应用现代微分几何和代数几何的理论与方法解决工程及医学领域的问题，主要聚焦于计算共形几何、计算拓扑、符号计算及其在计算机图形学、计算机视觉、几何建模和医学图像中的应用。
雷娜，大连理工大学国际信息与软件学院党总支书记，教授，博士生导师，北京成像技术高精尖创新中心研究员； 美国数学会 Mathematical Review评论员；中国计算机学会计算机视觉专业委员会委员; 中国工业与应用数学学会几何设计与计算专业委员会委员；中国数学会计算机数学专业委员会委员。 纽约州立大学石溪分校计算机系访问教授；德克萨斯大学奥斯汀分校计算工程与科学研究所 JTO research fellow； 清华大学数学科学中心访问教授；中科院数学与系统科学研究院访问学者。 IEEE Transactions on Visualization and Computer Graphics，Computer Aided Geometric Design, Graphical Models， The Visual Computer, Journal of Computational and Applied Mathematics等国际期刊审稿人, International Joint Conference of Artificial Intelligence, Geometric Modeling and Processing, Asian Conference on Design and Digital Engineering等国际会议的PC member。 主持国家自然科学基金重点项目、面上项目以及国家部委等重要项目多项；多次受邀在国际、国内重要会议上做大会报告及会前课程。
Efficient Optimal Transport Algorithm by Accelerated Gradient descent
Dongsheng An, Na Lei, Xianfeng Gu.
36th AAAI Conference on Artificial Intelligence, 2022.
Cortical Surface Shape Analysis Based on Alexandrov Polyhedra
Min Zhang, Yang Guo, Na Lei, Zhou Zhao, Jianfeng Wu, Xiaoyin Xu, Yalin Wang, and Xianfeng Gu.
In Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 14244-14252. 2021.
Cortical Morphometry Analysis based on Worst Transportation Theory
Min Zhang, Dongsheng An,Na Lei, Jianfeng Wu,TongZhao, Xiaoyin Xu, Yalin Wang, Xianfeng Gu.
In International Conference on Information Processing in Medical Imaging (pp. 163-176). Springer, Cham.
The Singularity Set of Optimal Transportation Maps
Zhongxuan Luo, Wei Chen, Na Lei, Yang Guo, Tong Zhao, Jiakun Liu, Xianfeng Gu.
In International Conference on Information Processing in Medical Imaging (pp. 163-176). Springer, Cham.
Prismatic mesh generation based on anisotropic volume harmonic field
Yiming Zhu, Shengfa Wang, Xiaopeng Zheng, Na Lei.
Advances in Aerodynamics, 2021, 3(1): 1-16.
Quadrilateral mesh generation III : Optimizing singularity configuration based on Abel–Jacobi theory
Xiaopeng Zheng, Yiming Zhu, Wei Chen, Na Lei, Zhongxuan Luo, Xianfeng Gu.
Computer Methods in Applied Mechanics and Engineering, 2021, 387: 114146.
FFT-OT: A Fast Algorithm for Optimal Transportation
Na Lei, Xianfeng Gu.
Proceedings of the IEEE/CVF International Conference on Computer Vision. 2021: 6280-6289.
Optimal Transportation Theory and Computation
Na Lei, Xianfeng Gu.
Proceedings of the IEEE/CVF International Conference on Computer Vision. 2021: 6280-6289.
Robust and accurate optimal transportation map by self-adaptive sampling
Yingshi Wang, Xiaopeng Zheng,Wei Chen,Xin Qi, Yuxue Ren, Na Lei, Xianfeng Gu.
Frontiers of Information Technology & Electronic Engineering, 2021, 22(9): 1207-1220.
Cortical Morphometry Analysis Based on Worst Transportation Theory
Min Zhang, Dongsheng An, Na Lei, Jianfeng Wu, Tong Zhao, Xiaoyin Xu, Yalin Wang & Xianfeng Gu.
International Conference on Information Processing in Medical Imaging. Springer, Cham, 2021: 163-176.
AE-OT-GAN: Training GANs from data specific latent distribution
Dongsheng An, Yang Guo, Min Zhang, Xin Qi, Na Lei, Xianfang Gu.
In European Conference on Computer Vision (pp. 548-564). Springer, Cham.
Characteristic Class of Isotopy for Surfaces
Yuxue Ren, Chengfeng Wen, Shengxian Zhen, Na Lei, Feng Luo, David Xianfeng Gu.
Journal of Systems Science and Complexity, 33(6), 2139-2156.
Quadrilateral Mesh Generation III: Optimizing Singularity Configuration Based on Abel-Jacobi Theory
Xiaopeng Zheng, Yiming Zhu, Na Lei, Zhongxuan Luo, Xianfeng Gu.
Computer Methods in Applied Mechanics and Engineering, 387, 114146.
Ricci Curvature Based Volumetric Segmentation of the Auditory Ossicles
Na Lei, Jisui Huang, Yuxue Ren, Emil Saucan, Zhenchang Wang.
arXiv preprint arXiv:2006.14788.
An interactive feature selection method based on learning-from-crowds
Shixia Liu, Na Lei, Liu Jiang, Changjian CHEN.
SCIENTIA SINICA Informationis, 2020, 50(6): 794-812.
Computational generation and conformal fabrication of woven fabric structures by harmonic foliation
Yang Guo, Qian Ye, Xiaopeng Zheng, Shikui Chen, Na Lei, Yuanqi Zhang, Xianfeng David Gu.
A Geometric Understanding of Deep Learning
Na Lei, Dongsheng An, Yang Guo, Kehua Su, Shixia Liu, Zhongxuan Luo, Shing-Tung Yau, Xianfeng Gu.
Engineering, 2020, 6(3): 361-374.
Comparison between variational optimal mass transportation and Lie advection
Kehua Su, Chenchen Li, Shifan Zhao, Na Lei, Lok Ming Lui, Shikui Chen, Xianfeng Gu.
Mathematics, Computation and Geometry of Data, 2021, 1(1): 99-130.
Secondary Polytope and Secondary Power Diagram
Na Lei, Wei Chen, Zhongxuan Luo, Hang Si, Xianfeng Gu.
Computational Mathematics and Mathematical Physics, 2019, 59(12): 1965-1981.
Study of Tunnel Surface Parameterization of 3-D Laser Point Cloud Based on Harmonic Map
Yujiao Liu, Ruofei Zhong, Wei Chen, Haili Sun, Yuxue Ren, Na Lei.
IEEE Geoscience and Remote Sensing Letters, 2019, 17(9): 1623-1627.
Quadrilateral mesh generation I : Metric based method
Wei Chen,Xiaopeng Zheng,Jingyao Ke, Na Lei, Zhongxuan Luo, Xianfeng Gu.
Computer Methods in Applied Mechanics and Engineering, 2019, 356: 652-668.
Surface Foliation Based Brain Morphometry Analysis
Chengfeng Wen, Na Lei, Ming Ma, Xin Qi, Wen Zhang, Yalin Wang, Xianfeng Gu.
Multimodal Brain Image Analysis and Mathematical Foundations of Computational Anatomy. Springer, Cham, 2019: 186-195.
Automatic and Robust Skull Registration Based on Discrete Uniformization
Junli Zhao, Xin Qi, Chengfeng Wen, Na Lei, Xianfeng Gu.
Proceedings of the IEEE/CVF International Conference on Computer Vision. 2019: 431-440.
Polycube Shape Space
Hui Zhao, Xuan Li, Wencheng Wang, Xiaoling Wang,Shaodong Wang, Na Lei, Xiangfeng Gu.
Computer Graphics Forum. 2019, 38(7): 311-322.
Quadrilateral Mesh Generation II:: Meromorphic Quartic Differentials and Abel-Jacobi Condition
Na Lei, Xiaopeng Zheng, Zhongxuan Luo, Feng Luo, Xianfeng Gub.
Computer methods in applied mechanics and engineering, 2020, 366: 112980.
A Construction of Anisotropic Meshes Based on Quasi-Conformal Mapping
Yuxue Ren, Na Lei, Hang Si, Xianfeng David Gu.
International Meshing Roundtable. Springer, Cham, 2018: 249-267.
Discrete Lie Flow: A Measure Controllable Parameterization Method
Kehua Su, Chenchen Li, Shifan Zhao, Na Lei, Xianfeng Gu.
Computer Aided Geometric Design, 2019, 72: 49-68.
Spherical optimal transportation
Li Cui, Xin Qi, Chengfeng Wen, Na Lei, Xinyuan Li, Min Zhang, Xianfeng Gu.
Computer-Aided Design, 2019, 115: 181-193.
A Geometric View of Optimal Transportation and Generative Model
Na Lei, Kehua Su, Li Cui, Shing-Tung Yau, Xianfeng David Gu.
Computer Aided Geometric Design, 2019, 68: 1-21.
Mesh Parametrization Driven by Unit Normal Flow
Hui Zhao, Kehua Su, Chenchen Li, Boyu Zhang, Lei Yang, Na Lei, Xiaoling Wang, Steven J.Gortler and Xianfeng Gu.
Computer Graphics Forum. 2020, 39(1): 34-49.
Mode Collapse and Regularity of Optimal Transportation Maps
Na Lei, Yang Guo, Dongsheng An, Xin Qi, Zhongxuan Luo, Shing-Tung Yau, Xianfeng Gu.
arXiv preprint arXiv:1902.02934, 2019.
Concurrent optimization of structural topology and infill properties with a CBF-based level set method
Long JIANG, Yang GUO, Shikui CHEN, Peng WEI, Na LEI, Xianfeng David GU.
Frontiers of Mechanical Engineering, 2019, 14(2): 171-189.
Curvature adaptive surface remeshing by sampling normal cycle
Kehua Su, Na Lei, Wei Chen, Li Cui, Hang Si, Shikui Chen, Xianfeng Gu.
Computer-Aided Design, 2019, 111: 1-12.
Topology optimization of conformal structures on manifolds using extended level set methods (X-LSM) and conformal geometry theory
Qian Ye, Yang Guo, Shikui Chen, Na Lei, Xianfeng David Gu.
Computer Methods in Applied Mechanics and Engineering, 2019, 344: 164-185.
Latent Space Optimal Transport for Generative Models
Huidong Liu, Yang Guo, Na Lei, Zhixin Shu, Shing-Tung Yau, Dimitris Samaras, Xianfeng Gu.
arXiv preprint arXiv:1809.05964, 2018.
Brain Morphometry Analysis with Surface Foliation Theory
Chengfeng Wen, Na Lei, Ming Ma, Xin Qi, Wen Zhang, Yalin Wang, David Xianfeng Gu.
arXiv preprint arXiv:1809.02870, 2018.
The Bulirsch‐Stoer algorithm for multivariate rational interpolation
Peng Xia, Tian Dong, Shugong Zhang, Na Lei.
Mathematical Methods in the Applied Sciences, 2018, 41(17): 7698-7710.
Multi-Material Topology Optimization of Structures Infilled With Conformal Metamaterials
Panagiotis Vogiatzis, Shikui Chen, Xianfeng David Gu, Ching-Hung Chuang, Hongyi Xu,Na Lei.
In International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (Vol. 51760, p. V02BT03A009). American Society of Mechanical Engineers.
Robust Edge-Preserved Surface Mesh Polycube Deformation
Hui Zhao, Na Lei, Xuan Li, Peng Zeng, Ke Xu, Xianfeng Gu.
Computational Visual Media, 4(1), 33-42.
Conformal Mesh Parameterization Using Discrete Calabi Flow
Hui Zhao, Xuan Li, Huabin Ge, Na Lei, Min Zhang, Xiaoling Wang, Xianfeng Gu.
Computer Aided Geometric Design, 63, 96-108.
The Normal Map Based on Area-Preserving Parameterization
Hui Zhao, Kehua Su, Ming Ma, Na Lei, Li Cui, Xianfeng Gu.
arXiv preprint arXiv:1808.01308.
Geometric Understanding of Deep Learning
Na Lei, Zhongxuan Luo, Shing-Tung Yau, David Xianfeng Gu.
On Tetrahedralisations Containing Knotted and Linked Line Segments
Hang Si, Yuxue Ren, Na Lei, Xianfeng Gu.
Procedia engineering, 2017, 203: 323-335.
Guaranteed quality isotropic surface remeshing based on uniformization
Ming Ma, Xiaokang Yu, Na Lei, Hang Si, Xianfeng Gu.
Procedia engineering, 2017, 203: 297-309.
Generalized Regular Quadrilateral Mesh Generation based on Surface Foliation
Na Lei, Xiaopeng Zheng, Hang Si, Zhongxuan Luo, Xianfeng Gu.
Procedia engineering, 2017, 203: 336-348.
Surface Registration via Foliation
Xiaopeng Zheng, Chengfeng Wen, Na Lei, Ming Ma, Xianfeng Gu.
Proceedings of the IEEE International Conference on Computer Vision. 2017: 938-947.
Intrinsic 3D Dynamic Surface Tracking based on Dynamic Ricci Flow and Teichmüller Map
Xiaokang Yu, Na Lei, Yalin Wang, Xianfeng Gu.
Proceedings of the IEEE International Conference on Computer Vision. 2017: 5390-5398.
Lagrange‐type basis for multivariate uniform integrable tensor‐product Birkhoff interpolation
Lili Xu,Na Lei.
Mathematical Methods in the Applied Sciences, 2017, 40(18): 6823-6831.
Robot Coverage Path planning for general surfaces using quadratic differentials
Yu-Yao Li, Chien-Chun Ni, Na Lei, Xianfeng David Gu, Jie Gao.
arXiv preprint arXiv:1701.07549, 2017.
Quadrilateral and hexahedral mesh generation based on surface foliation theory II
Na Lei, Xiaopeng Zheng, Zhongxuan Luo, David Xianfeng Gu.
Computer Methods in Applied Mechanics and Engineering, 2017, 321: 406-426.
Robust Surface Registration Using Optimal Mass Transport and Teichmüller Mapping
Ming Ma, Na Lei, Wei Chen, Kehua Su.
Graphical models, 2017, 90: 13-23.
Surface parameterization based on polar factorization
Xiaokang Yu, Na Lei, Xiaopeng Zheng, Xianfeng Gu.
Journal of computational and applied mathematics, 2018, 329: 24-36.
A Balanced Surface Parameterization Method and Its Application to Spline Fitting
Xiaopeng Zheng, Na Lei, Xiaokang Yu, Wei Chen, Mengci Song, Xianfeng Gu.
In 2016 6th International Conference on Digital Home (ICDH) (pp. 272-277). IEEE.
Quadrilateral and hexahedral mesh generation based on surface foliation theory
Na Lei, Xiaopeng Zheng, Jian Jiang, Yu-Yao Lin, Xianfeng Gu.
Computer Methods in Applied Mechanics and Engineering, 316, 758-781.
Measure controllable volumetric mesh parameterization
Kehua Su, Wei Chen, Na Lei, Li Cui, Jian Jiang, Xianfeng Gu.
Computer-Aided Design, 78, 188-198.
Volume preserving mesh parameterization based on optimal mass transportation
Kehua Su, Wei Chen, Na Lei, Junwei Zhang, Kun Qian, Xianfeng Gu.
Computer-Aided Design, 82, 42-56.
Area-preserving Mesh Parameterization for Poly-Annulus Surfaces Based on Optimal Mass Transportation
Kehua Su, Li Cui, Kun Qian, Na Lei, Junwei Zhang, Min Zhang, Xianfeng David Gu.
Computer Aided Geometric Design, 46, 76-91.
Dynamic unified surface Ricci flow
Wei Chen, Min Zhang, Na Lei, David Xianfeng Gu.
Geometry, Imaging and Computing, 2016, 3(1): 31-56.