Machine Learning and Polymer Self-Consistent Field Theory in Two Spatial Dimensions
This work addresses the computational bottleneck in polymer science for researchers, but it is incremental as it builds on prior 1D work.
The authors tackled the problem of accelerating parameter space exploration for block copolymers by extending a computational framework to two dimensions, using deep learning to predict intensive Hamiltonians and saddle point fields, achieving significant memory and computational cost savings.
A computational framework that leverages data from self-consistent field theory simulations with deep learning to accelerate the exploration of parameter space for block copolymers is presented. This is a substantial two-dimensional extension of the framework introduced in [1]. Several innovations and improvements are proposed. (1) A Sobolev space-trained, convolutional neural network (CNN) is employed to handle the exponential dimension increase of the discretized, local average monomer density fields and to strongly enforce both spatial translation and rotation invariance of the predicted, field-theoretic intensive Hamiltonian. (2) A generative adversarial network (GAN) is introduced to efficiently and accurately predict saddle point, local average monomer density fields without resorting to gradient descent methods that employ the training set. This GAN approach yields important savings of both memory and computational cost. (3) The proposed machine learning framework is successfully applied to 2D cell size optimization as a clear illustration of its broad potential to accelerate the exploration of parameter space for discovering polymer nanostructures. Extensions to three-dimensional phase discovery appear to be feasible.