Abstract : Complex, real-life systems in sociology, economics, and life sciences often consist of a large number of individuals. Through interactions among these individuals a collective behaviour may emerge over time and certain patterns may develop. Examples include pedestrian, evacuation and traffic models, opinion formation, wealth distribution, chemotaxis and flocking/swarming. The aim of the mini-symposium is to highlight recent advances in modelling, analysis, numerics and optimal control of kinetic and PDE models in this area.
[04044] Data-driven kinetic model for opinion dynamics and contacts
Format : Talk at Waseda University
Author(s) :
Giacomo Dimarco (University of Ferrara, Department of Mathematics and Computer Science)
Abstract : Opinion dynamics is an important area of research that studies how individuals
form and change their opinions in a social context. Understanding the mechanisms
that drive opinion formation and change is essential for predicting social phenomena,
such as political polarization and the spread of misinformation. In this talk, we
present a new model for opinion dynamics in presence of social media contacts,
using real-life data from Twitter in order to retrieve the parameters appearing in our
model so to make it as close as possible to what happens in reality.
[02360] Asymptotic-preserving neural networks for kinetic equations in socio-epidemics
Format : Talk at Waseda University
Author(s) :
Giulia Bertaglia (University of Ferrara)
Abstract : Data-driven approaches have proven to be powerful tools with a direct impact on society. However, the use of standard neural networks to investigate multiscale dynamics can lead to erroneous inferences and predictions, because the presence of small scales leads to reduced-order models that must be considered in the learning phase. In this talk, I will address these issues by presenting asymptotic-preserving neural networks, focusing on their use to study the spatial spread of epidemics.
[04507] Many-agent systems and mean-field models for semi-supervised learning
Format : Talk at Waseda University
Author(s) :
Lisa Maria Kreusser (University of Bath)
Marie-Therese Wolfram (University of Warwick)
Abstract : In many problems in data classification, it is desirable to assign labels to points in a point cloud where a certain number of them is already correctly labeled. In this talk, we propose a microscopic ODE approach, in which information about correct labels propagates to neighbouring points. Its dynamics are based on alignment mechanisms, often used in collective and consensus models. We derive the respective continuum description, which corresponds to an anisotropic diffusion equation with a reaction term. Solutions of the continuum model inherit interesting properties of the underlying point cloud. We discuss the qualitative behaviour of solutions and exemplify the results with micro- and macroscopic simulations.
[03820] Trends to equilibrium for nonlocal Fokker-Planck equations with discontinuous drift
Format : Talk at Waseda University
Author(s) :
Mattia Zanella (University of Pavia)
Abstract : We study equilibration rates for nonlocal Fokker-Planck equations with time-dependent diffusion coefficient and drift, modeling the relaxation of a large swarms of agents, feeling each other in terms of their distance, towards the steady profile characterized by a uniform spreading over a finite domain. The result follows by combining entropy methods for quantifying the decay of the solution towards its quasi-stationary distribution, with the properties of the quasi-stationary profile.
[04768] Kinetic modelling of swarming dynamics with transient leadership
Format : Talk at Waseda University
Author(s) :
Giacomo Albi (University of Verona)
Abstract : In this talk, we will focus on swarming dynamics with topological interactions and where leaders' emergence initializes spontaneous changes of direction. In this context, we will provide a kinetic model for leader-follower dynamics with mass transfer among the two populations modeled as a transition process on a space of labels. This model allows the transition from followers to leaders and vice-versa, with scalar-valued transition rates depending on the state of the system. Furthermore, we will propose an efficient stochastic algorithm for the identification of the $k$-nearest neighbors at mesoscopic level, and the simulation of the swarming dynamics. Several numerical experiments are presented for different scenarios both to validate the algorithm and to study the collective dynamics.
[02465] Kernel learning method for multiagent systems and its mean-field limit
Format : Talk at Waseda University
Author(s) :
Chiara Segala (RWTH Aachen University)
Michael Herty (RWTH Aachen University)
Christian Fiedler (RWTH Aachen University)
Abstract : Kernel methods are among the most popular and successful machine learning techniques. From a mathematical point of view, these methods rest on the concept of kernels and function spaces generated by kernels. Motivated by recent developments of learning approaches in the context of interacting particle systems, we investigate kernel methods acting on data with many measurement variables. We present efficient learning algorithms both on microscopic and mean-field level.
[03937] Bounded-confidence models of opinion dynamics on networks
Format : Talk at Waseda University
Author(s) :
Heather Zinn Brooks (Harvey Mudd College)
Abstract : In this talk, I will introduce you to a class of models of opinion dynamics on networks called bounded-confidence models. These relatively simple models can produce delightfully complicated dynamics and provide a rich source of study for the interplay between dynamics and structure. I will discuss some novel twists on bounded-confidence models that my collaborators and I have been developing, including information cascades, bifurcations in “smoothed” bounded-confidence models, and extensions to hypergraphs.
[03493] Mean-field models for many agent systems with co-evolving network structure
Format : Online Talk on Zoom
Author(s) :
Martin Burger (DESY and University of Hamburg)
Abstract : In this talk we discuss the derivation of kinetic and sub mean-field equations for processes related to processes on networks, such as opinion formation on social networks. We consider in particular the case when networks are co-evolving during other processes and discuss suitable descriptions as well as issues to derive simple closure relations. Moreover, we discuss aspects of pattern
formation such as consensus or the formation of echo chambers.
