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

TL;DR

This paper introduces a data-driven method to model non-Markovian reduced dynamics in molecular systems by learning non-Markovian features that encode history, resulting in stable, accurate models that capture complex memory effects.

Contribution

It proposes a novel approach to learn non-Markovian features and extended Markovian dynamics jointly, improving modeling of non-Markovian behavior without empirical adjustments.

Findings

Successfully models molecular systems with non-Markovian dynamics

Ensures numerical stability in reduced models

Effective for both 1D and 4D resolved variables

Abstract

One important problem in constructing the reduced dynamics of molecular systems is the accurate modeling of the non-Markovian behavior arising from the dynamics of unresolved variables. The main complication emerges from the lack of scale separations, where the reduced dynamics generally exhibits pronounced memory and non-white noise terms. We propose a data-driven approach to learn the reduced model of multi-dimensional resolved variables that faithfully retains the non-Markovian dynamics. Different from the common approaches based on the direct construction of the memory function, the present approach seeks a set of non-Markovian features that encode the history of the resolved variables, and establishes a joint learning of the extended Markovian dynamics in terms of both the resolved variables and these features. The training is based on matching the evolution of the correlation functions of the extended variables that can be directly obtained from the ones of the resolved variables. The constructed model essentially approximates the multi-dimensional generalized Langevin equation and ensures numerical stability without empirical treatment. We demonstrate the effectiveness of the method by constructing the reduced models of molecular systems in terms of both one-dimensional and four-dimensional resolved variables.