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DY: Fachverband Dynamik und Statistische Physik

DY 16: Machine Learning in Dynamical Systems and Statistical Physics (joint session DY/BP)

DY 16.3: Vortrag

Freitag, 1. Oktober 2021, 11:45–12:00, H2

Efficient Bayesian estimation of the generalized Langevin equation from data — •Clemens Willers and Kamps Oliver — Center for Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, Corrensstr. 2, 48149 Münster, Germany

A recent topic of research attracting broad interest is the modeling of stochastic time series whose dynamics includes memory effects. To cover this non-Markovian case, the Langevin equation, which is frequently used in many fields of science, is extended by a memory kernel, yielding the generalized Langevin equation (GLE). Since a direct derivation of the GLE from basic mechanisms through the well known Mori-Zwanzig formalism is not accessible in many cases, it is a relevant question how to estimate the model solely based on measured data.

In our work we develop a realization of Bayesian estimation of the GLE. The Bayesian approach allows for the determination of both estimates and their credibility in a straightforward manner. To facilitate this method, we consider the GLE with white noise. Although this is an approximation, we still deal with a very general model class representing systems with memory.

Importantly for applications, we realize the method in a numerically efficient manner through a piecewise constant parameterization of the drift and diffusion functions of the model, a reformulation of the likelihood, and an effective initial guess for the estimate.

We illustrate our method by an example from turbulence. Here we are able to reproduce the autocorrelation function of the original data set, which is an essential characteristic of a turbulent flow.