Model reduction techniques for the computation of extended Markov parameterizations for generalized Langevin equations

Martin Hanke (U Mainz)

Jun 24. 2021, 14:30 — 15:00

The generalized Langevin equation is a model for the motion of coarse-grained particles where dissipative forces are represented by a memory term. The standard numerical realization of such a model requires the implementation of a stochastic delay-differential equation and the estimation of a corresponding memory kernel. We present a new approach for computing a data-driven Markov model with extended variables for the motion of the particles, given equidistant samples of their velocity autocorrelation function. Our method bypasses the determination of the underlying memory kernel by representing it via up to about twenty auxiliary variables. The algorithm is based on a sophisticated variant of the Prony method for exponential interpolation and employs the positive real lemma from model reduction theory to extract the associated Markov model.

This is joint work with Niklas Bockius, Jeanine Shea, Gerhard Jung and Friederike Schmid.

 

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Memory Effects in Dynamical Processes: Theory and Computational Implementation (Online Workshop)
Organizer(s):
Christoph Dellago (U Vienna)
Anja Kuhnhold (U of Freiburg)
Hugues Meyer (U of Saarland)
Tanja Schilling (U of Freiburg)