Strong overall error analysis for the training of artificial neural networks via random initializations. - Arnulf Jentzen; Adrian Riekert (CoRR, 2020)

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 (CoRR, 2021)

Convergence analysis for gradient flows in the training of artificial neural networks with ReLU activation. - Arnulf Jentzen; Adrian Riekert (CoRR, 2021)

Existence, uniqueness, and convergence rates for gradient flows in the training of artificial neural networks with ReLU activation. - Simon Eberle; Arnulf Jentzen; Adrian Riekert; Georg S. Weiss (CoRR, 2021)

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; Adrian Riekert; Luca Scarpa (CoRR, 2021)

On the existence of global minima and convergence analyses for gradient descent methods in the training of deep neural networks. - Arnulf Jentzen; Adrian Riekert (CoRR, 2021)

Normalized gradient flow optimization in the training of ReLU artificial neural networks. - Simon Eberle; Arnulf Jentzen; Adrian Riekert; Georg S. Weiss (CoRR, 2022)

A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions. - Patrick Cheridito; Arnulf Jentzen; Adrian Riekert; Florian Rossmannek (J. Complex., 2022)

A proof of convergence for the gradient descent optimization method with random initializations in the training of neural networks with ReLU activation for piecewise linear target functions. - Arnulf Jentzen; Adrian Riekert (J. Mach. Learn. Res., 2022)

Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations. - Arnulf Jentzen; Adrian Riekert; Philippe von Wurstemberger (CoRR, 2023)

Deep neural network approximation of composite functions without the curse of dimensionality. - Adrian Riekert (CoRR, 2023)

Mathematical analysis of gradient methods in the training of artificial neural networks. - Adrian Riekert (2023)

Non-convergence to global minimizers for Adam and stochastic gradient descent optimization and constructions of local minimizers in the training of artificial neural networks. - Arnulf Jentzen; Adrian Riekert (CoRR, 2024)

Learning rate adaptive stochastic gradient descent optimization methods: numerical simulations for deep learning methods for partial differential equations and convergence analyses. - Steffen Dereich; Arnulf Jentzen; Adrian Riekert (CoRR, 2024)

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; Siyu Liang; Adrian Riekert; Philippe von Wurstemberger (CoRR, 2024)

Averaged Adam accelerates stochastic optimization in the training of deep neural network approximations for partial differential equation and optimal control problems. - Steffen Dereich; Arnulf Jentzen; Adrian Riekert (CoRR, 2025)

Non-convergence to the optimal risk for Adam and stochastic gradient descent optimization in the training of deep neural networks. - Thang Do; Arnulf Jentzen; Adrian Riekert (CoRR, 2025)

Sharp higher order convergence rates for the Adam optimizer. - Steffen Dereich; Arnulf Jentzen; Adrian Riekert (CoRR, 2025)

PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning. - Arnulf Jentzen; Julian Kranz; Adrian Riekert (CoRR, 2025)