Deep learning and self-consistent field theory: A path towards accelerating polymer phase discovery

Abstract A new framework that leverages data obtained from self-consistent field theory (SCFT) simulations with deep learning to accelerate the exploration of parameter space for block copolymers is presented. Deep neural networks are adapted and trained in Sobolev space to better capture the saddle point nature of the SCFT approximation. The proposed approach consists of two main problems: 1) the learning of an approximation to the effective Hamiltonian as a function of the average monomer density fields and the relevant physical parameters and 2) the prediction of saddle density fields given the polymer parameters. There is an additional challenge: the effective Hamiltonian has to be invariant under shifts (and rotations in 2D and 3D). A data-enhancing approach and an appropriate regularization are introduced to effectively achieve said invariance. In this first study, the focus is on one-dimensional (in physical space) systems to allow for a thorough exploration and development of the proposed methodology.