Neural Network Accelerated Self-Consistent Field Theory

Self-consistent field theory (SCFT) has demonstrated excellent capabilities in predicting self-assembled structures of block copolymers (BCP) at equilibrium. This method has been widely implemented in BCP self-assembly to understand its assembly process. Although SCFT gives accurate results, it is a relatively time-consuming method: SCFT involves solving differential equation numerically in matrix form at each time step and normally takes thousands of steps to reach the final structure at equilibrium, which makes it difficult to be applied to large 3D systems. In this work, we train a neural network (NN) to predict the evolving field during SCFT free energy minimization. After training the NN, we implement a hybrid algorithm combining SCFT with the trained NN. This NN-SCFT model helps to shorten the SCFT simulation time significantly (approximately x10 speedup), with convergence being achieved in all different cases (different volume ratio, and the chemical incompatibility between blocks). The NN-SCFT hybrid system, thus, provides a powerful tool for further exploration of larger BCP directed self-assembly systems and inverse self-assembly.