Lorenzo Pareschi
Professor of Numerical Analysis - University of Ferrara
Tuesday, January 31, 2023
Consensus based optimization with memory effects: random selection and applications
Wednesday, November 30, 2022
The kinetic theory of mutation rates
Lorenzo Pareschi, Giuseppe Toscani (preprint arXiv:2212.00146)
The Luria-Delbrück mutation model is a cornerstone of evolution theory and has been mathematically formulated in a number of ways. In this paper we illustrate how this model of mutation rates can be derived by means of classical statistical mechanics tools, in particular by modeling the phenomenon resorting to methodologies borrowed from classical kinetic theory of rarefied gases. The aim is to construct a linear kinetic model that can reproduce the Luria-Delbrück distribution starting from the elementary interactions that qualitatively and quantitatively describe the variation of mutated cells.
Monday, October 31, 2022
Global high-order numerical schemes for the time evolution of the general relativistic radiation magneto-hydrodynamics equations
Tuesday, August 2, 2022
An adaptive consensus based method for multi-objective optimization with uniform Pareto front approximation
In this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated using parametrized, single-objective sub-problems which are solved simultaneously. To this end a consensus based multi-objective optimization method on the search space combined with an additional heuristic strategy to adapt parameters during the computations is proposed. The adaptive strategy aims to distribute the particles uniformly over the image space by using energy-based measures to quantify the diversity of the system. The resulting metaheuristic algorithm is mathematically analyzed using a mean-field approximation and convergence guarantees towards optimal points is rigorously proven.
Monday, August 1, 2022
Stochastic Galerkin particle methods for kinetic equations of plasmas with uncertainties
The study of uncertainty propagation is of fundamental importance in plasma physics simulations. To this end, in the present work we propose a novel stochastic Galerkin (sG) particle methods for collisional kinetic models of plasmas under the effect of uncertainties. This class of methods is based on a generalized polynomial chaos (gPC) expansion of the particles' position and velocity. In details, we introduce a stochastic particle approximation for the Vlasov-Poisson system with a BGK term describing plasma collisions. A careful reformulation of such dynamics is needed to perform the sG projection and to obtain the corresponding system for the gPC coefficients.