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

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.