Neural Network-Based Tensor Model for Nematic Liquid Crystals with Accurate Microscopic Information

TL;DR

This paper introduces a neural network-based tensor model for nematic liquid crystals that surpasses traditional phenomenological models in accuracy and physical relevance, effectively capturing phase transitions and complex configurations.

Contribution

The paper presents a novel neural network-based tensor model supervised by molecular data, improving accuracy and physical fidelity over classical continuum theories.

Findings

Achieves energy accuracy comparable to molecular models.

Successfully captures the Isotropic-Nematic phase transition.

Efficiently predicts complex liquid crystal configurations in various domains.

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.