In this paper we consider a measure-theoretical formulation of the training of NeurODEs in
the form of a mean-field optimal control with L 2-regularization of the control. We derive first …

We prove a general criterion for the density in energy of suitable subalgebras of Lipschitz
functions in the metric Sobolev space H 1, p (X, d, m) associated with a positive and finite …

In this expository article, we give an overview of the concept of potential mean field games of
first order. We give a new proof that minimizers of the potential are equilibria by using a …

We propose and investigate general kinetic models with transition probabilities that can
describe the simultaneous change of multiple microscopic states of the interacting agents …

A mean-field selective optimal control problem of multipopulation dynamics via transient
leadership is considered. The agents in the system are described by their spatial position …

The mean-field analysis of a multipopulation agent-based model is performed. The model
couples a particle dynamics driven by a nonlocal velocity with a Markov-type jump process …

Motivated by the applications in leader-follower multi-agent dynamics, a class of optimal
control problems is investigated, where the goal is to influence the behavior of a given …

Assignment flows denote a class of dynamical models for contextual data labelling
(classification) on graphs. We derive a novel parametrisation of assignment flows that …

We introduce and study the class of totally dissipative multivalued probability vector fields
(MPVF) $\boldsymbol {\mathrm F} $ on the Wasserstein space $(\mathcal {P} _2 (\mathsf …

We study a multi-agent system for the modeling maritime crime. The model involves three
interacting populations of ships: commercial ships, pirate ships, and coast guard ships …