Research



My research activity has been mainly devoted to the analysis and construction of numerical methods and mathematical models for partial differential equations of hyperbolic and kinetic type. These problems have been addressed using different methodologies in various fields of applied sciences, ranging from classical physics and engineering (gas dynamics, semiconductor, plasma physics, granular materials, quantum mechanics) to socio-economic and life sciences (traffic flow, opinion formation, wealth distribution, finance, epidemiology). Recently, my interests have focused on problems of uncertainty quantification, optimal control and machine learning. 

Research group members
Prof. Giacomo Dimarco 
Dr Walter Boscheri
Dr Giulia Bertaglia (post-doc)
Sara Grassi (Phd student)
Giacomo Borghi (PhD student joint with U. Aachen)
Jonathan Franceschi (PhD student joint with U. Pavia)

Former members 
Dr Giacomo Albi
Dr Mattia Zanella


Main research interests
  • Numerical methods for kinetic equations. Fast spectral methods; Direct simulation Monte Carlo methods; Asymptotic-preserving schemes; Structure-preserving methods. 
  • Implicit-Explicit time integration methods. Hyperbolic systems with source terms; Multiscale PDEs; Low Mach number limit.
  • Numerical methods for nonlinear conservation laws. Relaxation schemes; Central schemes; semi-Lagrangian methods; Particle methods; Flows on networks. 
  • Kinetic models in the social sciences. Opinion formation; Learning processes; Wealth distributions; Finance; Epidemiology.
  • Uncertainty quantification for kinetic and hyperbolic equations. Multi-fidelity methods; Stochastic Galerkin methods; Multi-level Monte Carlo methods; Robust control.
  • Stochastic particle optimization. Particle swarm optimization; Consensus based optimization; Machine learning.

My recent works can be found in the publication page. Slides and videos of some of my recent lectures are also available in the lecture page.


Stochastic Particle Optimization: Constrained CBO on torus

Collective Behavior: From mill to flock

Kinetic Models in Epidemiology: COVID-19 spread in Lombardy

IMEX Methods: High order semi-Lagrangian DG schemes