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04/12/2023
Deep neural network approximation of composite functions without the curse of dimensionality
In this article we identify a general class of high-dimensional continuo...
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02/07/2023
Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations
In this article we propose a new deep learning approach to solve paramet...
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07/13/2022
Normalized gradient flow optimization in the training of ReLU artificial neural networks
The training of artificial neural networks (ANNs) is nowadays a highly r...
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12/17/2021
On the existence of global minima and convergence analyses for gradient descent methods in the training of deep neural networks
In this article we study fully-connected feedforward deep ReLU ANNs with...
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12/13/2021
Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions
In many numerical simulations stochastic gradient descent (SGD) type opt...
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08/18/2021
Existence, uniqueness, and convergence rates for gradient flows in the training of artificial neural networks with ReLU activation
The training of artificial neural networks (ANNs) with rectified linear ...
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08/10/2021
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 tar
Gradient descent (GD) type optimization methods are the standard instrum...
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07/09/2021
Convergence analysis for gradient flows in the training of artificial neural networks with ReLU activation
Gradient descent (GD) type optimization schemes are the standard methods...
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04/01/2021
A proof of convergence for stochastic gradient descent in the training of artificial neural networks with ReLU activation for constant target functions
In this article we study the stochastic gradient descent (SGD) optimizat...
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02/19/2021
A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions
Gradient descent optimization algorithms are the standard ingredients th...
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01/18/2021
Wasserstein Convergence Rate for Empirical Measures of Markov Chains
We consider a Markov chain on ℝ^d with invariant measure μ. We are inter...
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12/15/2020
