Combining Particle-Based Simulations and Machine Learning to Understand Defect Kinetics in Thin Films of Symmetric Diblock Copolymers

The self-assembly of soft matter provides a practical and scalable route toward the production of nanostructured materials, with minimal need for direct intervention at nanoscopic length scales. Symmetric diblock copolymers, which can self-assemble into a lamellar phase, are a prototype for this class of materials. In this work, we introduce a machine learning model that is trained by intermediate time-scale simulations of a soft, coarse-grained model. The aim of the model is to simulate defect kinetics in the lamellar morphology, as the material relaxes toward equilibrium. To do so, we exploit the physical characteristics of overdamped dynamics and formulate the problem of time evolution as a Markov chain. The trained artificial neural network (ANN) predicts a time-independent transition probability from one time step to the next. As a result, we arrive at a method that can be repeatedly applied to generate long-time trajectories. Predicting defect kinetics in this manner provides hitherto unavailable insights into the late-time dynamics of block copolymer relaxation. The neural network is purposely designed to be independent of input size, which enables training on small systems, and enabling predictions over large scales. As a demonstration of these capabilities, in this work, we leverage the ANN to obtain information about the statistics of defect motion and lifetimes over a long-range ordering process.