Machine learning and polymer self-consistent field theory in two spatial dimensions.

Area of Science:

• Computational materials science
• Polymer physics
• Machine learning applications

Background:

• Block copolymers self-assemble into diverse nanostructures.
• Exploring their parameter space is computationally intensive.
• Previous methods required significant computational resources.

Purpose of the Study:

• To develop an accelerated computational framework for block copolymer exploration.
• To extend existing methods to two-dimensional simulations.
• To enhance the discovery of polymer nanostructures.

Main Methods:

• Utilizing self-consistent field theory (SCFT) simulations integrated with deep learning.
• Employing a Sobolev space-trained convolutional neural network for field prediction.
• Implementing a generative adversarial network (GAN) to predict monomer density fields without gradient descent.

Main Results:

• The framework successfully handles increased dimensionality and enforces physical symmetries.
• The GAN approach significantly reduces memory and computational costs.
• Demonstrated application to 2D cell size optimization for polymer nanostructures.

Conclusions:

• The proposed machine learning framework accelerates the exploration of block copolymer parameter space.
• This approach offers substantial savings in computational resources.
• The framework shows potential for extension to 3D phase discovery.