Neural-Network Assisted Self-Consistent Field Theory for Block Copolymer Simulations

Self-consistent field theory (SCFT) provides impressive predictive capabilities for the equilibrium phases of a variety of block copolymer systems. When solved to high accuracy, qualitative as well as quantitative results can be compared to experiments. In this work, we exploit neural networks (NN) unique capability as a universal function approximator to evolve the fields in SCFT for several iterations during free energy minimization. To fully evolve the system, we use a hybrid algorithm mixing a proper PDE solver with the trained NN. The hybrid approach is verified on a diblock copolymer system. Convergence is achieved in all cases, independent of computational cell size, and molecular characteristics (volume fraction, and degree of block incompatibility). The lessons drawn from the NN-SCFT implementation can be extended to other energy minimization problems such as density functional theory (DFT).