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DTSTART:20070311T020000
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DTSTAMP:20260223T105502
DTSTART;TZID=America/Detroit:20260225T160000
DTEND;TZID=America/Detroit:20260225T170000
SUMMARY:Workshop / Seminar:Learning MFG via MFAC Flow
DESCRIPTION:We introduce the Mean-Field Actor-Critic (MFAC) flow\, a continuous-time learning dynamics for solving mean-field games (MFGs)\, drawing on ideas from reinforcement learning\, generative modeling\, and optimal transport. The MFAC framework jointly evolves the actor\, critic\, and distribution through gradient-based updates\, with the distribution governed by a novel Optimal Transport Geodesic Picard (OTGP) flow. The OTGP flow drives the distribution toward equilibrium along Wasserstein-2 geodesics. We rigorously analyze the MFAC flow using Lyapunov functionals and establish global exponential convergence under suitable time scales. The analysis highlights the coupled structure of the algorithm and offers practical guidelines for choosing learning rates. Numerical results further support the theory and demonstrate the effectiveness of the proposed approach. This is joint work with Mo Zhou (UCLA) and Haosheng Zhou (UCSB).
UID:141872-21889581@events.umich.edu
URL:https://events.umich.edu/event/141872
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
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DTSTAMP:20260211T135224
DTSTART;TZID=America/Detroit:20260225T160000
DTEND;TZID=America/Detroit:20260225T170000
SUMMARY:Workshop / Seminar:Probability and Analysis Seminar: Finite time singularities in the Landau equation with very hard potentials
DESCRIPTION:The Landau equation\, introduced by Lev Landau in 1936\, is one of the central equations in kinetic theory. We consider the Landau equation with very hard potentials $\gamma \in (\sqrt{3}\,2]$\, which is known to admit global smooth solutions for homogeneous data. Inspired by hydrodynamic limits from kinetic equations to fluid equations\, we construct smooth\, strictly positive initial data that develop a finite-time singularity by lifting imploding singularities from the compressible Euler equations. In self‑similar variables\, the solution becomes asymptotically hydrodynamic—the distribution function converges to a local Maxwellian\, while the hydrodynamic fields develop an asymptotically self‑similar implosion whose profile coincides with a smooth imploding profile of the compressible Euler equations.  To our knowledge\, this provides the first example of a collisional kinetic model which is globally well-posed in the homogeneous setting\, but admits finite time singularities for inhomogeneous data.\n \nThis is joint work with Jacob Bedrossian (UCLA)\, Maria Gualdani (UT Austin)\, Sehyun Ji (UChicago)\, Vlad Vicol (NYU)\, and Jincheng Yang (JHU).
UID:145282-21897003@events.umich.edu
URL:https://events.umich.edu/event/145282
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 4088
CONTACT:
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