Neural network-based tensor models for liquid crystals with molecular-level information

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Shi, Baoming and Majumdar, Apala and Zhang, Lei (2026) Neural network-based tensor models for liquid crystals with molecular-level information. Physical Review E, 113 (1). 015401. ISSN 2470-0053 (https://doi.org/10.1103/7v32-lr9w)

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Abstract

The phenomenological Landau–de Gennes (LdG) model is a powerful continuum theory to describe macroscopic liquid crystal (LC) phases. However, it is invariably less accurate and less physically informed than molecular-level models. We propose a neural network-based tensor (NN-tensor) model for LCs, supervised by an underlying molecular model. Our NN-tensor model not only attains energy precision comparable to the molecular model, but it also accurately captures the isotropic-nematic phase transition, which the LdG model cannot achieve. By embedding the NN-tensor model within a second neural network, we can efficiently compute stable LC configurations in a domain-free and mesh-free manner. We validate this approach with multiple examples for nematic LCs, demonstrating its ability to find physically relevant nematic configurations in diverse scenarios. We further apply the NN-tensor model to the more complex smectic LC phase. Strikingly, the NN-tensor model can quantitatively predict the smectic layer thickness and capture intricate microstructures such as Omega and T-shaped grain boundaries—features that current conventional approaches fail to resolve. These results demonstrate that the NN-tensor framework is a unified, efficient, and physically faithful route for computing rich LC configurations across multiple phases.

ORCID iDs

Shi, Baoming, Majumdar, Apala ORCID logoORCID: https://orcid.org/0000-0003-4802-6720 and Zhang, Lei;
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