7 papers
From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Properties
Gennaro Auricchio, Giovanni Brigati, Paolo Giudici +1
Selecting an appropriate divergence measure is a critical aspect of machine learning, as it directly impacts model performance. Among the most widely used, we find the Kullback-Lei…
Kinetic Optimal Transport (OTIKIN) -- Part 1: Second-Order Discrepancies Between Probability Measures
Giovanni Brigati, Jan Maas, Filippo Quattrocchi
This is the first part of a general description in terms of mass transport for time-evolving interacting particles systems, at a mesoscopic level. Beyond kinetic theory, our framew…
Hypocoercivity meets lifts
Giovanni Brigati, Francis Lörler, Lihan Wang
We unify the variational hypocoercivity framework established by D. Albritton, S. Armstrong, J.-C. Mourrat, and M. Novack, with the notion of second-order lifts of reversible diffu…
Multivariate Gini-type discrepancies
Gennaro Auricchio, Giovanni Brigati, Paolo Giudici +1
Measuring distances in a multidimensional setting is a challenging problem, which appears in many fields of science and engineering. In this paper, to measure the distance between…
Explicit convergence rates of underdamped Langevin dynamics under weighted and weak Poincaré--Lions inequalities
Giovanni Brigati, Gabriel Stoltz, Andi Q. Wang +1
We study the long-time behavior of the underdamped Langevin dynamics, in the case of so-called \emph{weak confinement}. Indeed, any distribution (in position an…
How to construct decay rates for kinetic Fokker--Planck equations?
Giovanni Brigati, Gabriel Stoltz
We study time averages for the norm of solutions to kinetic Fokker--Planck equations associated with general Hamiltonians. We provide fully explicit and constructive decay estimate…
Time averages for kinetic Fokker-Planck equations
Giovanni Brigati
We consider kinetic Fokker-Planck (or Vlasov-Fokker-Planck) equations on the torus with Maxwellian or fat tail local equilibria. Results based on weak norms have recently been achi…