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

We present an algorithmic approach that optimizes chain propagator computations in polymer field theory simulations, such as self-consistent field theory (SCFT) and field-theoretic simulation (FTS). These computations have recursive structures for branched polymers, with heavily overlapping subproblems. By employing dynamic programming and encoding computational dependencies as strings, we systematically avoid redundant computations for any mixture of branched block copolymers. Our approach achieves optimal time complexity for various polymeric systems, including multi-arm star-shaped polymers, comb polymers, bottlebrushes, dendrimers, and their mixtures. This work paves the way for the development of efficient open-source software and holds potential for applications in automated searches for inverse design. Our implementation is publicly available as open-source software.