发表机构
School of Mathematical Sciences, Peking University; Columbia University; Center for Applied Mathematics, Renmin University of China; School of Mathematical Sciences, Beijing International Center for Mathematical Research, Center for Quantitative Biology, Center for Machine Learning Research, Peking University（北京大学数学科学学院; 哥伦比亚大学; 中国人民大学应用数学中心; 北京大学数学科学学院、北京国际数学研究中心、定量生物学中心、机器学习研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出深度变分框架（DVF），结合修正的Landau-de Gennes模型，通过热身惩罚缓解神经网络频谱偏差，可准确计算不同受限几何下近晶型液晶的稳定构型，复现并预测相关结构。
AI 中文摘要
近晶型液晶是具有取向序和周期性密度调制的层状液晶相，虽可通过连续介质理论建模，但在复杂几何结构中计算其稳定构型仍具挑战性，尤其需解析与近晶层相关的高频密度调制时。我们提出深度变分框架（DVF），用于在修正的Landau-de Gennes模型内计算此类构型，其中耦合的取向和位置序参数在规则参考域上表示，而物理受限条件通过坐标映射纳入。热身惩罚可缓解神经网络对平滑非层状场的频谱偏差，从而可靠恢复振荡近晶态。与神经网络基线及有限差分松弛法的比较表明，该惩罚的关键作用及所得层状态的数值稳定性。DVF可复现不同受限几何中实验已确立的近晶A缺陷结构和层形态，还预测了切向锚定球中的 Chevron 状近晶C态。综上，这些结果证明DVF适用于计算实验相关受限几何和锚定条件下的稳定近晶构型。
英文摘要
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.
Comments13 pages, 6 figures
