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Memory effects in complex systems can be accurately captured using the generalized Langevin equation (GLE). A new Gaussian Process Optimization (GPO) method reliably estimates memory kernels even with low-resolution molecular dynamics data.

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Area of Science:

  • Computational Physics
  • Statistical Mechanics
  • Data Analysis

Background:

  • Memory effects are inherent in dimensionality reduction for complex many-body systems.
  • Generalized Langevin Equation (GLE) framework effectively models these effects in molecular dynamics (MD) data.
  • High-resolution time series data are often unavailable in experimental settings, posing challenges for parameter estimation.

Purpose of the Study:

  • To investigate the impact of data resolution on estimated GLE parameters.
  • To develop a reliable method for memory function estimation from low-resolution data.
  • To ensure accurate memory kernel estimation despite discretization time exceeding memory time.

Main Methods:

  • Direct memory extraction from time series data.
  • Introduction of a Gaussian Process Optimization (GPO) scheme.
  • Minimizing deviation between discretized two-point correlation functions from data and GLE simulations.

Main Results:

  • Direct memory extraction is accurate when discretization time is below memory time.
  • The GPO scheme reliably estimates memory functions even when discretization time exceeds memory time.
  • Accurate memory kernel estimation is achievable as long as discretization time is below the longest data timescale (e.g., barrier crossing time).

Conclusions:

  • Data resolution significantly impacts GLE parameter estimation.
  • The GPO scheme offers a robust solution for analyzing low-resolution molecular dynamics data.
  • This method enables accurate memory kernel extraction, crucial for understanding complex system dynamics.