My research interests cover a wide range of topics in applied mathematics, mostly related to multiscale modeling and numerical methods for phenomena described by nonlinear partial differential equations, in particular hyperbolic and kinetic equations. These problems have been addressed using different methodologies in various fields of applied sciences and scientific computing, ranging from classical physics and engineering (fluid dynamics, rarefied gases, semiconductors, plasma physics, granular materials, quantum mechanics) to socio-economic and life sciences (traffic flow, opinion formation, wealth distribution, finance, epidemiology, hemodynamics). 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 
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. Gas and plasma physics; Fast spectral methods; Direct simulation Monte Carlo methods; Hybrid methods; Asymptotic-preserving schemes; Structure-preserving methods. 
  • Implicit-Explicit (IMEX) methods for PDEs. Hyperbolic systems with source terms; Multiscale PDEs; Low Mach number limit; Fluid dynamic limit; Diffusion limit.
  • Numerical methods for conservation laws and fluid dynamics. Compressible and incompressible flows; Relaxation schemes; Central schemes; Semi-Lagrangian methods; Particle methods; Flows on networks.
  • Multi-agent and kinetic models in the social sciences. Collective behaviour; Opinion formation; Learning processes; Wealth distributions; Behavioural 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 and learning. Particle swarm optimization; Consensus based optimization; Machine Learning; Physics Informed Neural Networks.

TreeMap Chart according to Web of Science

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. Here below you find some simulations taken from some recent works.

Convection-diffusion of a tracer: high order semi-Lagrangian IMEX schemes

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