Tiejun Li (李铁军)

Numerical Analysis (in chinese): 《数值分析》(英国BEAT365官网出版社), with Pingwen Zhang. An errata is here.

Applied Stochastic Analysis, in GSM series, vol. 199 by American Mathematical Society, with Weinan E and Eric Vanden-Eijnden. An errata is here.

Algorithmic and Theoretical Studies for scRNA-seq Data Analysis: scRNA-seq data analysis provides a great platform for applied mathematicians, in which the stochastic dynamics, statistical data analysis and machine learning can be integrated to boost the understanding of cell developments. In this field, we collaborate with the biologists like Prof. Fuchou Tang (PKU), and the applied mathematicians like Prof. Luonan Chen (CAS), Qing Nie (UC Irvine), and Xiaojie Qiu (MIT) et al.

• Deciphering Cell-fate Trajectories Using Spatiotemporal Single-cell Transcriptomic Data, with Zhenyi Zhang, Zihan Wang, Yuhao Sun, Jiantao Shen, Qiangwei Peng, Peijie Zhou, npj Syst. Biol. Appl., 12:2 (2026).
• Integrating Dynamical Systems Modeling with Spatiotemporal scRNA-Seq Data Analysis, with Zhenyi Zhang, Yuhao Sun, Qiangwei Peng, Peijie Zhou, Entropy 27 (2025), 453.
• WFR-MFM: One-Step Inference for Dynamic Unbalanced Optimal Transport, with Xinyu Wang, Ruoyu Wang, Qiangwei Peng, Peijie Zhou, ICML 2026.
• WFR-FM: Simulation Free Dynamic Unbalanced Optimal Transport, with Qiangwei Peng, Zihan Wang, Junda Ying, Yuhao Sun, Qing Nie, Lei Zhang, Peijie Zhou, ICLR 2026.
• stVCR: Spatiotemporal Dynamics of Single Cells, with Qiangwei Peng, Peijie Zhou, Nature Methods, 23 (2026), 542-553.
• Variational Regularized Unbalanced Optimal Transport: Single Network, Least Action, with Yuhao Sun, Zhenyi Zhang, Zihan Wang, Peijie Zhou, NeurIPS 2025.
• Modeling Cell Dynamics and Interactions with Unbalanced Mean Field Schrödinger Bridge, with Zhenyi Zhang, Zihan Wang, Yuhao Sun, Peijie Zhou, NeurIPS 2025.
• Learning stochastic dynamics from snapshots through regularized unbalanced optimal transport, with Zhenyi Zhang, Peijie Zhou, ICLR 2025 Oral, 19888-19919.
• Storm: Incorporating transient stochastic dynamics to infer the RNA velocity with metabolic labeling information, with Qiangwei Peng, Xiaojie Qiu, PLoS Comput. Biol., 20 (2024), e1012606.
• Spatial transition tensor of single cells, with Peijie Zhou, Federico Bocci, Qing Nie, Nature Methods, 21 (2024), 1053-1062.
• Energy landscape decomposition for cell differentiation with proliferation effect, with Jifan Shi, Kazuyuki Aihara, and Luonan Chen, National Science Review, 9 (2022), nwac116.
• Integrating single-cell datasets with ambiguous batch information by incorporating molecular network features, with Ji Dong, Peijie Zhou, Yichong Wu, Wendong Wang, Yidong Chen, Xin Zhou, Haoling Xie, Jiansen Lu, Xiannian Zhang, Lu Wen, Wei Fu, and Fuchou Tang, Briefings in Bioinformatics, 23 (2022), bbab366.
• On the mathematics of RNA velocity II: algorithmic aspects, with Yizhuo Wang, Guoguo Yang, Peijie Zhou, CSIAM Trans. Appl. Math. 5 (2024), 182-220.
• On the mathematics of RNA velocity I: theoretical analysis, with Jifan Shi, Yichong Wu, and Peijie Zhou, CSIAM Trans. Appl. Math. 2 (2021), 1-55.
• Dissecting transition cells from single-cell transcriptome data through multiscale stochastic dynamics, with Peijie Zhou, Shuxiong Wang, Qing Nie, Nature Comm., 12 (2021), 5609.
• Quantifying pluripotency landscape of cell differentiation from scRNA-seq data by continuous birth-death process, with Jifan Shi, Luonan Chen, and Aihara, PLoS Comp. Biol. 15 (2019), e1007488.
• Quantifying Waddington’s epigenetic landscape: a comparison of single-cell potency measures, with Jifan Shi, Andrew E. Teschendorff, Weiyan Chen, and Luonan Chen, Briefings in Bioinformatics 21 (2020), 248-261.

Stochastic Dynamics and Data Analysis in Life Sciences: We are also trying to develop theory and algorithms for the stochastic problems in life sciences, especially the chemical reaction kinetics and genetic interactions in the cellular level. It is surprising that the stochastics can play so important role in life sciences. In this field, we collaborate with the physicists like Prof. Qi Ouyang, Fangting Li (PKU), and the applied mathematicians like Prof. Luonan Chen (CAS) et al.

• EPR-Net: Constructing non-equilibrium potential landscape via a variational force projection formulation, with Yue Zhao, Wei Zhang, Nat. Sci. Rev. 11 (2024), nwae052.
• Uncovering the cell fate decision in lysis-lysogeny transition and stem cell development via Markov state modeling, with Xiaoguang Li, Tongkai Li, and Chunhe Li, J. Chem. Phys., 155 (2021), 245101.
• Stochasticity triggers activation of the S-phase checkpoint pathway in budding yeast, with Peijie Zhou, Xin Gao, Xiaoli Li, Linxi Li, Caoyuan Niu, Qi Ouyang, Huiqiang Lou, and Fangting Li, Phys. Rev. X 11 (2021), 011004.
• No-oscillation theorem for the transient dynamics of the linear signal transduction pathway and beyond, with Tongkai Li and Shaoying Lu, Discret. Contin. Dyn. Syst. B 25 (2020), 2749-2774.
• Differential network inference via the fused D-trace loss with cross variables, with Yichong Wu, Xiaoping Liu, and Luonan Chen, Electr. J. Stat. 14 (2020), 1269-1301.
• Quantifying direct dependencies in biological network by multiscale association analysis, with Jifan Shi, Juan Zhao, and Luonan Chen, IEEE Trans. Comput. Biol. Bioinform. 17 (2020), 449-458.
• Detecting direct associations in a network by information theoretic approaches, with Jifan Shi, Juan Zhao, and Luonan Chen, Sci. China Math. 62 (2019), 823-838.
• Large deviations for two-scale chemical kinetic processes, with Feng Lin, Comm. Math. Sci. 15 (2017), 123-163.
• Two-scale large deviations for chemical reaction kinetics through second quantization path integral, with Feng Lin, J. Phys. A: Math. Theor. 49 (2016), 135204.
• Construction of the landscape for multi-stable systems: Potential landscape, quasi-potential, A-type integral and beyond, with Peijie Zhou, J. Chem. Phys. 144 (2016), 094109.
• Energy landscape reveals that the budding yeast cell cycle is a robust and adaptive multi-stage process, with Cheng Lv, Xiaoguang Li and Fangting Li, PLoS Comp. Biol. 11 (2015), e1004156. SI
• Constructing the energy landscape for genetic switching system driven by intrinsic noise, with Cheng Lv, Xiaoguang Li and Fangting Li, PLoS One 9 (2014), e88167. SI
• Highly accurate tau-leaping methods for simulating chemically reacting systems, with Yucheng Hu, J. Chem. Phys 130 (2009), 124109.
• Analysis of explicit tau-leaping schemes for simulating chemically reacting systems, SIAM Multi. Mod. Simul. 6 (2007), 417-436.

Channel Estimation in Wireless Communications: We are trying to develop powerful strategies for the channel estimation in wirelss communications, which include highly efficient optimization methods in compressive sensing and really applicable methods in real application scenarios.

• DDA-Net: Accurate TDD Channel Estimation via Deep Unfolding the Doppler-Delay-Angle Representation of Channel Signals, with Yufei Ma, Xu Zhu, arXiv 2026.
• Covering-radius and Collinearity- Minimizing Pilots for Channel Estimation in TDD Systems, with Xu Zhu, Yi Zeng, arXiv 2026.
• Alternating Subspace Method for Sparse Recovery of Signals, with Xu Zhu, Yufei Ma, Xiaoguang Li, arXiv 2026.
• QNOMP: A Quasi-Newton-based Joint Multipath Optimization Method for Super-resolution Channel Estimation and Extrapolation, with Yi Zeng, Mingguang Han, Xiaoguang Li, IEEE Access, 13 (2025), 212652.
• DMRA: An adaptive line spectrum estimation method through dynamical multi-resolution of atoms, with Mingguang Han, Yi Zeng, Xiaoguang Li, IEEE Trans. Sig. Proc., 73 (2025), 1759-1774.

Other Selected Publications

Stochastic Dynamics and Data Analysis in Life Sciences: We are also trying to develop theory and algorithms for the stochastic problems in life sciences, especially the chemical reaction kinetics and genetic interactions in the cellular level. It is surprising that the stochastics can play so important role in life sciences. In this field, we collaborate with the physicists like Prof. Qi Ouyang, Fangting Li (PKU), and the applied mathematicians like Prof. Luonan Chen (CAS) et al.

• Riemannian Denoising Diffusion Probabilistic Models, with Zichen Liu, Wei Zhang, Comm. Math. Sci. 24 (2026), 1267-1295.
• Improving the Euclidean Diffusion Generation of Manifold Data by Mitigating Score Function Singularity, with Zichen Liu, Wei Zhang, NeurIPS 2025.
• Revisiting the central limit theorems of stochastic gradient type methods, with Tiannan Xiao, Guoguo Yang, Comm. Math. Sci., 22 (2024), 1427-1454.
• Transition path theory for Langevin dynamics on manifolds: optimal control and data-driven solver, with Yuan Gao, Xiaoguang Li, and Jianguo Liu, SIAM Multi. Model. Simul. 21 (2023), 1-33.
• Gamma-Limit of the Onsager-Machlup Functional on the Space of Curves, with Xiaoguang Li, SIAM J. Math. Anal. 53 (2021), 1-31.
• The graph limit of the minimizer of the Onsager-Machlup functional and its computation, with Qiang Du, Xiaoguang Li and Weiqing Ren, Sci. China Math. 64 (2021), 239-280.
• Analysis of the closure approximation for a class of stochastic differential equations, with Yunfeng Cai, Jiushu Shao and Zhiming Wang, Numer. Math. Theor. Meth. Appl. 10 (2017), 299-330.
• Finding transition pathways on manifolds, with Xiaoguang Li and Xiang Zhou, SIAM Multi. Model. Simul. 14 (2016), 173-206.
• Towards a critical transition theory under different temporal scales and noise strengths, with Jifan Shi and Luonan Chen, Phys. Rev. E 93 (2016), 032137.
• Adiabatic elimination for systems with inertia driven by compound Poisson colored noise, with Bin Min and Zhiming Wang, Phys. Rev. E 89 (2014), 022144.
• Marcus canonical integral for non-Gaussian processes and its computation: Pathwise simulation and tau-leaping algorithm, with Bin Min and Zhiming Wang, J. Chem. Phys. 138 (2013), 104118.
• Nucleation rate calculations for the phase transition of diblock copolymers under stochastic Cahn-Hilliard dynamics, with Wei Zhang and Pingwen Zhang, SIAM Multi. Model. Simul. 11 (2013), 385-409.
• Transport in weak dynamic disorder: a unified theory, with Bin Min, Phys. Rev. E 88 (2013), 052140.
• Numerical study for the nucleation of one-dimensional stochastic Cahn-Hilliard dynamics, with Wei Zhang and Pingwen Zhang, Comm. Math. Sci. 10 (2012), 1105-1132.
• Subdiffusive spreading of a Bose-Einstein condensate in random potentials, with Weizhu Bao, Bin Min, and M. Rosenkranz, Phys. Rev. A 86 (2012), 053612.
• Localized basis of eigen-subspaces and operator compression, with Weinan E and Jianfeng Lu, Proc. Nat. Acad. Sci. USA, 107 (2010), 1273.
• Probabilistic framework for network partition, with Weinan E and Jian Liu, Phys. Rev. E 80 (2009), 026106.
• Optimal partition and effective dynamics of complex networks, with Weinan E and Eric Vanden-Eijnden, Proc. Nat. Acad. Sci. USA, 105 (2008), 7907-7912. SI
• S-ROCK methods for stiff Ito SDEs, with Assyr Abdulle, Comm. Math. Sci. 6 (2008), 845-868.
• Mathematical analysis of multiscale models of complex fluids, with Pingwen Zhang, Comm. Math. Sci. 5 (2007), 1-51.
• On the Poisson approximation for photon distribution for faint lasers, with Yucheng Hu, Xiang Peng and Hong Guo, Phys. Lett. A, 367 (2007), 173-176.
• Local existence for the dumbbell model of polymeric fluids, with Hui Zhang and Pingwen Zhang, Comm. PDE, 29 (2004), 903-923.
• Well-posedness for the dumbbell model of polymeric fluids, with Weinan E and Pingwen Zhang, Comm. Math. Phys. 248 (2004), 409-427.
• Stochastic models of polymeric liquids at small Deborah number, with Eric Vanden-Eijnden, Pingwen Zhang, and Weinan E, J. Non-Newtonian Fluid Mech. 121 (2004), 117-125.

We have funding for postdoc positions. If you have interests to perform research in stochastic modeling and computations, e.g. mathematical life sciences, machine learning, numerical methods for SDEs, applications in rare events, etc. Please send your CV and application letter to me directly.