Titel
Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs
Autor*in
Fabian Laakmann
Mathematical Institute, University of Oxford
Abstract
We 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.
Stichwort
Deep neural networksParametric PDEsApproximation ratesCurse of dimensionTransport equations
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
Erschienen in
Titel
Advances in Computational Mathematics
Band
47
ISSN
1019-7168
Erscheinungsdatum
2021
Publication
Springer Science and Business Media LLC
Erscheinungsdatum
2021
Zugänglichkeit
Rechte
Rechteangabe
© The Author(s) 2021
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