Journal Publications

1. Hua Su, Haoran Wang, Lei Zhang*, Jin Zhao, Xiangcheng Zheng. Improved high-index saddle dynamics for finding saddle points and solution landscape, arXiv:2502.03694. [Link].
   
   
2. Xiaoyi Zhang, Zhiyuan Li*, Lei Zhang*. Constructing a holistic map of cell fate decision by hyper solution landscape, bioRxiv 2024.11.28.625944. [Link].
   
   
3. Yuankai Liu, Lei Zhang, Jin Zhao. Neural Network-based High-index Saddle Dynamics Method for Searching Saddle Points and Solution Landscape arXiv:2411.16200. [Link].
   
   
4. Baoming Shi, Apala Majumdar, Lei Zhang*. Neural Network-Based Tensor Model for Nematic Liquid Crystals with Accurate Microscopic Information, arXiv:2411.12224. [Link].
   
   
5. Yuze Zhang, Xuelong Gu, Yushun Wang, Xianmin Xu*, Lei Zhang*. Solution landscape of droplet on rough surfaces: wetting transition and directional transport, arXiv:2410.04829. [Link].
   
   
6. Shuonan Wu, Bing Yu, Yuhai Tu*, Lei Zhang*. Solution landscape of reaction-diffusion systems reveals a nonlinear mechanism and spatial robustness of pattern formation, arXiv:2408.10095. [Link].
   
   
7. Dawei Wu, Baoming Shi, Yucen Han, Pingwen Zhang, Apala Majumdar, Lei Zhang*. A diffuse-interface Landau-de Gennes model for free-boundary nematic liquid crystals, arXiv:2407.21437. [Link]
   
   
8. Lei Zhang, Pingwen Zhang, Xiangcheng Zheng*. Exponential Lyapunov stability of high-index saddle dynamics with or without acceleration, submitted.
   
   
9. Tunan Kao, He Zhang, Lei Zhang*, Jin Zhao. pETNNs: Partial Evolutionary Tensor Neural Networks for Solving Time-dependent Partial Differential Equations, arXiv:2403.06084. [Link]
   
   
10. Shuai Miao, Ziqi Liu, Lei Zhang*, Pingwen Zhang, Xiangcheng Zheng. Construction and analysis for Adams explicit discretization of high-index saddle dynamics, submitted.
    
    
11. Miao Huang, Junda Ying, Yuxuan Wang, Haijun Zhou, Lei Zhang*, Weikang Wang*. Geometric Quantification of Cell Phenotype Transition Manifolds with Information Geometry, bioRxiv, 2023-12. [Link]
    
    
12. Baoming Shi, Yucen Han, Chengdi Ma, Apala Majumdar, Lei Zhang. A Modified Landau-de Gennes Theory for Smectic Liquid Crystals: Phase Transitions and Structural Transitions, accepted by SIAM J. Appl. Math.. [Link]
    
    
13. Yue Luo, Lei Zhang*, Xiangcheng Zheng. Accelerated high-index saddle dynamics method for searching high-index saddle points, Journal of Scientific Computing, 102:31 (2025). [Link]
    
    
14. Ting Jiang, Lei Li, Qianqian Hu, Xianyu Kuang, Lei Zhang, Wenjie Zeng, Daisuke Miki, Binglian Zheng*. The DNA methylation–demethylation balance prevents development of multiple megaspore mother cells in Arabidopsis, The Plant Cell, koaf023 (2025). [Link]
    
    
15. Shun Wang, Tengfei Wang, Shuonan Wu, Lei Zhang*, Xiufen Zou*. Mathematical Modeling and Solution Landscape Reveal Cancer Progression Dynamics in Tumor Ecological Microenvironment, SIAM J. Appl. Math., 85(1), 50-77 (2025). [Link]
    
    
16. Lei Zhang, Pingwen Zhang, Xiangcheng Zheng. Understanding high-index saddle dynamics via numerical analysis, Comm Math Sci., 23(2), 541-560 (2025). [Link]
    
    
17. Tiejun Zhou, Lei Zhang, Pingwen Zhang, An-Chang Shi, Kai Jiang*. Nucleation and phase transition of decagonal quasicrystals, J. Chem. Phys., 161, 164503 (2024).[Link]
    
    
18. Lu Li, Bing Yu, Pengyue Gao, Jian Lv*, Lei Zhang*, Yanchao Wang*, Yanming Ma*. Representing crystal potential energy surfaces via a stationary-point network, Acta Materialia, 281, 120403 (2024).[Link]
    
    
19. Bin Du, He Zhang, Xiangle Cheng, Lei Zhang*. Neural Quantile Optimization for Edge-Cloud Computing, Computer Networks, 253, 110713 (2024). [Link]
    
    
20. Qirui Guo, Musu Yuan, Lei Zhang*, Minghua Deng*. scPLAN: A hierarchical computational framework for single transcriptomics data annotation, integration and cell-type label refinement, Briefings in Bioinformatics, 25.4 (2024). [Link]
    
    
21. Yue Luo, Lei Zhang*, Pingwen Zhang, Zhiyi Zhang, Xiangcheng Zheng. Semi-implicit method of high-index saddle dynamics and application to construct solution landscape, Numerical Methods for Partial Differential Equations, e23123 (2024). [Link]
    
    
22. Baoming Shi, Yucen Han, Apala Majumdar, Lei Zhang. Multistability for Nematic Liquid Crystals in Cuboids with Degenerate Planar Boundary Conditions, SIAM J. Appl. Math., 84 (2), 756-781 (2024). [Link]
    
    
23. Lei Zhang, Pingwen Zhang, Xiangcheng Zheng*. Probabilistic Error Estimate for Numerical Discretization of High-Index Saddle Dynamics with Inaccurate Models, Ann. Appl. Math., 40(1), 1-20 (2024). [Link]
    
    
24. Jianyuan Yin, Zhen Huang, Yongyong Cai, Qiang Du, Lei Zhang*. Revealing Excited States of Rotational Bose-Einstein Condensates, The Innovation, 5(1), 100546 (2024). [Link]
    
    
25. Yucen Han, Baoming Shi, Lei Zhang, Apala Majumdar. A Reduced Landau-de Gennes Study for Nematic Equilibria in Three-Dimensional Prisms, IMA Journal of Applied Mathematics, hxad031 (2023). [Link]
    
    
26. Gang Xue, Xiaoyi Zhang, Wanqi Li, Lu Zhang, Zongxu Zhang, Xiaolin Zhou, Di Zhang, Lei Zhang*, Zhiyuan Li*. A Logic-incorporated Gene Regulatory Network Deciphers Principles in Cell Fate Decisions, eLife 12:RP88742 (2023). [Link]
    
    
27. Lei Zhang, Pingwen Zhang, Xiangcheng Zheng. Error estimate for semi-implicit method of sphere-constrained high-index saddle dynamics, Chinese Annals of Mathematics, Series B, 44(5), 765–780 (2023). [Link]
    
    
28. Lei Zhang. Construction of solution landscapes for complex systems, Mathematica Numerica Sinica, 45(3), 267-283 (2023). [Link]
    
    
29. Lei Zhang*, Pingwen Zhang, Xiangcheng Zheng. A model-free shrinking-dimer saddle dynamics for finding saddle point and solution landscape, Japan Journal of Industrial and Applied Mathematics (2023). [Link]
    
    
30. Donghang Zhang, Lei Zhang*. Spectral Deferred Correction Method for Landau-Brazovskii Model with Convex Splitting Technique, Journal of Computational Physics, 491 (2023) 112348. [Link]
    
    
31. Lei Zhang, Pingwen Zhang, Xiangcheng Zheng*. Discretization and index-robust error analysis for constrained high-index saddle dynamics on high-dimensional sphere, Science China Mathematics (2023). [Link]
    
    
32. Baoming Shi, Yucen Han, Jianyuan Yin, Apala Majumdar, Lei Zhang*. Hierarchies of Critical Points of a Landau-de Gennes Free Energy on Three-Dimensional Cuboids, Nonlinearity, 36, 2631 (2023). [Link]
    
    
33. Yuze Zhang, Xuguang Yang, Lei Zhang, Yiteng Li, Tao Zhang, Shuyu Sun*. Energy landscape analysis for two-phase multi-component NVT flash systems by using ETD type high-index saddle dynamics, Journal of Computational Physics, 477, 111916 (2023).
    
    
34. Xiangyu Kuang, Guoye Guan, Chao Tang*, Lei Zhang*. MorphoSim: An efficient and scalable phase-field framework for accurately simulating multicellular morphologies, npj Systems Biology and Applications, (2023) 9:6. [Link]
    
    
35. Guoye Guan, Xiangyu Kuang, Chao Tang*, Lei Zhang*. Comparison between phase-field model and coarse-grained model for characterizing cell-resolved morphological and mechanical properties in a multicellular system, Communications in Nonlinear Science and Numerical Simulation, 117, 106966 (2023).[Link]
    
    
36. Lei Zhang, Pingwen Zhang, Xiangcheng Zheng. Mathematical and numerical analysis to shrinking-dimer saddle dynamics with local Lipschitz conditions, CSIAM Trans. Appl. Math., 4(1), 157-176 (2023).[Link]
    
    
37. Lei Zhang, Pingwen Zhang, Xiangcheng Zheng. Error estimates for Euler discretization of high-index saddle dynamics, SIAM Journal on Numerical Analysis, 60(5), 2925-2944 (2022). [Link]
    
    
38. Yue Luo, Xiangcheng Zheng, Xiangle Cheng, Lei Zhang. Convergence analysis of discrete high-index saddle dynamics, SIAM Journal on Numerical Analysis, 60(5), 2731-2750 (2022). [Link]
    
    
39. Baoming Shi, Yucen Han, Lei Zhang. Nematic liquid crystals in a rectangular confinement: solution landscape and bifurcation, SIAM J. Appl. Math.82(5), 1808-1828 (2022). [Link]
    
    
40. Lingxia Qiao, Zhi-Bo Zhang, Wei Zhao, Ping Wei*, Lei Zhang*. Network design principle for robust oscillatory behaviors with respect to biological noise, eLife, 11:e76188 (2022). [Link]
    
    
41. Xiaomei Yao, Jie Xu, Lei Zhang*. Transition pathways in Cylinder-Gyroid interface, Commun. Comput. Phys., 32, 810-828 (2022). [Link]
    
    
42. Bing Yu, Xiangcheng Zheng, Pingwen Zhang, Lei Zhang*. Computing solution landscape of nonlinear space-fractional problems via fast approximation algorithm, Journal of Computational Physics, 468, 111513 (2022). [Link]
    
    
43. Chunmei Guan, Lingxia Qiao, Yuanyuan Xiong, Lei Zhang*, Yuling Jiao*. Coactivation of antagonistic genes stabilizes polarity patterning during shoot organogenesis, Science Advances, 8, eabn0368 (2022). [Link]
    
    
44. Yucen Han, Joseph Harris, Apala Majumdar, Lei Zhang. Elastic anisotropy in the reduced Landau-de Gennes model for square domains, Proceedings of the Royal Society A, 478:20210966 (2022). [Link]
    
    
45. Xiaolu Guo, Tao Tang, Minxuan Duan, Lei Zhang*, Hao Ge*. The nonequilibrium mechanism of noise-enhanced drug synergy in HIV latency reactivation, iScience, 25, 104358 (2022). [Link]
    
    
46. Xiaomei Yao, Lei Zhang*, Jeff Z.Y. Chen*. Defect patterns of two-dimensional nematic liquid crystals in confinement, Physical Review E, 105, 044704 (2022). [Link]
    
    
47. Jianyuan Yin, Zhen Huang, Lei Zhang*. Constrained high-index saddle dynamics for the solution landscape with equality constraints, Journal of Scientific Computing, 91:62 (2022). [Link]
    
    
48. Xiangyu Kuang, Guoye Guan, Ming-Kin Wong, Lu-Yan Chan, Zhongying Zhao, Chao Tang*, Lei Zhang*. Computable early Caenorhabditis elegans embryo with a phase field model, PLOS Computational Biology 18(1): e1009755 (2022). [Link]
    
    
49. Jianyuan Yin, Lei Zhang*, Pingwen Zhang. Solution Landscape of the Onsager Model Identifies Non-axisymmetric Critical Points. Physica D: Nonlinear Phenomena,430, 133081 (2022). [Link]
    
    
50. Jianyuan Yin, Kai Jiang, An-Chang Shi*, Pingwen Zhang*, Lei Zhang*. Transition pathways connecting crystals and quasicrystals, Proceedings of the National Academy of Sciences, 118 (49), e2106230118 (2021). [Link][Code]
    
    
51. Yuze Zhang, Yiteng Li, Lei Zhang, Shuyu Sun*. Construction of a Minimum Energy Path for the VT Flash Model by the String Method Coupled with the Exponential Time Differencing Scheme, Commun. Comput. Phys., 30, 1529-1544 (2021). [Link]
    
    
52. Yucen Han, Jianyuan Yin, Yucheng Hu, Apala Majumdar, Lei Zhang*. Solution Landscapes of the Simplified Ericksen-Leslie Model and its Comparison with the Reduced Landau-de Gennes Model, Proceedings of the Royal Society A, 477:20210458 (2021). [Link].
    
    
53. Wei Wang, Lei Zhang, Pingwen Zhang. Modeling and Computation of Liquid Crystals, Acta Numerica, 30, 765-851 (2021). [Link]
    
    
54. Zhen Xu, Yucen Han, Jianyuan Yin, Bing Yu, Yasumasa Nishiura*, Lei Zhang*. Solution landscapes of the diblock copolymer-homopolymer model under two-dimensional confinement, Physical Review E, 104, 014505 (2021). [Link]
    
    
55. Wei Zhao, Lingxia Qiao, Shiyu Yan, Qing Nie*, Lei Zhang*. Modeling of histone modifications reveals formation mechanism and function of bivalent chromatin, iScience, 24, 102732 (2021). [Link][Code]
    
    
56. Yuanyuan Xiong, Binbin Wu, Fei Du, Xiaolu Guo, Caihuan Tian, Jinrong Hu, Shouqin Lu, Mian Long, Lei Zhang*, Ying Wang*, Yuling Jiao*. A crosstalk between auxin and brassinosteroid regulates leaf shape by modulating growth anisotropy, Molecular Plant, 14, 949–962 (2021). [Link]
    
    
57. Yucen Han, Jianyuan Yin, Pingwen Zhang, Apala Majumdar, Lei Zhang*. Solution landscape of a reduced Landau--de Gennes model on a hexagon, Nonlinearity, 34, 2048-2069 (2021). [Link]
    
    
58. Ruotai Li, Qiang Du, Lei Zhang*. Numerical discretization of variational phase field model for phase transitions in ferroelectric thin films, Commun. Comput. Phys., 29, 729-746 (2021). [Link]
    
    
59. Bing Yu, Lei Zhang*. Global optimization-based dimer method for finding saddle points, Discrete Contin. Dyn. Syst. Ser. B 26(1): 741-753 (2021). [Link]
    
    
60. Jianyuan Yin, Bing Yu, Lei Zhang*. Searching the solution landscape by generalized high-index saddle dynamics, Sci. China Math. 64, 1801–1816 (2021). [Link]
    
    
61. Kuan Tao, Jin Wang, Xiangyu Kuang, Weikang Wang, Feng Liu*, Lei Zhang*. Tuning cell motility via cell tension with a mechanochemical cell migration model, Biophysical Journal, 118, 2894–2904 (2020). [Link]
    
    
62. Yucen Han, Apala Majumdar, Lei Zhang. A Reduced Study for Nematic Equilibria on Two-Dimensional Polygons, SIAM J. Appl. Math., 80(4), 1678–1703 (2020). [Link]
    
    
63. Qiang Du, Ruotai Li, Lei Zhang. Variational Phase Field Formulations of Polarization and Phase Transition in Ferroelectric Thin Films, SIAM J. Appl. Math., 80(3), 1590–1606 (2020). [Link]
    
    
64. Jianyuan Yin, Yiwei Wang, Jeff Z.Y. Chen*, Pingwen Zhang*, Lei Zhang*. Construction of a pathway map on a complicated energy landscape, Physical Review Letters 124, 090601 (2020). [Link]
    
    
65. Qing Nie*, Lingxia Qiao, Yuchi Qiu, Lei Zhang*, Wei Zhao. Noise control and utility: from gene regulatory network to spatial patterning, Sci. China Math 63, 425–440 (2020). [Link]
    
    
66. Yucen Han, Zirui Xu, An-Chang Shi*,Lei Zhang*. Pathways connecting two opposed bilayers with a fusion pore: A molecularly-informed phase field approach, Soft Matter, 2020, 16, 366-374. [Link]
    
    
67. Jianyuan Yin, Lei Zhang. Pingwen Zhang, High-index Optimization-based Shrinking Dimer Method for Finding High-Index Saddle Points, SIAM Journal on Scientific Computing, 41 (6), A3576-A3595. 2019.[Link]
    
    
68. Lingxia Qiao, Wei Zhao, Chao Tang*, Qing Nie*, Lei Zhang*. Network Topologies That Can Achieve Dual Function of Adaptation and Noise Attenuation, Cell Systems 9, 1–15, 2019.[Link]
    
    
69. Yucen Han, Yucheng Hu*, Pingwen Zhang*, Lei Zhang*. Transition Pathways between Defect Patterns in Confined Nematic Liquid Crystals, J. Comput. Phys. 396 (2019) 1–11.[Link]
    
    
70. Chunhe Li*, Lei Zhang*,Qing Nie*, Landscape reveals critical network structures for sharpening gene expression boundaries, BMC Systems Biology 12:67, 2018. [Link]
    
    
71. Lina Meinecke, Praveer Sharma, Huijing Du, Lei Zhang, Qing Nie*, Thomas Schilling*. Modeling craniofacial development reveals spatiotemporal constraints on robust patterning of the mandibular arch, PLoS Comput Biol 14(11): e1006569, 2018. [Link]
    
    
72. Boyan Li, Lei Zhang*, Chengliang Li, Qiulin Li, Jun Chen, Guogang Shu, Yuqing Weng, Ben Xu, Shenyang Hu*, Wei Liu*. Phase Field Simulation of Critical Nuclei and Minimum Energy Paths of Cu/Mn/Ni Precipitates in Fe-Cu-Mn (Ni) Alloys, Journal of Nuclear Materials 507, 59-67, 2018. [Link]
    
    
73. Peijia Yu, Qing Nie*, Chao Tang*, Lei Zhang*. Nanog induced intermediate state in regulating stem cell differentiation and reprogramming, BMC Systems Biology 12:22, 2018. [Link]
    
    
74. Bihai Shi, Xiaolu Guo, Ying Wang, Yuanyuan Xiong, Jin Wang, Ken-ichiro Hayashi, Jinzhi Lei, Lei Zhang*, Yuling Jiao*. Feedback from Lateral Organs Controls Shoot Apical Meristem Growth by Modulating Auxin Transport, Developmental Cell, 44, 204-216, 2018. [Link]
    
    
75. Boyan Li, Lei Zhang*, Chengliang Li, Shenyang Hu, Qiulin Li, Jun Chen, Guogang Shu, Yuqing Weng, Ben Xu*, Wei Liu*. Finding Non-Classical Critical Nuclei and Minimum Energy Path of Cu Precipitates in Fe-Cu Alloys, Modelling Simul. Mater. Sci. Eng. 25 085006, 2017. [pdf]
    
    
76. Yanru An, Guosheng Xue, Xiaowei Zhou, Weichuan Yu, Toyotaka Ishibashi, Lei Zhang*, Yan Yan*. Apical constriction is driven by a pulsatile apical myosin network in delaminating Drosophila neuroblasts, Development, 144, 2153-2164, 2017. [Link]
    
    
77. Weikang Wang, Kuan Tao, Jin Wang, Gen Yang, Qi Ouyang, Yugang Wang, Lei Zhang*, Feng Liu*. Exploring the inhibition effect of membrane tension on cell polarization, PLoS Comput Biol 13(1): e1005354. doi:10.1371/ journal.pcbi.1005354, 2017. [Link]
    
    
78. Lei Zhang, Weiqing Ren, Amit Samanta, Qiang Du*. Recent Developments in Computational Modeling of Nucleation in Phase Transformations, npj Computational Materials (2016) 2, 16003. [pdf]
    
    
79. Lei Zhang, Qiang Du, Zhenzhen Zheng. Optimization-based Shrinking Dimer Method for Finding Transition States, SIAM Journal on Scientific Computing 38:1, A528-A544, 2016. [pdf]
    
    
80. Amanda Cinquin, Likun Zheng, Harry P. Taylor, Adrian Paz, Lei Zhang, Michael Chiang, Josh Snow, Qing Nie, Olivier Cinquin*. Semi-permeable Diffusion Barriers Enhance Patterning Robustness in the C. elegans Germline, Developmental Cell 35, 405-417, 2015. [pdf]
    
    
81. Tian Hong, Ernest S. Fung, Lei Zhang, Edwin S. Monuki*, Qing Nie*. Semi-adaptive response and noise attenuation in bone morphogenetic protein signalling, J. R. Soc. Interface 12: 20150258, 2015.[pdf]
    
    
82. Lei Zhang, Jingyan Zhang, Qiang Du*. Finding Critical Nuclei in Phase Transformations by Shrinking Dimer Dynamics and its Variants, Commun. Comput. Phys., 16, pp. 781-798, 2014. [pdf]
    
    
83. Yulan Li*, Shenyang Hu, Lei Zhang, Xin Sun. Non-classical nuclei and growth kinetics of Cr precipitates in FeCr alloys during aging, Modelling Simul. Mater. Sci. Eng., 22, 025002, 2014. [pdf]
    
    
84. Dongyong Wang, Lei Zhang, Qing Nie*. Array-representation Integration Factor Method for High-dimensional Systems, J. Comput. Phys., 258, 585-600, 2014. [pdf]
    
    
85. Lei Zhang, Kelly Radtke, Likun Zheng, Anna Cai, Tom Schilling*, Qing Nie*. Noise Drives Sharpening of Gene Expression Boundaries in the Zebrafish Hindbrain, Molecular Systems Biology 8:613, 2012. [pdf]
    
    
86. Lei Zhang, Arthur Lander, Qing Nie*. A Reaction-Diffusion Mechanism Influences Cell Lineage Progression as a Basis for Formation, Regeneration, and Stability of Intestinal Crypts, BMC Systems Biology 6:93, 2012. [pdf]
    
    
87. Lei Zhang, Long-qing Chen, Qiang Du*. Simultaneous Prediction of Morphologies of a Critical Nucleus and an Equilibrium Precipitate in Solids, Commun. Comput. Phys., 7, 674-682, 2010. [pdf]
    
    
88. Tae Wook Heo*, Lei Zhang, Qiang Du, and Long-Qing Chen. Incorporating Non-classical Nuclei in Phase-field Simulations, Scripta Materialia, 63, 8-11, 2010. [pdf]
    
    
89. Lei Zhang*, Long-qing Chen, Qiang Du. Diffuse-Interface Approach to Predicting Morphologies of Critical Nucleus and Equilibrium Structure for Cubic to Tetragonal Transformations, J. Comput. Phys., 229, 6574-6584, 2010. [pdf]
    
    
90. Qiang Du, Lei Zhang. A constrained string method and its numerical analysis, Commun. Math. Sci., 7, 1039-1051, 2009. [pdf]
    
    
91. Lei Zhang, Long-qing Chen, Qiang Du*. Mathematical and Numerical Aspects of Phase-field Approach to Critical Morphology in Solids, Journal of Scientific Computing, 37, 89-102, 2008. [pdf]
    
    
92. Lei Zhang, Long-qing Chen, Qiang Du*. Diffuse-Interface Description of Strain-Dominated Morphology of Critical Nuclei in Phase Transformations, Acta Materialia, 56, 3568-3576, 2008. [pdf]
    
    
93. Lei Zhang*, Long-qing Chen*, Qiang Du*. Morphology of critical nuclei in solid state phase transformations, Physical Review Letters, 98, No.25, 265703, 2007. [pdf]

Conference Publications and Monograph

1. Lei Zhang, Long-qing Chen, Qiang Du. Phase-field Prediction of Critical Nucleus Morphology in Solids", Proceeding of the Fourth International Conference on Multiscale Materials Modeling, Tallahassee, FL, pp. 514-517, October 2008. [pdf]