Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions

no code implementations • 13 Dec 2021 • Martin Hutzenthaler, Arnulf Jentzen, Katharina Pohl, Adrian Riekert, Luca Scarpa

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 it remains an open problem of research to provide a mathematical convergence analysis which rigorously explains the success of SGD type optimization methods in the training of DNNs.

An overview on deep learning-based approximation methods for partial differential equations

no code implementations • 22 Dec 2020 • Christian Beck, Martin Hutzenthaler, Arnulf Jentzen, Benno Kuckuck

It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs).