Picture for Adrian Riekert

Adrian Riekert

An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning

Add code
Aug 23, 2024
Viaarxiv icon

Learning rate adaptive stochastic gradient descent optimization methods: numerical simulations for deep learning methods for partial differential equations and convergence analyses

Add code
Jun 20, 2024
Viaarxiv icon

Non-convergence to global minimizers for Adam and stochastic gradient descent optimization and constructions of local minimizers in the training of artificial neural networks

Add code
Feb 07, 2024
Viaarxiv icon

Deep neural network approximation of composite functions without the curse of dimensionality

Add code
Apr 12, 2023
Viaarxiv icon

Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations

Add code
Feb 07, 2023
Viaarxiv icon

Normalized gradient flow optimization in the training of ReLU artificial neural networks

Add code
Jul 13, 2022
Figure 1 for Normalized gradient flow optimization in the training of ReLU artificial neural networks
Viaarxiv icon

On the existence of global minima and convergence analyses for gradient descent methods in the training of deep neural networks

Add code
Dec 17, 2021
Figure 1 for On the existence of global minima and convergence analyses for gradient descent methods in the training of deep neural networks
Figure 2 for On the existence of global minima and convergence analyses for gradient descent methods in the training of deep neural networks
Viaarxiv icon

Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions

Add code
Dec 13, 2021
Figure 1 for Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions
Viaarxiv icon

Existence, uniqueness, and convergence rates for gradient flows in the training of artificial neural networks with ReLU activation

Add code
Aug 18, 2021
Viaarxiv icon

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

Add code
Aug 10, 2021
Viaarxiv icon