108 citations · 375 across the 30 of their papers we have counts for
4 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…
Mean-field limit of a hybrid system for multi-lane multi-class traffic
Xiaoqian Gong, Benedetto Piccoli, Giuseppe Visconti
This article aims to study coupled mean-field equation and ODEs with discrete events motivated by vehicular traffic flow. Precisely, multi-lane traffic flow in presence of human-dr…
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…