Research Insterests

• 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.

Publications

Submitted

1. M. Briani, G. Puppo, G. Visconti
   On implicit time methods and discontinuous Galerkin space reconstruction for conservation laws.
   Submitted, 2024. Preprint link

2. M. Herty, C. Segala, G. Visconti
   Controllability of continuous networks and a kernel-based learning approximation.
   Submitted, 2024. Preprint link

3. 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)

1. 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

2. 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

3. G. Puppo, M. Semplice, G. Visconti
   Quinpi: integrating conservation laws with CWENO implicit methods
   Commun. Appl. Math. Comput., 5:343-369, 2023. Paper link

4. 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

5. 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

6. 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

7. S. Gerster, F. Nagel, A. Sikstel, G. Visconti
   Numerical boundary control for semilinear hyperbolic systems.
   Math. Control Relat. Fields, Accepted, 2022. Paper link

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. M. Herty, G. Visconti
    Continuous Limits for Constrained Ensemble Kalman Filter
    Inverse Probl., 36(7):0750062020, 2020. Paper link

16. M. Herty, L. Pareschi, G. Visconti
    Mean field models for large data-clustering problems
    Netw. Heterog. Media, 15(3):463-487, 2020. Paper link

17. M. Semplice, G. Visconti
    Efficient implementation of adaptive order reconstructions
    J. Sci. Comput., 83(1):6, 2020. Paper link

18. 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

19. 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

20. M. Herty, G. Visconti
    Kinetic Methods for Inverse Problems
    Kinet. Relat. Models, 12(5):1109-1130, 2019. Paper link

21. 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

22. 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

23. 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

24. I. Cravero, G. Puppo, M. Semplice, G. Visconti
    Cool WENO Schemes
    Comput. Fluids, 169:71-86, 2018. Paper link

25. I. Cravero, G. Puppo, M. Semplice, G. Visconti
    CWENO: uniformly accurate reconstructions for balance laws
    Math. Comp., 87(312):1689-1719, 2018. Paper link

26. 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

27. 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

28. 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

29. 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

1. 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

2. 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

3. 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

4. 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.

5. 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

1. 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

2. 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

3. 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

1. M. Semplice and G. Visconti
   claw1dArena version 1.1, C++ library, 10.5281/zenodo.3627092, January 2020}

Thesis

1. 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