Neural Network-Based Tensor Model for Nematic Liquid Crystals with Accurate Microscopic Information
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917841231413248 |
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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 |