Development of a machine learning-based closure relation for polymer integral equation theory

Theoretical approaches such as polymer reference interaction site model (PRISM) theory can compute quantitative thermodynamic and structural properties much more efficiently than traditional molecular dynamics simulations (MD). Thus, PRISM theory could serve as a fast and reliable computational screening method to discover novel polymeric materials and formulations. Despite the great advantages of PRISM theory, it can face issues with poor accuracy and numerical stability for some classes of polymeric systems, typically attributed to limitations in the analytical closure relations used to generate a numerical solution to the PRISM equations. In this work, we describe our efforts to develop a data-driven machine learning (ML)-based closure relationship to improve the accuracy and applicability of PRISM theory. We used coarse-grained MD simulations across a range of chain lengths, intermolecular interaction strengths, and thermodynamic conditions, to generate an initial dataset for closure development on a simple homopolymer system. Then, we evaluated multiple ML approaches to develop an improved closure function. Our goal is to develop an ML closure that minimizes regression errors while simultaneously satisfying the PRISM governing equations. We then describe our ongoing work to evaluate the ML closure’s transferability to unknown conditions, and to expand the work to other important classes of polymeric systems (e.g., copolymers, blends, polymer nanocomposites).