Likelihood-based non-Markovian models from molecular dynamics.

Area of Science:

• Statistical Mechanics
• Computational Chemistry
• Biophysics

Background:

• Complex systems analysis often requires reducing high-dimensional data to low-dimensional collective variables for better physical understanding.
• Generalized Langevin equations (GLEs) are used to model the dynamics of these reduced variables, but require accurate coefficient estimation from simulations.
• GLEs incorporate a memory kernel that captures the interactions between the collective variables and their environment.

Purpose of the Study:

• To introduce and implement a novel approach for deriving generalized Langevin equations.
• To ensure the derived GLEs efficiently capture the essential dynamics of complex systems.
• To provide a method for generating accurate reduced models from high-dimensional simulation data.

Main Methods:

• Developed a maximum likelihood estimation framework for fitting generalized Langevin equation coefficients.
• Implemented the approach using simulation data from complex systems.
• Focused on optimizing the memory kernel estimation within the GLE framework.

Main Results:

• Successfully generated reduced models of complex systems using the maximum likelihood approach.
• Demonstrated the efficiency of the method in capturing system dynamics.
• The approach provides a robust way to estimate GLE coefficients, including the memory kernel.

Conclusions:

• The maximum likelihood approach offers an efficient strategy for creating accurate, low-dimensional models of complex systems.
• This method facilitates the study of dynamical properties in diverse fields, including chemical reactions, biomolecular conformational changes, and phase transitions.
• The developed technique enhances the physical understanding and computational tractability of complex system dynamics.