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2020 – today
- 2024
[i14]Arnulf Jentzen, Adrian Riekert:
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 abs/2402.05155 (2024)- [i13]Steffen Dereich, Arnulf Jentzen, Adrian Riekert:
Learning rate adaptive stochastic gradient descent optimization methods: numerical simulations for deep learning methods for partial differential equations and convergence analyses. CoRR abs/2406.14340 (2024) - [i12]Lukas Gonon, Arnulf Jentzen, Benno Kuckuck, Siyu Liang
, Adrian Riekert, Philippe von Wurstemberger:
An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning. CoRR abs/2408.13222 (2024) - 2023
- [b1]Adrian Riekert:
Mathematical analysis of gradient methods in the training of artificial neural networks. University of Münster, Germany, 2023, pp. 1-276 - [i11]Arnulf Jentzen, Adrian Riekert, Philippe von Wurstemberger:
Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations. CoRR abs/2302.03286 (2023) - [i10]Adrian Riekert:
Deep neural network approximation of composite functions without the curse of dimensionality. CoRR abs/2304.05790 (2023) - 2022
- [j2]Patrick Cheridito, Arnulf Jentzen, Adrian Riekert, Florian Rossmannek:
A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions. J. Complex. 72: 101646 (2022) - [j1]Arnulf Jentzen, Adrian Riekert:
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. 23: 260:1-260:50 (2022) - [i9]Simon Eberle, Arnulf Jentzen, Adrian Riekert, Georg S. Weiss:
Normalized gradient flow optimization in the training of ReLU artificial neural networks. CoRR abs/2207.06246 (2022) - 2021
- [i8]Patrick Cheridito, Arnulf Jentzen, Adrian Riekert, Florian Rossmannek:
A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions. CoRR abs/2102.09924 (2021) - [i7]Arnulf Jentzen, Adrian Riekert:
A proof of convergence for stochastic gradient descent in the training of artificial neural networks with ReLU activation for constant target functions. CoRR abs/2104.00277 (2021) - [i6]Arnulf Jentzen, Adrian Riekert:
Convergence analysis for gradient flows in the training of artificial neural networks with ReLU activation. CoRR abs/2107.04479 (2021) - [i5]Arnulf Jentzen, Adrian Riekert:
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 abs/2108.04620 (2021) - [i4]Simon Eberle, Arnulf Jentzen, Adrian Riekert, Georg S. Weiss:
Existence, uniqueness, and convergence rates for gradient flows in the training of artificial neural networks with ReLU activation. CoRR abs/2108.08106 (2021) - [i3]Martin Hutzenthaler, Arnulf Jentzen, Katharina Pohl, Adrian Riekert, Luca Scarpa:
Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions. CoRR abs/2112.07369 (2021) - [i2]Arnulf Jentzen, Adrian Riekert:
On the existence of global minima and convergence analyses for gradient descent methods in the training of deep neural networks. CoRR abs/2112.09684 (2021) - 2020
- [i1]Arnulf Jentzen, Adrian Riekert:
Strong overall error analysis for the training of artificial neural networks via random initializations. CoRR abs/2012.08443 (2020)
Coauthor Index
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