Numerical schemes for partial differential equations. In particular, high order finite volume schemes for hyperbolic conservation and balance laws. CWENO reconstruction procedures.
Multirate and implicit schemes for stiff equations.
Filtering methods for the numerical solution of inverse problems and parameter estimation problems.
Multiscale mathematical models (microscopic-mesoscopic-macroscopic scales) for multi-agent systems: traffic flow, data flow, neural networks, etc.
M. Briani, G. Puppo, G. Visconti
On implicit time methods and discontinuous Galerkin space reconstruction for conservation laws.
Submitted, 2024. Preprint link
M. Herty, C. Segala, G. Visconti
Controllability of continuous networks and a kernel-based learning approximation.
Submitted, 2024. Preprint link
S. Gerster, A. Sikstel, G. Visconti
Haar-type stochastic Galerkin formulations for hyperbolic systems with Lipschitz continuous flux function.
Submitted, 2022. Preprint link
Journal papers (link to Scopus page)
G. Puppo, M. Semplice, G. Visconti
Quinpi: Integrating stiff hyperbolic systems with implicit high order finite volume schemes.
Commun. Comput. Phys., 35(1):30-70, 2024. Paper link
X. Gong, B. Piccoli, G. Visconti
Mean-field limit of a hybrid system for multi-lane multi-class traffic
ESAIM Contr. Op. Ca. Va., 2023. Paper link
G. Puppo, M. Semplice, G. Visconti
Quinpi: integrating conservation laws with CWENO implicit methods
Commun. Appl. Math. Comput., 5:343-369, 2023. Paper link
M. Herty, G. Puppo, G. Visconti
Model of vehicle interactions with autonomous cars and its properties
Discrete Cont. Dyn.-B, 28(2):833-853, 2023. Paper link
X. Gong, M. Herty, B. Piccoli, G. Visconti
Crowd Dynamics: Modeling and control of multi-agent systems.
Annual Review of Control, Robotics, and Autonomous Systems, 6:, 2023. Paper link
M. Herty, A. Thuenen, T. Trimborn, G. Visconti
Continuous limits of residual neural networks in case of large input data
Communications in Applied and Industrial Mathematics, 13(1):96-120, 2022. Paper link
S. Gerster, F. Nagel, A. Sikstel, G. Visconti
Numerical boundary control for semilinear hyperbolic systems.
Math. Control Relat. Fields, Accepted, 2022. Paper link
D. Armbruster, M. Herty, G. Visconti
A Stabilization of a Continuous Limit of the Ensemble Kalman Inversion
SIAM J. Numer. Anal., 60(3):1494-1515, 2022. Paper link
M. Herty, E. Iacomini, G. Visconti
Recent trends on nonlinear filtering for inverse problems.
Communications in Applied and Industrial Mathematics, 13(1):10-20, 2022. Paper link
M. Herty, T. Trimborn, G. Visconti
Mean-Field and Kinetic Descriptions of Neural Differential Equations
Found. Data Sci., 4(2):271-298, 2022. Paper link
C. D. Hauck, M. Herty, G. Visconti
Qualitative Properties of Mathematical Model for Data Flow
Netw. Heterog. Media, 16(4):513-533, 2021. Paper link
X. Gong, B. Piccoli, G. Visconti
Mean-field of optimal control problems for hybrid model of multilane traffic
IEEE Control Systems Letters, 5(6):1964-1969, 2021. Paper link
K. Bobzin, W. Wietheger, H. Heinemann, S. R. Dokhanchi, M. Rom, G. Visconti
Prediction of particle properties in plasma spraying based on machine learning
J. Therm. Spray Tech., 30:1751-1764, 2021. Paper link
T. Trimborn, S. Gerster, G. Visconti
Spectral methods to study the robustness of residual neural networks with infinite layers
Found. Data Sci., 2(3):257-278, 2020. Paper link
M. Herty, G. Visconti
Continuous Limits for Constrained Ensemble Kalman Filter
Inverse Probl., 36(7):0750062020, 2020. Paper link
M. Herty, L. Pareschi, G. Visconti
Mean field models for large data-clustering problems
Netw. Heterog. Media, 15(3):463-487, 2020. Paper link
M. Semplice, G. Visconti
Efficient implementation of adaptive order reconstructions
J. Sci. Comput., 83(1):6, 2020. Paper link
M. Herty, G. Puppo, S. Roncoroni, G. Visconti
The BGK approximation of kinetic models for traffic
Kinet. Relat. Models, 13(2):279-307, 2020. Paper link
I. Cravero, M. Semplice, G. Visconti
Optimal definition of the nonlinear weights in multidimensional Central WENOZ reconstructions
SIAM J. Numer. Anal., 57(5):2328-2358, 2019. Paper link
M. Herty, G. Visconti
Kinetic Methods for Inverse Problems
Kinet. Relat. Models, 12(5):1109-1130, 2019. Paper link
M. Herty, A. Tosin, G. Visconti, M. Zanella
Hybrid stochastic kinetic description of two-dimensional traffic dynamics
SIAM J. Appl. Math., 78(5):2737-2762, 2018. Paper link
M. Herty, S. Moutari, G. Visconti
Macroscopic modeling of multi-lane motorways using a two-dimensional second-order model of traffic flow
SIAM J. Appl. Math., 78(4):2252-2278, 2018. Paper link
M. Herty, A. Fazekas, G. Visconti
A two-dimensional data-driven model for traffic flow on highways
Netw. Heterog. Media, 13(2):217-240, 2018. Paper link
I. Cravero, G. Puppo, M. Semplice, G. Visconti
Cool WENO Schemes
Comput. Fluids, 169:71-86, 2018. Paper link
I. Cravero, G. Puppo, M. Semplice, G. Visconti
CWENO: uniformly accurate reconstructions for balance laws
Math. Comp., 87(312):1689-1719, 2018. Paper link
G. Visconti, M. Herty, G. Puppo, A. Tosin
Multivalued fundamental diagrams of traffic flow in the kinetic Fokker-Planck limit
Multiscale Model. Simul., 15:1267-1293, 2017. Paper link
G. Puppo, M. Semplice, A. Tosin, G. Visconti
Kinetic models for traffic flow resulting in a reduced space of microscopic velocities
Kinet. Relat. Models, 10(3):823-854, 2017. Paper link
G. Puppo, M. Semplice, A. Tosin, G. Visconti
Analysis of a multi-population kinetic model for traffic flow
Commun. Math. Sci., 15(2):379-412, 2017. Paper link
G. Puppo, M. Semplice, A. Tosin, G. Visconti
Fundamental diagrams in traffic flow: the case of heterogeneous kinetic models
Commun. Math. Sci., 14(3):643-669, 2016. Paper link
Book Chapters
G. Visconti, S. Tozza, M. Semplice, G. Puppo
A conservative a-posteriori time-limiting procedure in Quinpi schemes.
In G. Albi, W. Boscheri, M. Zanella, editors, Advances in Numerical Methods for Hyperbolic Balance Laws and Related Problems
SEMA SIMAI Springer Series, vol. 32. Springer, Cham., 2023. Paper link
M. Herty, G. Puppo, G. Visconti
From kinetic to macroscopic models and back
In G. Puppo and A. Tosin, editors, Mathematical descriptions of traffic flow: micro, macro and kinetic models
ICIAM2019 SEMA SIMAI Springer Series, 12:17-34. Springer International Publishing, 2021. Paper link
M. Herty, A. Tosin, G. Visconti, M. Zanella
Reconstruction of traffic speed distributions from kinetic models with uncertainties
In G. Puppo and A. Tosin, editors, Mathematical descriptions of traffic flow: micro, macro and kinetic models
ICIAM2019 SEMA SIMAI Springer Series, 12:1-16. Springer International Publishing, 2021. Paper link
M. Herty, M. Rom, G. Visconti
Neuronale Netze und Filtermethoden im Praxiseinsatz (Neural networks and filter methods in practice) in Einsparung kostenintensiver Experimente und Simulationen durch Maschinelles Lernen
In D. Trauth, T. Bergs and W. Prinz, editors, Monetarisierung von technischen Daten, Springer Vieweg, pp. 691-709, 2021.
L. Il Grande, E. Venturino, G. Visconti et al
Models of symbiotic associations in food chains
In Alejandro F. Camisao and Celio C. Pedroso, editors, Symbiosis: Evolution, Biology and Ecological Effects
Nova Science Publishers, Hauppauge, NY, 189-234, 2012.
Peer Reviewed Proceedings
X. Gong, B. Piccoli, G. Visconti
Mean-field of optimal control problems for hybrid model of multilane traffic
Proceedings of the American Control Conference, 1485-1490, 2021. Paper link
M. Schwenzer, G. Visconti, M. Ay, T. Bergs, M. Herty, D. Abel
Identifying trending coefficients with an ensemble Kalman filter -- A demonstration on a force model for milling
IFAC-PapersOnLine, 53(2):2292-2298, 2020. Paper link
M. Herty, G. Visconti
Analysis of risk levels for traffic on a multi-lane highway
IFAC-PapersOnLine, 51(9):43-48, 2018. Paper link
Miscellaneous
M. Semplice and G. Visconti
claw1dArena version 1.1, C++ library, 10.5281/zenodo.3627092, January 2020}
Thesis
G. Visconti
Single- and multi-population kinetic models for vehicular traffic reproducing fundamental diagrams and with low computational complexity
PhD Theses, University of Insubria, 2016. Link