Maximilian Braun | Searcharxiv

arXiv2026

On data-driven parameterizations of multidimensional generalized Langevin dynamics in the presence of a quadratic potential

We propose a numerical algorithm to construct a Markov model with an extended list of variables to parameterize the equation of motion of a multidimensional coarse-grained physical system in an external potential, when memory effects are relevant. Our method uses autocorrelation data of the stationary velocities, but it avoids the inverse problem of finding the corresponding memory kernel from these data in a first step. Rather, the data are used to construct a Prony series approximation of the autocorrelation function, and the parameters of this Prony series provide the corresponding Markov model. Numerical results for molecular dynamics data show a good match for parameterized models with five auxiliary variables for a one-dimensional, and twelve auxiliary variables for a two-dimensional system.

cond-mat.stat-mech↗

arXiv2025

Determining extended Markov parameterizations for vector-valued generalized Langevin Equations

The generalized Langevin equation is used as a model for various coarse-grained physical processes, e.g., the time evolution of the velocity of a given larger particle in an implicitly represented solvent, when the relevant time scales of the dynamics of the larger particle and the solvent particles are not strictly separated. Since this equation involves an integrated history of past velocities, considerable efforts have been made to approximate this dynamics by data-driven Markov models, where auxiliary variables are used to compensate for the memory term. In recent works we have developed two algorithms which can be used for this purpose, provided the dynamics in question are scalar processes. Here we extend these algorithms to vector-valued processes. As a physical test bed we consider an S-shaped particle sliding on a planar substrate, which gives rise to a truly two-dimensional velocity process. The two algorithms provide Markov approximations of this process with 10-20 auxiliary variables and a very accurate fit of the given autocorrelation data over the entire time interval where these data are non-negligible.

cond-mat.stat-mech↗