Optimal approximation rates for Lipschitz controls

2002 ◽  
Author(s):  
G.P. Grammel
Keyword(s):  
Optimal Approximation ◽  
Approximation Rates ◽  
Lipschitz Controls

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.

scholarly journals Optimal Approximation of Skorohod Integrals

2016 ◽  
Vol 31 (1) ◽  
pp. 206-231
Author(s):  
Andreas Neuenkirch ◽  
Peter Parczewski
Keyword(s):  
Optimal Approximation

Optimal approximation algorithm of feature coefficients and identification of target

1994 ◽  
Vol 11 (1) ◽  
pp. 57-63
Author(s):  
Liao Supeng ◽  
Li Xingguo ◽  
Fang Dagang
Keyword(s):  
Approximation Algorithm ◽  
Optimal Approximation
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