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

نویسندگان

چکیده

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

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ژورنال

عنوان ژورنال: Advances in Computational Mathematics

سال: 2021

ISSN: ['1019-7168', '1572-9044']

DOI: https://doi.org/10.1007/s10444-020-09834-7