40 citations · 405 across the 53 of their papers we have counts for
5 papers · 1 filter
Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions
Martin Hutzenthaler, Arnulf Jentzen, Katharina Pohl +2
In many numerical simulations stochastic gradient descent (SGD) type optimization methods perform very effectively in the training of deep neural networks (DNNs) but till this day…
Random separation property for stochastic Allen-Cahn-type equations
Federico Bertacco, Carlo Orrieri, Luca Scarpa
We study a large class of stochastic -Laplace Allen-Cahn equations with singular potential. Under suitable assumptions on the (multiplicative-type) noise we first prove existenc…
The Energy-Dissipation Principle for stochastic parabolic equations
Luca Scarpa, Ulisse Stefanelli
The Energy-Dissipation Principle provides a variational tool for the analysis of parabolic evolution problems: solutions are characterized as so-called null-minimizers of a global…
Rate-independent stochastic evolution equations: parametrized solutions
Luca Scarpa, Ulisse Stefanelli
By extending to the stochastic setting the classical vanishing viscosity approach we prove the existence of suitably weak solutions of a class of nonlinear stochastic evolution equ…
The Cahn-Hilliard equation with forward-backward dynamic boundary condition via vanishing viscosity
Pierluigi Colli, Takeshi Fukao, Luca Scarpa
An asymptotic analysis for a system with equation and dynamic boundary condition of Cahn-Hilliard type is carried out as the coefficient of the surface diffusion acting on the phas…