Dynamic Programming for Chain Propagator Computation of Branched Block Copolymers in Polymer Field Theory Simulations

Abstract

We present an algorithmic approach to optimize chain propagator computations in polymer field theory simulations, including self-consistent field theory (SCFT) calculations and field-theoretic simulations (FTSs). Propagator calculations for branched block copolymers often involve recursive structures and overlapping subproblems, resulting in redundant computations. By employing dynamic programming (DP) and encoding computational dependencies as strings, our method systematically eliminates these redundancies in mixtures of branched polymers. The algorithm achieves optimal time complexity for various polymeric systems, including star-shaped, comb, dendrimer polymers, and homopolymer mixtures, by reusing and aggregating propagators for symmetric and repetitive structures. This enhances computational efficiency and reduces memory usage, addressing a key limitation in developing versatile polymer field theory simulation software. Our approach streamlines the simulation of complex branched polymers without requiring manual software adjustments, facilitating more efficient workflows for polymer researchers. Furthermore, the method enables automated searches for inverse design by optimizing computations across diverse branched polymer architectures, contributing to the discovery and design of novel polymeric materials. The algorithm is implemented in open-source software, ensuring accessibility for further development and broader application in computational polymer science.