Explore the intricacies of Langevin Dynamics in this seminar presented by Gautam Iyer from Carnegie Mellon University. Delve into the overdamped Langevin equation, a stochastic differential equation governing particle dynamics driven by potential gradients and random fluctuations. Discover how this equation's stationary distribution forms the basis of the Langevin Monte Carlo algorithm for sampling. Learn about the challenges posed by potentials with multiple local minima and the exponential convergence times they can cause. Investigate a novel method that introduces a "mixing drift" to dramatically reduce convergence time to polynomial order. Gain insights into this collaborative research effort with Alex Christie, Yuanyuan Feng, and Alexei Novikov, aimed at speeding up Langevin Dynamics through innovative mixing techniques.
Overview
Syllabus
Seminar In the Analysis and Methods of PDE (SIAM PDE): Gautam Iyer
Taught by
Society for Industrial and Applied Mathematics
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