Neural Network-Based Tensor
Models for Liquid Crystals
with Molecular-level Information
报告专家：张磊 教授（北京大学）
报告时间：1月16日（周五）15:00-16:00
报告地点：国家天元数学西南中心516
报告摘要：
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 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.
专家简介：
张磊，北京大学博雅特聘教授，任职于北京国际数学研究中心，兼任定量生物学中心、国际机器学习中心副主任。2001年本科毕业于北京大学，2004年在中科院数学与系统科学研究院获硕士学位，2008年在美国宾州州立大学获博士学位。研究领域为计算和应用数学、交叉科学，包括稀有事件与解景观的算法与应用，定量生物学，计算物理与材料科学等。研究成果在PRL、PNAS、Acta Numerica、Cell Systems, Nature Communications, Science Advances、SIAM系列期刊发表。(曾)主持国家基金委创新研究群体、国家杰出青年科学基金、科技部重点研发专项、基金委原创探索计划项目、基金委优秀青年科学基金、中组部高层次青年人才计划等项目。2027年国际工业与应用数学大会（ICIAM）大会邀请报告人，曾获教育部自然科学一等奖、王选杰出青年学者奖、英国皇家学会牛顿高级学者。目前担任中国工业与应用数学学会(CSIAM)副理事长，SIAM J. Appl. Math, Science China Mathematics, CSIAM Trans. Appl. Math等国内外期刊的编委。
邀请人：唐庆粦
