A consensus-based algorithm for multi-objective optimization and its mean-field description

Giacomo Borghi, Michael Herty, Lorenzo Pareschi (preprint arXiv:2203.16384)

We present a multi-agent algorithm for multi-objective optimization problems, which extends the class of consensus-based optimization methods and relies on a scalarization strategy. The optimization is achieved by a set of interacting agents exploring the search space and attempting to solve all scalar sub-problems simultaneously. We show that those dynamics are described by a mean-field model, which is suitable for a theoretical analysis of the algorithm convergence. Numerical results show the validity of the proposed method.

From agent-based models to the macroscopic description of fake-news spread: the role of competence in data-driven applications

 Jonathan Franceschi, Lorenzo Pareschi, Mattia Zanella (preprint arXiv:2202.10809)

Fake news spreading, with the aim of manipulating individuals' perceptions of facts, is now recognized as a major problem in many democratic societies. Yet, to date, little has been understood about how fake news spreads on social networks, what the influence of the education level of individuals is, when fake news is effective in influencing public opinion, and what interventions might be successful in mitigating their effect. In this paper, starting from the recently introduced kinetic multi-agent model with competence by the first two authors, we propose to derive reduced-order models through the notion of social closure in the mean-field approximation that has its roots in the classical hydrodynamic closure of kinetic theory.

Effects of vaccination efficacy on wealth distribution in kinetic epidemic models

Emanuele Bernardi, Lorenzo Pareschi, Giuseppe Toscani, Mattia Zanella (Entropy 24(2):216, 2022)

The spreading of Covid-19 pandemic has highlighted the close link between economics and health in the context of emergency management. A widespread vaccination campaign is considered the main tool to contain the economic consequences. This paper will focus, at the level of wealth distribution modelling, on the economic improvements induced by the vaccination campaign in terms of its effectiveness rate. The economic trend during the pandemic is evaluated resorting to a mathematical model joining a classical compartmental model including vaccinated individuals with a kinetic model of wealth distribution based on binary wealth exchanges.

Multi-fidelity methods for uncertainty propagation in kinetic equations

Giacomo Dimarco, Liu Liu, Lorenzo Pareschi, Xueyu Zhu (to appear in Panoramas & Synthèses, Société Mathématique de France, preprint arXiv:2112.00932)

The construction of efficient methods for uncertainty quantification in kinetic equations represents a challenge due to the high dimensionality of the models: often the computational costs involved become prohibitive. On the other hand, precisely because of the curse of dimensionality, the construction of simplified models capable of providing approximate solutions at a computationally reduced cost has always represented one of the main research strands in the field of kinetic equations.

Constrained consensus-based optimization

Giacomo Borghi, Michael Herty, Lorenzo Pareschi (preprint arXiv:2111.10571)

In this work we are interested in the construction of numerical methods for high dimensional constrained nonlinear optimization problems by particle-based gradient-free techniques. A consensus-based optimization (CBO) approach combined with suitable penalization techniques is introduced for this purpose. The method relies on a reformulation of the constrained minimization problem in an unconstrained problem for a penalty function and extends to the constrained settings the class of CBO methods.

Bi-fidelity stochastic collocation methods for epidemic transport models with uncertainties

Giulia Bertaglia, Liu Liu, Lorenzo Pareschi, Xueyu Zhu (to appear in Network and Heterogeneous Media, preprint arXiv:2110.14579)

Uncertainty in data is certainly one of the main problems in epidemiology, as shown by the recent COVID-19 pandemic. The need for efficient methods capable of quantifying uncertainty in the mathematical model is essential in order to produce realistic scenarios of the spread of infection. In this paper, we introduce a bi-fidelity approach to quantify uncertainty in spatially dependent epidemic models.