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.

翻译：提出了一种计算框架，该框架利用自洽场理论模拟数据与深度学习，加速嵌段共聚物参数空间的探索。这是文献[1]所引入框架的实质性二维扩展。本文提出了多项创新与改进：（1）采用索博列夫空间训练的卷积神经网络（CNN），以处理离散化局部平均单体密度场的指数级维度增长，并强实施加所预测场论强度哈密顿量的空间平移与旋转不变性；（2）引入生成对抗网络（GAN），无需借助训练集的梯度下降方法，即可高效准确地预测鞍点局部平均单体密度场。该GAN方法显著节省了内存与计算成本；（3）所提出的机器学习框架成功应用于二维晶胞尺寸优化，清晰展示了其在加速发现聚合物纳米结构的参数空间探索方面的广泛潜力。向三维相发现的扩展似乎是可行的。