108 citations · 375 across the 30 of their papers we have counts for
37 papers
Micro-to-macro derivation and stability analysis of an Aw-Rascle-Zhang-type model with driver-dependent acceleration
Stephan Gerster, Giuseppe Visconti
We introduce a new traffic flow model. The main idea is to describe acceleration effects in the Aw-Rascle-Zhang model through an additional driver-dependent equation, thereby allow…
Ensemble Kalman Inversion as an Inertial Interacting Particle System
Michael Herty, Pierpaolo Porretta, Giuseppe Visconti
Ensemble Kalman Inversion (EKI) is a derivative-free, ensemble-based method for inverse and optimization problems. A central limitation of its continuous-time dynamics is premature…
Agent-Based Optimal Control for Image Processing
Alessio Oliviero, Simone Cacace, Giuseppe Visconti
We investigate the use of multi-agent systems to solve classical image processing tasks, such as colour quantization and segmentation. We frame the task as an optimal control probl…
Second-order multilane traffic flow models: from the microscopic to the macroscopic scale
Matteo Piu, Giuseppe Visconti, Gabriella Puppo
This study addresses multilane vehicular traffic modelling, focusing on the rigorous transition from microscopic (individual vehicle-based) to macroscopic (aggregate flow-based) de…
Relaxation and stability analysis of a third-order multiclass traffic flow model
Stephan Gerster, Giuseppe Visconti
Traffic flow modeling spans a wide range of mathematical approaches, from microscopic descriptions of individual vehicle dynamics to macroscopic models based on aggregate quantitie…
Dissipation-dispersion analysis of fully-discrete implicit discontinuous Galerkin methods and application to stiff hyperbolic problems
Maya Briani, Gabriella Puppo, Giuseppe Visconti
The application of discontinuous Galerkin (DG) schemes to hyperbolic systems of conservation laws requires a careful interplay between space discretization, carried out with local…
Controllability of continuous networks and a kernel-based learning approximation
Michael Herty, Chiara Segala, Giuseppe Visconti
Residual deep neural networks are formulated as interacting particle systems leading to a description through neural differential equations, and, in the case of large input data, t…
Quinpi: Integrating stiff hyperbolic systems with implicit high order finite volume schemes
Gabriella Puppo, Matteo Semplice, Giuseppe Visconti
Many interesting physical problems described by systems of hyperbolic conservation laws are stiff, and thus impose a very small time-step because of the restrictive CFL stability c…
Recent Trends on Nonlinear Filtering for Inverse Problems
Michael Herty, Elisa Iacomini, Giuseppe Visconti
Among the class of nonlinear particle filtering methods, the Ensemble Kalman Filter (EnKF) has gained recent attention for its use in solving inverse problems. We review the origin…
Numerical boundary control for semilinear hyperbolic systems
Stephan Gerster, Felix Nagel, Aleksey Sikstel +1
This work is devoted to the design of boundary controls of physical systems that are described by semilinear hyperbolic balance laws. A computational framework is presented that yi…
Haar-type stochastic Galerkin formulations for hyperbolic systems with Lipschitz continuous flux function
Stephan Gerster, Aleksey Sikstel, Giuseppe Visconti
This work is devoted to the Galerkin projection of highly nonlinear random quantities. The dependency on a random input is described by Haar-type wavelet systems. The classical Haa…
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…
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…
Quinpi: integrating conservation laws with CWENO implicit methods
G. Puppo, M. Semplice, G. Visconti
Many interesting applications of hyperbolic systems of equations are stiff, and require the time step to satisfy restrictive stability conditions. One way to avoid small time steps…
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…
A Stabilization of a Continuous Limit of the Ensemble Kalman Inversion
Dieter Armbruster, Michael Herty, Giuseppe Visconti
The Ensemble Kalman Filter (EnKF) belongs to the class of iterative particle filtering methods and can be used for solving control--to--observable inverse problems. In this context…
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…
Identifying trending coefficients with an ensemble Kalman filter
M. Schwenzer, G. Visconti, M. Ay +3
This paper extends the ensemble Kalman filter (EnKF) for inverse problems to identify trending model coefficients. This is done by repeatedly inflating the ensemble while maintaini…
Mean-Field and Kinetic Descriptions of Neural Differential Equations
M. Herty, T. Trimborn, G. Visconti
Nowadays, neural networks are widely used in many applications as artificial intelligence models for learning tasks. Since typically neural networks process a very large amount of…
Reconstruction of traffic speed distributions from kinetic models with uncertainties
M. Herty, A. Tosin, G. Visconti +1
In this work we investigate the ability of a kinetic approach for traffic dynamics to predict speed distributions obtained through rough data. The present approach adopts the forma…
Continuous Limits for Constrained Ensemble Kalman Filter
Michael Herty, Giuseppe Visconti
The Ensemble Kalman Filter method can be used as an iterative particle numerical scheme for state dynamics estimation and control--to--observable identification problems. In applic…
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…
Efficient implementation of adaptive order reconstructions
Matteo Semplice, Giuseppe Visconti
Including polynomials with small degree and stencil when designing very high order reconstructions is surely beneficial for their non oscillatory properties, but may bring loss of…
Mean field models for large data-clustering problems
Michael Herty, Lorenzo Pareschi, Giuseppe Visconti
We consider mean-field models for data--clustering problems starting from a generalization of the bounded confidence model for opinion dynamics. The microscopic model includes info…