Spectral properties and time asymptotic behaviour of linear transport equations in slab geometry

2001 ◽  
Vol 24 (10) ◽  
pp. 689-711 ◽  
Author(s):  
Khalid Latrach ◽  
Abdelkader Dehici
2021 ◽  
Vol 47 (1) ◽  
Author(s):  
Fabian Laakmann ◽  
Philipp Petersen

AbstractWe demonstrate that deep neural networks with the ReLU activation function can efficiently approximate the solutions of various types of parametric linear transport equations. For non-smooth initial conditions, the solutions of these PDEs are high-dimensional and non-smooth. Therefore, approximation of these functions suffers from a curse of dimension. We demonstrate that through their inherent compositionality deep neural networks can resolve the characteristic flow underlying the transport equations and thereby allow approximation rates independent of the parameter dimension.


2019 ◽  
Vol 90 (8) ◽  
pp. 375-388 ◽  
Author(s):  
S. Kelbij Star ◽  
Francesco Belloni ◽  
Gert Van den Eynde ◽  
Joris Degroote

Sign in / Sign up

Export Citation Format

Share Document