Identifying Memory Effects in Short-Time Dynamics of Polymer Systems by Machine Learning

Memory effects are intrinsic properties of flexible macromolecular systems emerging originally from their hierarchical microstructures and multiscale dynamic behaviors of polymer chains during nonequilibrium processes. The nonlocal temporal dependence of transport coefficients (e.g., the Onsager coefficient), a fundamental manifestation of memory effects that govern the dynamic evolution of collective observables, still poses significant challenges for analytical formulations. Herein, we propose a machine-learning-based framework to extract the history-dependent Onsager coefficient directly from the density evolution data, generated from particle-based single-chain in mean-field simulations, thereby enabling these coefficients to accurately capture underlying microscopic characteristics. This framework, termed the dynamic density functional theory-ordinary differential equation (DDFT-ODE) Net, embeds equations of DDFT into the ODE network, enhancing the physical consistency and computational efficiency of the framework. Our study of the relaxation of density fluctuations in an ideal symmetric diblock copolymer melt reveals that memory effects play a dominant role in determining density evolution processes at early times. Further analysis of the memory kernel function of the Onsager coefficient identifies two characteristic relaxation times, which are both smaller than the Rouse time, a signature suggesting that memory effects are closely related to short-time segmental motions. By defining two types of time averages and comparing their asymptotic behaviors at the long-time limit, we establish connections linking the history-dependent Onsager coefficient, the instantaneous Onsager coefficient, and the memory-free one, which provide a theoretical foundation for quantitatively evaluating the reliability of various DDFT implementations. Our data-driven framework is easily extensible to other different systems, combining different particle-based simulations and continuum field-based DDFT schemes, thereby providing a useful framework for developing structure–property correlations in complex polymer systems.