Microstructural descriptors for data-driven prediction of energetics and structures of polymer mesophases

Block copolymers are a class of soft-matter systems of particular interest since their composition, size, and architecture can be carefully controlled during synthesis and they can form a wide variety of ordered and disordered mesophases. A quantitative computational framework, self-consistent field theory (SCFT), is also available to assess phase structure and stability, but it is computationally expensive. In this work, we develop a set of sensitive lower-order microstructural descriptors for species density fields, which are generalizations of those previously designed for characterizing two-phase heterogeneous materials and are physically interpretable. Subsequently, we train a theory-embedded machine learning model that incorporates these microstructural descriptors to accurately predict the energetics and structures of copolymer mesophases, using training data generated by SCFT simulations. Because of the inherent translational and rotational invariance of the new microstructural descriptors, our machine learning model achieves perfect global shift-invariance, i.e., the energetics of polymer density fields should be invariant under shifts and rotations. The machine-learned model will help accelerate the discovery of novel functional polymeric materials, benefitting both forward prediction and inverse design.