Mean Field Limits for Weakly Interacting Diffusions: Phase Transitions, Multiscale Analysis, Metastability and Inference
Time: 2023-02-28
Published By: Wenqiong Li
Speaker(s): Grigorios A. Pavliotis (Imperial College London)
Time: 16:00-17:00 March 7, 2023
Venue: Online
Abstract: We consider a system of N weakly interacting particles driven by white noise. The mean-field limit of this system is described by the (nonlinear and nonlocal) McKean-Vlasov-Fokker-Planck PDE. We present a detailed analysis of continuous and discontinuous phase transitions for the McKeanVlasov PDE on the torus. We study the combined diffusive/mean-field limit of systems of weakly interacting diffusions with a periodic interaction potential. We show that, in the presence of phase transitions, the two limits do not commute. We then show the equivalence between uniform propagation of chaos, a uniform-in-N Logarithmic Sobolev inequality, the absence of phase transitions for the mean-field limit, and of Gaussian fluctuations around the McKean-Vlasov PDE. We discuss about dynamical metastability for systems that exhibit discontinuous phase transitions. Finally, we develop inference methodologies for estimating parameters in the drift of the McKean SDE using either the stochastic gradient descent algorithm or eigenfunction martingale estimators.
Speaker: Prof. G. A. Pavliots is Professor of Applied Mathematics at the Department of Mathematics, Imperial College London. His expertise is in applied analysis and statistical dynamics, particularly numerical, analytical and statistical methods for multiscale dynamical systems, statistical dynamics, interacting particle systems and PDEs of Fokker-Planck type, and applications to the development of algorithms for sampling and optimization. He is on the editorial boards of SIAM Multiscale Model. Sim., SIAM Uncertainty Quantification, Comm. Math. Sci., IMA J. Applied Mathematics, stochastics and PDEs.
ID：889 6676 1223 Passcode: 222578
