Data-driven construction of stochastic reduced dynamics encoded with non-Markovian features

Area of Science:

• Computational chemistry
• Molecular dynamics
• Statistical mechanics

Background:

• Modeling molecular systems requires capturing non-Markovian behavior due to unresolved variables.
• Lack of scale separation leads to memory effects and non-white noise in reduced dynamics.
• Existing methods struggle with accurate memory function construction.

Purpose of the Study:

• To develop a data-driven approach for learning reduced models of multi-dimensional molecular systems.
• To faithfully retain non-Markovian dynamics in the reduced model.
• To provide a numerically stable and empirically free method.

Main Methods:

• A data-driven approach is proposed to learn non-Markovian features encoding historical data.
• Joint learning of extended Markovian dynamics is established using resolved variables and features.
• Training involves matching correlation functions of extended variables derived from resolved variables.

Main Results:

• The method successfully constructs reduced models that retain non-Markovian dynamics.
• The approach approximates the multi-dimensional generalized Langevin equation.
• Effectiveness demonstrated for both 1D and 4D resolved molecular systems.

Conclusions:

• The proposed data-driven method accurately models non-Markovian molecular dynamics.
• This approach offers a stable and empirically free alternative to traditional methods.
• It provides a robust framework for studying complex molecular systems.