120 citations · 243 across the 55 of their papers we have counts for
9 papers · 1 filter
Continuous limits of residual neural networks in case of large input data
M. Herty, A. Thuenen, T. Trimborn +1
Residual deep neural networks (ResNets) are mathematically described as interacting particle systems. In the case of infinitely many layers the ResNet leads to a system of coupled…
Description of random level sets by polynomial chaos expansions
Markus Bambach, Stephan Gerster, Michael Herty +1
We present a novel approach to determine the evolution of level sets under uncertainties in the velocity fields. This leads to a stochastic description of the level sets. To comput…
Uncertainty Quantification in Hierarchical Vehicular Flow Models
Michael Herty, Elisa Iacomini
We consider kinetic vehicular traffic flow models of BGK type. Considering different spatial and temporal scales, those models allow to derive a hierarchy of traffic models includi…
Efficient simulation of coupled gas and power networks under uncertain demands
E. Fokken, S. Göttlich, M. Herty
We introduce an approach and a software tool, Grazer, for solving coupled energy networks composed of gas and electric power networks. Those networks are coupled to stochastic fluc…
Model of vehicle interactions with autonomous cars and its properties
M. Herty, G. Puppo, G. Visconti
We study a hierarchy of models based on kinetic equations for the descriptions of traffic flow in presence of autonomous and human--driven vehicles. The autonomous cars considered…
Model-Order Reduction For Hyperbolic Relaxation Systems
Sara Grundel, Michael Herty
We propose a novel framework for model-order reduction of hyperbolic differential equations. The approach combines a relaxation formulation of the hyperbolic equations with a discr…