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

Fuente: arXiv
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Main Authors: Shi, Baoming, Majumdar, Apala, Zhang, Lei
Format: Preprint
Published: 2024
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author Shi, Baoming
Majumdar, Apala
Zhang, Lei
author_facet Shi, Baoming
Majumdar, Apala
Zhang, Lei
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2411_12224
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Neural Network-Based Tensor Model for Nematic Liquid Crystals with Accurate Microscopic Information
Shi, Baoming
Majumdar, Apala
Zhang, Lei
Soft Condensed Matter
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.
title Neural Network-Based Tensor Model for Nematic Liquid Crystals with Accurate Microscopic Information
topic Soft Condensed Matter
url https://arxiv.org/abs/2411.12224