Accelerating Langevin Field-Theoretic Simulation of Polymers with Deep Learning

Langevin field-theoretic simulation (L-FTS) is a promising
tool
in polymer field theory that can account for the compositional fluctuation
effect, which is neglected in the self-consistent field theory (SCFT).
However, L-FTS is a computationally expensive tool, and it may take
more than a week to accurately calculate ensemble averages of thermodynamic
quantities. In our previous study, we introduced a deep neural network
(DNN) that estimates the saddle point of the pressure field to reduce
the subsequent Anderson mixing (AM) iterations. Herein, we propose
a novel DNN that can be successively applied to determine the saddle
point without using conventional field-update algorithms. Major deep
learning (DL) models for semantic segmentation in computer vision
are adopted to construct the optimal DNN architecture. Our model utilizing
atrous convolutions in parallel is accurate and computationally efficient,
and it is robust to the simulation parameter changes and can consequently
be reused after single training. We demonstrate that our DNN can achieve
speedup of factor 6 or more compared to the AM method without affecting
accuracy. Open-source code for our deep Langevin FTS (DL-FTS) enables
an easy and rapid Python scripting of SCFT and L-FTS incorporated
with CPU or GPU parallelization and DL.