Tuesday, January 31, 2023

Consensus based optimization with memory effects: random selection and applications

 Giacomo Borghi, Sara Grassi, Lorenzo Pareschi (preprint arXiv:2301.13242)

In this work we extend the class of Consensus-Based Optimization (CBO) metaheuristic methods by considering memory effects and a random selection strategy. The proposed algorithm iteratively updates a population of particles according to a consensus dynamics inspired by social interactions among individuals. The consensus point is computed taking into account the past positions of all particles. While sharing features with the popular Particle Swarm Optimization (PSO) method, the exploratory behavior is fundamentally different and allows better control over the convergence of the particle system.

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

Manuel R. Izquierdo, Lorenzo Pareschi, Borja Miñano, Joan Massó, Carlos Palenzuela (preprint arXiv:2211.00027)

Modeling correctly the transport of neutrinos is crucial in some astrophysical scenarios such as core-collapse supernovae and binary neutron star mergers. In this paper, we focus on the truncated-moment formalism, considering only the first two moments (M1 scheme) within the grey approximation, which reduces Boltzmann seven-dimensional equation to a system of 3+1 equations closely resembling the hydrodynamic ones. Solving the M1 scheme is still mathematically challenging, since it is necessary to model the radiation-matter interaction in regimes where the evolution equations become stiff and behave as an advection-diffusion problem.

Tuesday, August 2, 2022

An adaptive consensus based method for multi-objective optimization with uniform Pareto front approximation

Giacomo Borghi, Michael Herty, Lorenzo Pareschi (preprint arXiv:2208.01362)

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

Andrea Medaglia, Lorenzo Pareschi, Mattia Zanella (preprint arXiv:2208.00692)

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.