Hypocoercivity: the example of linear transport

2006 ◽  
pp. 33-53 ◽  
Author(s):  
Laurent Desvillettes
Keyword(s):  
Linear Transport

scholarly journals Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs

2021 ◽  
Vol 47 (1) ◽  
Author(s):  
Fabian Laakmann ◽  
Philipp Petersen
Keyword(s):  
Neural Networks ◽  
Deep Neural Networks ◽  
Initial Conditions ◽  
Activation Function ◽  
Transport Equations ◽  
High Dimensional ◽  
Linear Transport ◽  
Approximation Rates ◽  
Curse Of Dimension ◽  
Efficient Approximation

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.

Asymptotic theory of the linear transport equation in anisotropic media

2008 ◽  
Vol 49 (8) ◽  
pp. 083504 ◽  
Author(s):  
Richard Sanchez ◽  
Jean Ragusa ◽  
Emiliano Masiello
Keyword(s):  
Transport Equation ◽  
Asymptotic Theory ◽  
Anisotropic Media ◽  
Linear Transport ◽  
Linear Transport Equation

A linear transport equation for wave phenomena

1987 ◽  
Vol 16 (8) ◽  
pp. 1041-1094 ◽  
Author(s):  
Marijan Ribarič ◽  
Luka Sušteršič
Keyword(s):  
Transport Equation ◽  
Linear Transport ◽  
Linear Transport Equation ◽  
Wave Phenomena
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