7 papers
SensLI: Sensitivity-Based Layer Insertion for Neural Networks
Leonie Kreis, Evelyn Herberg, Frederik Köhne +2
The training of neural networks requires tedious and often manual tuning of the network architecture. We propose a systematic approach to inserting new layers during the training p…
Time Regularization in Optimal Time Variable Learning
Evelyn Herberg, Roland Herzog, Frederik Köhne
Recently, optimal time variable learning in deep neural networks (DNNs) was introduced in arXiv:2204.08528. In this manuscript we extend the concept by introducing a regularization…
Lecture Notes: Neural Network Architectures
Evelyn Herberg
These lecture notes provide an overview of Neural Network architectures from a mathematical point of view. Especially, Machine Learning with Neural Networks is seen as an optimizat…
An Optimal Time Variable Learning Framework for Deep Neural Networks
Harbir Antil, Hugo Díaz, Evelyn Herberg
Feature propagation in Deep Neural Networks (DNNs) can be associated to nonlinear discrete dynamical systems. The novelty, in this paper, lies in letting the discretization paramet…
Variational discretization of one-dimensional elliptic optimal control problems with BV functions based on the mixed formulation
Evelyn Herberg, Michael Hinze
We consider optimal control of an elliptic two-point boundary value problem governed by functions of bounded variation (BV). The cost functional is composed of a tracking term for…
Variational discretization approach applied to an optimal control problem with bounded measure controls
Evelyn Herberg, Michael Hinze
We consider a parabolic optimal control problem with an initial measure control. The cost functional consists of a tracking term corresponding to the observation of the state at fi…
Maximal discrete sparsity in parabolic optimal control with measures
Evelyn Herberg, Michael Hinze, Henrik Schumacher
We consider variational discretization of a parabolic optimal control problem governed by space-time measure controls. For the state discretization we use a Petrov-Galerkin method…