Hydrodynamic models of preference formation in multi-agent societies

Lorenzo Pareschi, Giuseppe Toscani, Andrea Tosin, Mattia Zanella
(24/12/2018, preprint arXiv:1901.00486)

In this paper, we discuss the passage to hydrodynamic equations for kinetic models of opinion formation. The considered kinetic models feature an opinion density depending on an additional microscopic variable, identified with the personal preference. This variable describes an opinion-driven polarisation process, leading finally to a choice among some possible options, as it happens e.g. in referendums or elections.

Multi-scale variance reduction methods based on multiple control variates for kinetic equations with uncertainties

Giacomo Dimarco, Lorenzo Pareschi
(12/12/2018,  preprint arXiv:1812.05485)

The development of efficient numerical methods for kinetic equations with stochastic parameters is a challenge due to the high dimensionality of the problem. Recently we introduced a multiscale control variate strategy which is capable to accelerate considerably the slow convergence of standard Monte Carlo methods for uncertainty quantification. Here we generalize this class of methods to the case of multiple control variates.

Multi-scale control variate methods for uncertainty quantification in kinetic equations

Giacomo Dimarco, Lorenzo Pareschi 
(25/10/2018. preprint arXiv:1810.10844)

Kinetic equations play a major rule in modeling large systems of interacting particles. Uncertainties may be due to various reasons, like lack of knowledge on the microscopic interaction details or incomplete informations at the boundaries. These uncertainties, however, contribute to the curse of dimensionality and the development of efficient numerical methods is a challenge.

Uncertainty Quantification for Hyperbolic and Kinetic Equations

Shi Jin, Lorenzo Pareschi (Eds.)
SEMA SIMAI Springer Series
277 pages, 2018

This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems. The contributions address a range of different aspects, including: polynomial chaos expansions, perturbation methods, multi-level Monte Carlo methods, importance sampling, and moment methods. The interest in these topics is rapidly growing, as their applications have now expanded to many areas in engineering, physics, biology and the social sciences. Accordingly, the book provides the scientific community with a topical overview of the latest research efforts.