Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs
Sign Up to like & getrecommendations! Published in 2021 at "Advances in Computational Mathematics"
DOI: 10.1007/s10444-020-09834-7
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… read more here.
Keywords: efficient approximation; parametric linear; transport equations; linear transport ... See more keywords
Efficient Approximation of High-Dimensional Functions With Neural Networks.
Sign Up to like & getrecommendations! Published in 2021 at "IEEE transactions on neural networks and learning systems"
DOI: 10.1109/tnnls.2021.3049719
Abstract: In this article, we develop a framework for showing that neural networks can overcome the curse of dimensionality in different high-dimensional approximation problems. Our approach is based on the notion of a catalog network, which… read more here.
Keywords: efficient approximation; neural networks; high dimensional; dimensional functions ... See more keywords