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
Linear Transport in Porous Media
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Computational and Theoretical Transport"
DOI: 10.1080/23324309.2020.1842453
Abstract: Abstract The linear transport theory is developed to describe the time dependence of the number density of tracer particles in porous media. The advection is taken into account. The transport equation is numerically solved by… read more here.
Keywords: transport porous; porous media; geometry; linear transport ... See more keywords
Measuring the bending modulus of lipid bilayers with cholesterol.
Sign Up to like & getrecommendations! Published in 2021 at "Physical review. E"
DOI: 10.1103/physreve.104.044405
Abstract: The effect of cholesterol on the bending modulus of DOPC lipid bilayers has become a controversial topic that has implications for methods of measuring the bending modulus. Recent results using neutron spin echo and nuclear… read more here.
Keywords: transport properties; linear transport; lipid bilayers; involve linear ... See more keywords