26 citations · 96 across the 22 of their papers we have counts for
5 papers · 1 filter
An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning
Lukas Gonon, Arnulf Jentzen, Benno Kuckuck +3
The approximation of solutions of partial differential equations (PDEs) with numerical algorithms is a central topic in applied mathematics. For many decades, various types of meth…
Deep neural network approximation of composite functions without the curse of dimensionality
Adrian Riekert
In this article we identify a general class of high-dimensional continuous functions that can be approximated by deep neural networks (DNNs) with the rectified linear unit (ReLU) a…
Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations
Arnulf Jentzen, Adrian Riekert, Philippe von Wurstemberger
In this article we propose a new deep learning approach to approximate operators related to parametric partial differential equations (PDEs). In particular, we introduce a new stra…
A proof of convergence for stochastic gradient descent in the training of artificial neural networks with ReLU activation for constant target functions
Arnulf Jentzen, Adrian Riekert
In this article we study the stochastic gradient descent (SGD) optimization method in the training of fully-connected feedforward artificial neural networks with ReLU activation. T…
A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions
Patrick Cheridito, Arnulf Jentzen, Adrian Riekert +1
Gradient descent optimization algorithms are the standard ingredients that are used to train artificial neural networks (ANNs). Even though a huge number of numerical simulations i…