within the PGD Framework
http://hdl.handle.net/10985/18681
kPCA-Based Parametric Solutions Within the PGD Framework
GONZÁLEZ, David; AGUADO, José Vicente; ABISSET-CHAVANNE, Emmanuelle; CHINESTA, Francisco
Parametric solutions make possible fast and reliable real-time simulations which, in turn allow real time optimization, simulation-based control and uncertainty propagation. This opens unprecedented possibilities for robust and efficient design and real-time decision making. The construction of such parametric solutions was addressed in our former works in the context of models whose parameters were easily identified and known in advance. In this work we address more complex scenarios in which the parameters do not appear explicitly in the model—complex microstructures, for instance. In these circumstances the parametric model solution requires combining a technique to find the relevant model parameters and a solution procedure able to cope with high-dimensional models, avoiding the well-known curse of dimensionality. In this work, kPCA (kernel Principal Component Analysis) is used for extracting the hidden model parameters, whereas the PGD (Proper Generalized Decomposition) is used for calculating the resulting parametric solution.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/186812018-01-01T00:00:00ZGONZÁLEZ, DavidAGUADO, José VicenteABISSET-CHAVANNE, EmmanuelleCHINESTA, FranciscoParametric solutions make possible fast and reliable real-time simulations which, in turn allow real time optimization, simulation-based control and uncertainty propagation. This opens unprecedented possibilities for robust and efficient design and real-time decision making. The construction of such parametric solutions was addressed in our former works in the context of models whose parameters were easily identified and known in advance. In this work we address more complex scenarios in which the parameters do not appear explicitly in the model—complex microstructures, for instance. In these circumstances the parametric model solution requires combining a technique to find the relevant model parameters and a solution procedure able to cope with high-dimensional models, avoiding the well-known curse of dimensionality. In this work, kPCA (kernel Principal Component Analysis) is used for extracting the hidden model parameters, whereas the PGD (Proper Generalized Decomposition) is used for calculating the resulting parametric solution.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.Learning slosh dynamics by means of data
http://hdl.handle.net/10985/17933
Learning slosh dynamics by means of data
MOYA, Beatriz; GONZÁLEZ, David; ALFARO, Iciar; CHINESTA, Francisco; CUETO, Elías G.
In this work we study several learning strategies for fluid sloshing problems based on data. In essence, a reduced-order model of the dynamics of the free surface motion of the fluid is developed under rigorous thermodynamics settings. This model is extracted from data by exploring several strategies. First, a linear one, based on the employ of Proper Orthogonal Decomposition techniques is analyzed. Second, a strategy based on the employ of Locally Linear Embedding is studied. Finally, Topological Data Analysis is employed to the same end. All the three distinct possibilities rely on a numerical integration scheme to advance the dynamics in time. This thermodynamically consistent integrator is developed on the basis of the General Equation for Non-Equilibrium Reversible–Irreversible Coupling, GENERIC [M. Grmela and H.C Oettinger (1997). Phys. Rev. E. 56 (6): 6620–6632], framework so as to guarantee the satisfaction of first principles (particularly, the laws of thermodynamics). We show how the resulting method employs a few degrees of freedom, while it allows for a realistic reconstruction of the fluid dynamics of sloshing processes under severe real-time constraints. The proposed method is shown to run faster than real time in a standard laptop.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/179332019-01-01T00:00:00ZMOYA, BeatrizGONZÁLEZ, DavidALFARO, IciarCHINESTA, FranciscoCUETO, Elías G.In this work we study several learning strategies for fluid sloshing problems based on data. In essence, a reduced-order model of the dynamics of the free surface motion of the fluid is developed under rigorous thermodynamics settings. This model is extracted from data by exploring several strategies. First, a linear one, based on the employ of Proper Orthogonal Decomposition techniques is analyzed. Second, a strategy based on the employ of Locally Linear Embedding is studied. Finally, Topological Data Analysis is employed to the same end. All the three distinct possibilities rely on a numerical integration scheme to advance the dynamics in time. This thermodynamically consistent integrator is developed on the basis of the General Equation for Non-Equilibrium Reversible–Irreversible Coupling, GENERIC [M. Grmela and H.C Oettinger (1997). Phys. Rev. E. 56 (6): 6620–6632], framework so as to guarantee the satisfaction of first principles (particularly, the laws of thermodynamics). We show how the resulting method employs a few degrees of freedom, while it allows for a realistic reconstruction of the fluid dynamics of sloshing processes under severe real-time constraints. The proposed method is shown to run faster than real time in a standard laptop.