Interplay of moments and entropy in Fokker-Planck kinetics

by Dr Hossein Gorji (EMPA)

Thursday 3 Oct 2024, 13:30 → 14:30 Europe/Zurich

OHSA/B17

Abstract:

In the pursuit of expanding the applicability of the kinetic models across a broader range of Knudsen numbers, the Fokker-Planck models have attracted some attention in recent years. This is mainly due to their amenity to Monte-Carlo particle methods and their link to the diffusive limit of the Boltzmann equation. Besides their flexibility in capturing the dynamic of distribution functions, the Fokker-Planck models allow us to circumvent direct computation of particle- particle collisions. By interpreting discrete collisions as a random force continuously varying in time, the Fokker-Planck approximation provides a remedy to the overwhelming collision operations. The latter can become a limiting factor in the performance of Direct-Simulation Monte-Carlo (DSMC), especially if near-hydrodynamic regime is of concern.

We present a general recipe for constructing Fokker-Planck models, admitting both entropy and moment constraints. Furthermore, we investigate the intricate relationships between the Fokker-Planck kinetic approximation and random maps. The latter has gained popularity in machine-learning communities in order to address learning tasks in probability spaces. The connections between the Fokker-Planck kinetics and Schrödinger bridge problem are clarified. Our results highlight the relevance of Fokker-Planck approximations across different areas of kinetic theory and machine-learning. We conclude by examining open questions that arise from applications of the Fokker-Planck kinetic models, covering both modeling and numerical aspects.

 

Bio:
Dr. Gorji is a scientist at Laboratory for Computational Engineering at Empa, and is also affiliated to USC Viterbi as Adjunct Research Assistant Professor. Prior to these, he held several positions as Postdoc (Department of Mathematics, RWTH Aachen), Visiting Scholar (Department of Mathematics, California Institute of Technology), and Ambizione Fellow (Department of Mathematics, EPFL). He obtained his PhD from Mechanical Engineering department of ETH Zurich in October 2014, honored with ETH medal for outstanding dissertation. 

Dr. Gorji's research interest covers mathematical modeling of phenomena related to stochastic particle systems and networks with applications over a wide range of orders: from molecular to societal scales. His focus revolves around stochastic models in the form of data-driven scientific-computing tools to gain insights into processes arising in complex systems: multi-scale flows, biomedical flows, and epidemiology.