Can I read Estimatable variation neural networks and their application to ODEs and scalar hyperbolic conservation laws on EtoBox?

Estimatable variation neural networks and their application to ODEs and scalar hyperbolic conservation laws by Lukáčová-Medviďová, Mária; Schneider, Simon is a scholarly article available to read on EtoBox.

What is Estimatable variation neural networks and their application to ODEs and scalar hyperbolic conservation laws about?

We introduce estimatable variation neural networks (EVNNs), a class of neural networks that allow a computationally cheap estimate on the $BV$ norm motivated by the space $BMV$ of functions with bounded M-variation. We prove a universal approximation theorem for EVNNs and discuss possible implementations. We construct sequences of loss functionals for ODEs and scalar hyperbolic conservation laws for which a vanishing loss leads to convergence. Moreover, we show the existence of sequences of loss minimizing neural networks if the solution is an element of $BMV$. Several numerical test cases illustrate that it is possible to use standard techniques to minimize these loss functionals for EVNNs.

Author

Lukáčová-Medviďová, Mária; Schneider, Simon

Published

2024

Language

EN