Machine Learning for Modelling Microstructure Evolution in Polymer Mixtures

Our aim is to enhance our modelling capabilities for microstructure evolution with machine learning. In particular, we focus on Gaussian processes (GPs), a popular non-parametric class of models used extensively in ML and uncertainty quantification, which have well documented predictive abilities. In our preliminary studies, we apply existing GP methodology to microstructure evolution to determine the feasibility of generating an emulator to supplement more traditional, computationally intense, approaches. As an exemplar, we focus on the non-linear Cahn-Hilliard equation for describing phase separation in blends. Spatio-temporal problems are particularly challenging for ML due to their high dimensionaility, hence we use a method recently proposed for using machine learning to predict video images, based on the idea of light cones, in which the present is only dependent on the past in the immediate spatial neighbourhood, analogous to real-space time-stepping numerical schemes for PDEs. We will present results which highlight the both the strengths and challenges of using ML for modelling microstructure.