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This study introduces a deep variational framework (DVF) to compute stable configurations of confined smectic liquid crystals, addressing the challenge of resolving high-frequency density modulations in complex geometries. By incorporating a warmup penalty to counteract the spectral bias of neural networks, the DVF successfully recovers oscillatory smectic states and reproduces known defect structures and layer morphologies. The framework's effectiveness is validated through comparisons with traditional methods, showcasing its capability to predict new smectic states in various confinement scenarios.
The deep variational framework not only recovers established smectic-A defect structures but also predicts novel configurations like a chevron-like smectic-C state in confined geometries.
Smectic liquid crystals are layered liquid-crystalline phases characterized by orientational order and periodic density modulation. Although their structures can be modeled using continuum theories, computing stable configurations remains challenging in complex geometries, particularly when the high-frequency density modulations associated with smectic layering should be resolved. We propose a deep variational framework (DVF) for computing these configurations within the modified Landau--de Gennes model, in which the coupled orientational and positional order parameters are represented on a regular reference domain while physical confinement is incorporated through coordinate mappings. A warmup penalty mitigates the spectral bias of neural networks toward smooth, nonlayered fields, enabling robust recovery of oscillatory smectic states. Comparisons with a neural-network baseline and finite-difference relaxation demonstrate the essential role of this penalty and the numerical stability of the resulting layered states. The DVF reproduces experimentally established smectic-A defect structures and layer morphologies across diverse confinement geometries and further predicts a chevron-like smectic-C state in a tangent-anchored sphere. Together, these results demonstrate the applicability of the DVF to computing stable smectic configurations across experimentally relevant confinement geometries and anchoring conditions.