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...

Hernández, Quercus Badias, Alberto Gonzalez, David Chinesta, Francisco Cueto, Elias

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...

Öttinger, Hans Christian Peletier, Mark A. Montefusco, Alberto
Published in
Journal of Non-Equilibrium Thermodynamics

Understanding the fluctuations by which phenomenological evolution equations with thermodynamic structure can be enhanced is the key to a general framework of nonequilibrium statistical mechanics. These fluctuations provide an idealized representation of microscopic details. We consider fluctuation-enhanced equations associated with Markov processe...

Grmela, Miroslav Klika, Václav Pavelka, Michal
Published in
Entropy

We place the Landau theory of critical phenomena into the larger context of multiscale thermodynamics. The thermodynamic potentials, with which the Landau theory begins, arise as Lyapunov like functions in the investigation of the relations among different levels of description. By seeing the renormalization-group approach to critical phenomena as ...

Cao, Bing-Yang Grmela, Miroslav Guo, Zeng-Yuan Hua, Yu-Chao Nie, Ben-Dian
Published in
Journal of Non-Equilibrium Thermodynamics

Phonon hydrodynamics uses the fields of the total energy and the heat flux as state variables. We extend it by promoting the microscopic internal energy field into the status of an extra independent state variable. The governing equations of both the phonon and the extended (two temperature) phonon hydrodynamics are formulated as particular realiza...

González, David García-González, Alberto Chinesta, Francisco Cueto, Elías
Published in
Materials

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 experime...

Öttinger, Hans Christian Struchtrup, Henning Torrilhon, Manuel
Published in
Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

In this work, we make a further step in bringing together different approaches to non-equilibrium thermodynamics. The structure of the moment hierarchy derived from the Boltzmann equation is at the heart of rational extended thermodynamics (RET, developed by Ingo Müller and Tommaso Ruggeri). Whereas the full moment hierarchy has the structure expre...

Grmela, M Klika, V Pavelka, M
Published in
Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

Reduction of a mesoscopic dynamical theory to equilibrium thermodynamics brings to the latter theory the fundamental thermodynamic relation (i.e. entropy as a function of the thermodynamic state variables). The reduction is made by following the mesoscopic time evolution to its conclusion, i.e. to fixed points at which the time evolution ceases to ...

Nie, Ben-Dian Cao, Bing-Yang Guo, Zeng-Yuan Hua, Yu-Chao
Published in
Entropy

Thermomass theory was developed to deal with the non-Fourier heat conduction phenomena involving the influence of heat inertia. However, its structure, derived from an analogy to fluid mechanics, requires further mathematical verification. In this paper, General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) framework, whic...

Shang, Xiaocheng Öttinger, Hans Christian
Published in
Proceedings. Mathematical, Physical, and Engineering Sciences

We study the optimal design of numerical integrators for dissipative systems, for which there exists an underlying thermodynamic structure known as GENERIC (general equation for the nonequilibrium reversible–irreversible coupling). We present a frame-work to construct structure-preserving integrators by splitting the system into reversible and irre...