Neural Network-Based Tensor Model for Nematic Liquid Crystals with Accurate Microscopic Information
Abstract
The phenomenological Landau-de Gennes (LdG) model is a powerful continuum theory to describe the macroscopic state of nematic liquid crystals. However, it is invariably less accurate and less physically informed than the molecular-level models due to the lack of physical meaning of the parameters. We propose a neural network-based tensor (NN-Tensor) model for nematic liquid crystals, supervised by the molecular model. Consequently, the NN-Tensor model not only attains energy precision comparable to the molecular model but also accurately captures the Isotropic-Nematic phase transition, which the LdG model cannot achieve. The NN-Tensor model is further embedded in another neural network to predict liquid crystal configurations in a domain-free and mesh-free manner. We apply the NN-Tensor model to nematic liquid crystals in a number of two-dimensional and three-dimensional domains to demonstrate it can efficiently identify rich liquid crystal configurations in both regular and non-regular confinements.
Cite
@article{arxiv.2411.12224,
title = {Neural Network-Based Tensor Model for Nematic Liquid Crystals with Accurate Microscopic Information},
author = {Baoming Shi and Apala Majumdar and Lei Zhang},
journal= {arXiv preprint arXiv:2411.12224},
year = {2024}
}