Machine Learning and Polymer Self-Consistent Field Theory in Two Spatial Dimensions

TL;DR

This paper introduces a novel machine learning framework combining deep learning and self-consistent field theory to efficiently explore polymer nanostructures in two dimensions, significantly reducing computational costs and enabling faster phase discovery.

Contribution

It extends previous 1D frameworks to 2D, employing Sobolev CNNs and GANs for improved accuracy and efficiency in polymer simulation predictions.

Findings

Successful application to 2D cell size optimization

Significant savings in memory and computational cost

Potential extension to 3D phase discovery

Abstract

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.