Facultat de Física

Departament de Física de la Matèria Condensada

Moment-Constrained Langevin Dynamics: From Kinetic Models to Optimal Transport

Hossein Gorji

Laboratory for Computational Engineering (EMPA-ETH Domain, Switzerland & University of Southern California, USA).

In the pursuit of bridging numerical and modeling gaps between kinetic and continuum descriptions, the Langevin models play a central role. This is mainly due to their amenity to Monte-Carlo particle methods and their link to the diffusive limit of the kinetic models. Besides their flexibility in capturing the dynamic of distribution functions, the Langevin dynamic allows us to circumvent direct computation of particle-particle collisions, by interpreting discrete collisions as a random force continuously varying in time. We devise a general recipe for constructing Langevin models, admitting both entropy and moment constraints, in the context of gas and liquid kinetic models. Furthermore, we investigate the intricate relationship between the Langevin processes and random maps. The latter has gained popularity in machine-learning communities to address learning tasks in probability spaces. The connections between the Fokker-Planck kinetics and Optimal Transport are clarified. Our results highlight the relevance of Langevin dynamics across different areas of kinetic theory and machine-learning.