arXiv subjects

Giuseppe Visconti

Publications and source records attributed to Giuseppe Visconti.

28 records · Page 2Linked to original sources

arXiv2019

Kinetic Methods for Inverse Problems

The Ensemble Kalman Filter method can be used as an iterative numerical scheme for parameter identification or nonlinear filtering problems. We study the limit of infinitely large ensemble size and derive the corresponding mean-field limit of the ensemble method. The solution of the inverse problem is provided by the expected value of the distribution of the ensembles and the kinetic equation allows, in simple cases, to analyze stability of these solutions. Further, we present a slight but stable modification of the method which leads to a Fokker-Planck-type kinetic equation. The kinetic methods proposed here are able to solve the problem with a reduced computational complexity in the limit of a large ensemble size. We illustrate the properties and the ability of the kinetic model to provide solution to inverse problems by using examples from the literature.

math.NA↗

arXiv2018

Optimal definition of the nonlinear weights in multidimensional Central WENOZ reconstructions

Central WENO reconstruction procedures have shown very good performances in finite volume and finite difference schemes for hyperbolic conservation and balance laws in one and more space dimensions, on different types of meshes. Their most recent formulations include WENOZ-type nonlinear weights, but in this context a thorough analysis of the global smoothness indicator $τ$ is still lacking. In this work we first prove results on the asymptotic expansion of one- and multi-dimensional Jiang-Shu smoothness indicators that are useful for the rigorous design of a CWENOZ schemes, also beyond those considered in this paper. Next, we introduce the optimal definition of $τ$ for the one-dimensional CWENOZ schemes and for one example of two-dimensional CWENOZ reconstruction. Numerical experiments of one and two dimensional test problems show the correctness of the analysis and the good performance of the new schemes.

math.NA↗

arXiv2017

Hybrid stochastic kinetic description of two-dimensional traffic dynamics

In this work we present a two-dimensional kinetic traffic model which takes into account speed changes both when vehicles interact along the road lanes and when they change lane. Assuming that lane changes are less frequent than interactions along the same lane and considering that their mathematical description can be done up to some uncertainty in the model parameters, we derive a hybrid stochastic Fokker-Planck-Boltzmann equation in the quasi-invariant interaction limit. By means of suitable numerical methods, precisely structure preserving and direct Monte Carlo schemes, we use this equation to compute theoretical speed-density diagrams of traffic both along and across the lanes, including estimates of the data dispersion, and validate them against real data.

math.NA↗

arXiv2017

A two-dimensional data-driven model for traffic flow on highways

Based on experimental traffic data obtained from German and US highways, we propose a novel two-dimensional first-order macroscopic traffic flow model. The goal is to reproduce a detailed description of traffic dynamics for the real road geometry. In our approach both the dynamic along the road and across the lanes is continuous. The closure relations, being necessary to complete the hydrodynamic equation, are obtained by regression on fundamental diagram data. Comparison with prediction of one-dimensional models shows the improvement in performance of the novel model.

physics.soc-ph↗

arXiv2017

Analysis of risk levels for traffic on a multi-lane highway

We present an analysis of risk levels on multi-lane roads. The aim is to use the crash metrics to understand which direction of the flow mainly influences the safety in traffic flow. In fact, on multi-lane highways interactions among vehicles occur also with lane changing and we show that they strongly affect the level of potential conflicts. In particular, in this study we consider the Time-To-Collision as risk metric and we use the experimental data collected on the A3 German highway.

physics.soc-ph↗

arXiv2017

Cool WENO schemes

This work is dedicated to the development and comparison of WENO-type reconstructions for hyperbolic systems of balance laws. We are particularly interested in high order shock capturing non-oscillatory schemes with uniform accuracy within each cell and low spurious effects. We need therefore to develop a tool to measure the artifacts introduced by a numerical scheme. To this end, we study the deformation of a single Fourier mode and introduce the notion of distorsive errors, which measure the amplitude of the spurious modes created by a discrete derivative operator. Further we refine this notion with the idea of temperature, in which the amplitude of the spurious modes is weighted with its distance in frequency space from the exact mode. Following this approach linear schemes have zero temperature, but to prevent oscillations it is necessary to introduce nonlinearities in the scheme, thus increasing their temperature. However it is important to heat the linear scheme just enough to prevent spurious oscillations. With several tests we show that the newly introduced CWENOZ schemes are cooler than other existing WENO-type operators, while maintaining good non-oscillatory properties.

math.NA↗

arXiv2016

Multivalued fundamental diagrams of traffic flow in the kinetic Fokker-Planck limit

Starting from interaction rules based on two levels of stochasticity we study the influence of the microscopic dynamics on the macroscopic properties of vehicular flow. In particular, we study the qualitative structure of the resulting flux-density and speed-density diagrams for different choices of the desired speeds. We are able to recover multivalued diagrams as a result of the existence of a one-parameter family of stationary distributions, whose expression is analytically found by means of a Fokker-Planck approximation of the initial Boltzmann-type model.

cond-mat.stat-mech↗

arXiv2016

Kinetic models for traffic flow resulting in a reduced space of microscopic velocities

The purpose of this paper is to study the properties of kinetic models for traffic flow described by a Boltzmann-type approach and based on a continuous space of microscopic velocities. In our models, the particular structure of the collision kernel allows one to find the analytical expression of a class of steady-state distributions, which are characterized by being supported on a quantized space of microscopic speeds. The number of these velocities is determined by a physical parameter describing the typical acceleration of a vehicle and the uniqueness of this class of solutions is supported by numerical investigations. This shows that it is possible to have the full richness of a kinetic approach with the simplicity of a space of microscopic velocities characterized by a small number of modes. Moreover, the explicit expression of the asymptotic distribution paves the way to deriving new macroscopic equations using the closure provided by the kinetic model.

math.NA↗

arXiv2016

Analysis of a heterogeneous kinetic model for traffic flow

In this work we extend a recent kinetic traffic model to the case of more than one class of vehicles, each of which is characterized by few different microscopic features. We consider a Boltzmann-like framework with only binary interactions, which take place among vehicles belonging to the various classes. Our approach differs from the multi-population kinetic model based on a lattice of speeds because here we assume continuous velocity spaces and we introduce a parameter describing the physical velocity jump performed by a vehicle that increases its speed after an interaction. The model is discretized in order to investigate numerically the structure of the resulting fundamental diagrams and the system of equations is analyzed by studying well posedness. Moreover, we compute the equilibria of the discretized model and we show that the exact asymptotic kinetic distributions can be obtained with a small number of velocities in the grid. Finally, we introduce a new probability law in order to attenuate the sharp capacity drop occurring in the diagrams of traffic.

math.NA↗

arXiv2015

Fundamental diagrams in traffic flow: the case of heterogeneous kinetic models

Experimental studies on vehicular traffic provide data on quantities like density, flux, and mean speed of the vehicles. However, the diagrams relating these variables (the fundamental and speed diagrams) show some peculiarities not yet fully reproduced nor explained by mathematical models. In this paper, resting on the methods of kinetic theory, we introduce a new traffic model which takes into account the heterogeneous nature of the flow of vehicles along a road. In more detail, the model considers traffic as a mixture of two or more populations of vehicles (e.g., cars and trucks) with different microscopic characteristics, in particular different lengths and/or maximum speeds. With this approach we gain some insights into the scattering of the data in the regime of congested traffic clearly shown by actual measurements.

math.NA↗