Adrian Riekert

22 papers Journal 21

Year	Rank	Type	Title / Venue / Authors
2025	J	`jnl`	Averaged Adam accelerates stochastic optimization in the training of deep neural network approximations for partial differential equation and optimal control problems. CoRR Steffen Dereich, Arnulf Jentzen, Adrian Riekert
2025	J	`jnl`	Non-convergence to Global Minimizers for Adam and Stochastic Gradient Descent Optimization and Constructions of Local Minimizers in the Training of Artificial Neural Networks. SIAM/ASA J. Uncertain. Quantification Arnulf Jentzen, Adrian Riekert
2025	J	`jnl`	Non-convergence to the optimal risk for Adam and stochastic gradient descent optimization in the training of deep neural networks. CoRR Thang Do, Arnulf Jentzen, Adrian Riekert
2025	J	`jnl`	PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning. CoRR Arnulf Jentzen, Julian Kranz, Adrian Riekert
2025	J	`jnl`	Sharp higher order convergence rates for the Adam optimizer. CoRR Steffen Dereich, Arnulf Jentzen, Adrian Riekert
2024	J	`jnl`	An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning. CoRR Lukas Gonon, Arnulf Jentzen, Benno Kuckuck, Siyu Liang, Adrian Riekert, Philippe von Wurstemberger
2024	J	`jnl`	Learning rate adaptive stochastic gradient descent optimization methods: numerical simulations for deep learning methods for partial differential equations and convergence analyses. CoRR Steffen Dereich, Arnulf Jentzen, Adrian Riekert
2024	J	`jnl`	Non-convergence to global minimizers for Adam and stochastic gradient descent optimization and constructions of local minimizers in the training of artificial neural networks. CoRR Arnulf Jentzen, Adrian Riekert
2023	J	`jnl`	Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations. CoRR Arnulf Jentzen, Adrian Riekert, Philippe von Wurstemberger
2023	J	`jnl`	Deep neural network approximation of composite functions without the curse of dimensionality. CoRR Adrian Riekert
2023	—	`—`	Mathematical analysis of gradient methods in the training of artificial neural networks. Adrian Riekert
2022	J	`jnl`	A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions. J. Complex. Patrick Cheridito, Arnulf Jentzen, Adrian Riekert, Florian Rossmannek
2022	J	`jnl`	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. J. Mach. Learn. Res. Arnulf Jentzen, Adrian Riekert
2022	J	`jnl`	Normalized gradient flow optimization in the training of ReLU artificial neural networks. CoRR Simon Eberle, Arnulf Jentzen, Adrian Riekert, Georg S. Weiss
2021	J	`jnl`	A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions. CoRR Patrick Cheridito, Arnulf Jentzen, Adrian Riekert, Florian Rossmannek
2021	J	`jnl`	A proof of convergence for stochastic gradient descent in the training of artificial neural networks with ReLU activation for constant target functions. CoRR Arnulf Jentzen, Adrian Riekert
2021	J	`jnl`	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. CoRR Arnulf Jentzen, Adrian Riekert
2021	J	`jnl`	Convergence analysis for gradient flows in the training of artificial neural networks with ReLU activation. CoRR Arnulf Jentzen, Adrian Riekert
2021	J	`jnl`	Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions. CoRR Martin Hutzenthaler, Arnulf Jentzen, Katharina Pohl, Adrian Riekert, Luca Scarpa
2021	J	`jnl`	Existence, uniqueness, and convergence rates for gradient flows in the training of artificial neural networks with ReLU activation. CoRR Simon Eberle, Arnulf Jentzen, Adrian Riekert, Georg S. Weiss
2021	J	`jnl`	On the existence of global minima and convergence analyses for gradient descent methods in the training of deep neural networks. CoRR Arnulf Jentzen, Adrian Riekert
2020	J	`jnl`	Strong overall error analysis for the training of artificial neural networks via random initializations. CoRR Arnulf Jentzen, Adrian Riekert