Deep learning for gradient flows using the Brezis–Ekeland principle

Carini, Laura, Jensen, Max, and Nürnberg, Robert. "Deep learning for gradient flows using the Brezis–Ekeland principle." Archivum Mathematicum (2023): 249-261. <http://eudml.org/doc/298974>.

@article{Carini2023,
abstract = {We propose a deep learning method for the numerical solution of partial differential equations that arise as gradient flows. The method relies on the Brezis–Ekeland principle, which naturally defines an objective function to be minimized, and so is ideally suited for a machine learning approach using deep neural networks. We describe our approach in a general framework and illustrate the method with the help of an example implementation for the heat equation in space dimensions two to seven.},
author = {Carini, Laura, Jensen, Max, Nürnberg, Robert},
journal = {Archivum Mathematicum},
keywords = {machine learning; deep neural networks; gradient flows; Brezis–Ekeland principle; adversarial networks; differential equations},
language = {eng},
number = {3},
pages = {249-261},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Deep learning for gradient flows using the Brezis–Ekeland principle},
url = {http://eudml.org/doc/298974},
year = {2023},
}

TY - JOUR
AU - Carini, Laura
AU - Jensen, Max
AU - Nürnberg, Robert
TI - Deep learning for gradient flows using the Brezis–Ekeland principle
JO - Archivum Mathematicum
PY - 2023
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
IS - 3
SP - 249
EP - 261
AB - We propose a deep learning method for the numerical solution of partial differential equations that arise as gradient flows. The method relies on the Brezis–Ekeland principle, which naturally defines an objective function to be minimized, and so is ideally suited for a machine learning approach using deep neural networks. We describe our approach in a general framework and illustrate the method with the help of an example implementation for the heat equation in space dimensions two to seven.
LA - eng
KW - machine learning; deep neural networks; gradient flows; Brezis–Ekeland principle; adversarial networks; differential equations
UR - http://eudml.org/doc/298974
ER -