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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 8: Machine Learning in Dynamics and Statistical Physics II (joint session DY/SOE)

SOE 8.2: Talk

Tuesday, March 19, 2024, 09:45–10:00, BH-N 243

Accurate Memory Kernel Extraction from Discretized Time-Series Data — •Lucas Tepper — Department of Physics, Freie Universität Berlin

Memory effects emerge whenever the dynamics of complex many-body systems are projected onto low-dimensional observables. Accounting for memory effects using the framework of the generalized Langevin equation (GLE) has proven efficient, accurate and insightful, particularly when working with high-resolution time series data. However, in experimental systems, high-resolution data is often unavailable, raising questions about the effect of the data resolution on the estimated GLE parameters. Using molecular dynamics (MD) data of a small, alpha-helix-forming peptide, I demonstrate that the direct memory extraction remains accurate when the discretization time is below the memory time. For discretization times exceeding the memory time, I show that a Gaussian Process Optimization (GPO) scheme estimates accurate memory kernels by minimizing the deviation of discretized two-point correlation functions between MD and GLE simulations. The GPO scheme stays accurate for discretization times below the longest time scale in the data, typically the barrier crossing time.

Keywords: generalized Langevin Equation; time discretization; Gaussian Process Optimization; Volterra equations; GLE