120 citations · 243 across the 55 of their papers we have counts for
9 papers · 1 filter
Derivation and stability analysis of macroscopic multi-lane models for vehicular traffic flow
Matteo Piu, Michael Herty, Gabriella Puppo
The mathematical modeling and the stability analysis of multi-lane traffic in the macroscopic scale is considered. We propose a new first order model derived from microscopic dynam…
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…
Modeling, Control and Numerics of Gas Networks
Martin Gugat, Michael Herty
In this article we survey recent progress on mathematical results on gas flow in pipe networks with a special focus on questions of control and stabilization. We briefly present th…
New Coupling Conditions for Isentropic Flow on Networks
Yannick Holle, Michael Herty, Michael Westdickenberg
We introduce new coupling conditions for isentropic flow on networks based on an artificial density at the junction. The new coupling conditions can be derived from a kinetic model…
From kinetic to macroscopic models and back
M. Herty, G. Puppo, G. Visconti
We study kinetic models for traffic flow characterized by the property of producing backward propagating waves. These waves may be identified with the phenomenon of stop-and-go wav…
Qualitative Properties of Mathematical Model For Data Flow
C. D. Hauck, M. Herty, G. Visconti
In this paper, properties of a recently proposed mathematical model for data flow in large-scale asynchronous computer systems are analyzed. In particular, the existence of special…