Optimization of Linear Sequence-controlled Copolymers for Maximizing Adsorption Capacity

The optimization of polymer structures aims to determine an optimal sequence or topology that achieves a given target property or structural performance. This inverse design problem involves searching within a vast combinatorial phase space defined by components, sequences, and topologies, and is often computationally intractable due to its NP-hard nature. At the core of this challenge lies the need to evaluate complex correlations among structural variables, a classical problem in both statistical physics and combinatorial optimization. To address this, we adopt a mean-field approach that decouples direct variable-variable interactions into effective interactions between each variable and an auxiliary field. The simulated bifurcation (SB) algorithm is employed as a mean-field-based optimization framework. It constructs a Hamiltonian dynamical system by introducing generalized momentum fields, enabling efficient decoupling and dynamic evolution of strongly coupled structural variables. Using the sequence optimization of a linear copolymer adsorbing on a solid surface as a case study, we demonstrate the applicability of the SB algorithm to high-dimensional, non-differentiable combinatorial optimization problems. Our results show that SB can efficiently discover polymer sequences with excellent adsorption performance within a reasonable computational time. Furthermore, it exhibits robust convergence and high parallel scalability across large design spaces. The approach developed in this work offers a new computational pathway for polymer structure optimization. It also lays a theoretical foundation for future extensions to topological design problems, such as optimizing the number and placement of side chains, as well as the co-optimization of sequence and topology.