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
Constructive Solution of Inverse Parametric Linear/Quadratic Programming Problems
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Optimization Theory and Applications"
DOI: 10.1007/s10957-016-0968-0
Abstract: Parametric convex programming has received a lot of attention, since it has many applications in chemical engineering, control engineering, signal processing, etc. Further, inverse optimality plays an important role in many contexts, e.g., image processing,… read more here.
Keywords: solution inverse; constructive solution; control; linear quadratic ... See more keywords
Four parametric linear Euler sums
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2019.123661
Abstract: Abstract In this paper, firstly, we aim to investigate analytic continuations of altogether four types of parametric linear Euler sums, by using the Euler-Maclaurin summation formula and the Euler-Boole summation formula. Secondly, we show how… read more here.
Keywords: euler; formula; linear euler; euler sums ... See more keywords