Research



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, optimization and machine learning. A major direction of my current research is the integration of advanced numerical methods and modern data-driven techniques toward predictive modeling of multiscale plasma dynamics.

Grants
FIS2 Advanced Grant ADAMUS (link)
Marie-Curie Doctoral Network DATAHYKING (link)
Royal Society Wolfson Fellowship (link)
PRIN 2022 (link)

Research group members
Dr. Giulia Bertaglia (RTT)
Dr. Elisa Iacomini (RTD-a)
Dr. Federica Ferrarese (Post-doc, University of Ferrara)
Dr. Giacomo Borghi (PDRA, Heriot Watt University)
Dr. Jonathan Franceschi (Post-doc, University of Ferrara)
Abu Safyan Ali (PhD student)
Frederic Blondeel (DataHyking PhD student joint with U. Leuven)
Theresa Koefler (DataHyking PhD student joint with U. Kaiserlautern)
Domenico Caparello (DataHyking PhD student joint with U. Nice)
Sara Veneruso  (DataHyking PhD student joint with U. Aachen)  
Hyesung Im (MAC-MIGs PhD student Maxwell Institute and Heriot Watt University)
Monica Caloi (Adamus PhD student, from 1/11/25)
Stefano Magrini Alunno (Adamus PhD student, from 1/11/25) 

Former members 

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 multiscale 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; 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.
  • Optimal control of multiscale systems. Optimal control for kinetic and fluid models; Model predictive control (MPC); Feedback stabilisation of plasma instabilities; Data-driven and surrogate-assisted control; 

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.

Dynamic domain decomposition of the multiscale Boltzmann equation
(D. Caparello, L. Pareschi, T. Rey, arXiv:2505.03360, 2025)

Two stream instability with uncertainty in a collisionless plasma 
(A. Medaglia, L. Pareschi, M. Zanella, JCP 2023)

Convection-diffusion of a tracer: high order semi-Lagrangian IMEX schemes
(W. Boscheri, M. Tavelli, L. Pareschi, JSC 2022)

Stochastic Particle Optimization: Constrained CBO on torus
(M. Fornasier, H. Huang, L. Pareschi, P. Sünnen M3AS 2020)

Kinetic Models in Epidemiology: COVID-19 spread in Lombardy
(G. Bertaglia, W. Boscheri, G. Dimarco, L. Pareschi, MBE 2021)

Collective Behavior: Uncertainty triggering instability
(G. Albi, L. Pareschi, M. Zanella, MPE 2015)
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