Bonn-Paris Webinar November 18 20, 2020: Philipp Höllmer

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Bonn-Paris Webinar Wednesday, 18 November 2020, 12h00

Speaker: Philipp Höllmer (University of Bonn)

Title: Fast sequential Markov chains

Abstract: In this talk, I will motivate and present a non-reversible Markov-chain Monte Carlo (MCMC) algorithm for particle systems, in which the direction of motion evolves deterministically. The sequential direction-sweep MCMC can be applied to a wide range of original reversible or non-reversible Markov chains, such as the Metropolis algorithm or the event-chain Monte Carlo (ECMC) algorithm. I will discuss sequential MCMC for a simplified two-dimensional dipole model, and show how it profoundly modifies the Markov-chain trajectory. Long excursions, with persistent rotation in one direction, alternate with long sequences of rapid zigzags resulting in persistent rotation in the opposite direction. Finally, I will show that sequential MCMC is able to reduce mixing times. Here, an especially large speedup can be obtained by using a large set of possible directions instead of only allowing directions that are parallel to the cartesian axes. This renders sequential MCMC in particular useful for greatly accelerating ECMC simulations of molecular systems in the future.


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