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
منابع مشابه
APPROXIMATION OF 3D-PARAMETRIC FUNCTIONS BY BICUBIC B-SPLINE FUNCTIONS
In this paper we propose a method to approximate a parametric 3 D-function by bicubic B-spline functions
متن کاملExact and numerical solutions of linear and non-linear systems of fractional partial differential equations
The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Computational Mathematics
سال: 2021
ISSN: ['1019-7168', '1572-9044']
DOI: https://doi.org/10.1007/s10444-020-09834-7