Structure-preserving neural networks
TypeArticles dans des revues avec comité de lecture
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) ). 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.
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HERNÁNDEZ, Quercus; BADÍAS, Alberto; GONZÁLEZ, David; CHINESTA, Francisco; CUETO, Elías (Elsevier, 2021)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 ...
HERNANDEZ, Quercus; BADIAS, Alberto; GONZALEZ, David; CHINESTA, Francisco; CUETO, Elias (Elsevier BV, 2021)We present an algorithm to learn the relevant latent variables of a large-scale discretized physical system and predict its time evolution using thermodynamically-consistent deep neural networks. Our method relies on sparse ...
BADÍAS, Alberto; CURTIT, Sarah; GONZÁLEZ, David; ALFARO, Iciar; CHINESTA, Francisco; CUETO, Elías G. (Wiley, 2019)While modern CFD tools are able to provide the user with reliable and accurate simulations, there is a strong need for interactive design and analysis tools. State-of-the-art CFD software employs massive resources in terms ...
BADÍAS, Alberto; GONZÁLEZ, David; ALFARO, Icíar; CHINESTA, Francisco; CUETO, Elías (Wiley, 2020)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 ...
BADIAS, Alberto; ALFARO, Iciar; GONZALEZ, David; CHINESTA, Francisco; CUETO, Elias (elsevier, 2018)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 ...