Models for polymer dynamics from dimensionality reduction techniques

TL;DR

This paper explores how linear dimensionality reduction techniques like PCA and tICA can model polymer dynamics, revealing connections to established theories and extending to nonequilibrium processes such as spinodal decomposition.

Contribution

It demonstrates that PCA and tICA can identify known polymer modes and develop continuum models for nonequilibrium phenomena, integrating memory effects and generalizing existing theories.

Findings

tICA reproduces Rouse modes for ideal polymer dynamics

tICA dynamics align with dynamic self-consistent field theory

Extended models include memory effects for spinodal decomposition

Abstract

Polymer dynamics is analyzed through the lens of linear dimensionality reduction methods, in particular principal (PCA) and time-lagged independent component analysis (tICA). For a polymer undergoing ideal Rouse dynamics, the slow modes identified by these transformations coincide with the conventional Rouse modes. When applied to the Fourier modes of the segment density, we show that tICA generates dynamics equivalent to dynamic self-consistent field theory (D-SCFT) with a wavevector-dependent Onsager coefficient and a free energy functional subject to the random phase approximation (RPA). We then introduce a hidden variable method and a time-local approach to include temporal memory in the tICA-generated dynamics, and generalize it to construct continuum models for the nonequilibrium case of spinodal decomposition of a symmetric diblock copolymer melt.