Tian-Zhi Li 李天志
About me
I am a final-year PhD student at Peking University (PKU), working with Professors Zhisheng Duan and Jinzhi Wang. From Dec 2024 to Nov 2025, I was fortunate to work as a visiting PhD at Nanyang Technological University (NTU), Singapore, with Professor François Gay-Balmaz. Prior to that, I received my B.Sc. in Mathematics from Beijing Institute of Technology (BIT) in 2021 under the supervision of Professor Donghua Shi.
Research Interest
My research interest lies at geometric modeling and simulation of dynamical systems, which includes the following topics:
Geometric Mechanics & Control (especially Stochastic & Nonholonomic)
Geometric Numerical Integration (Variational Integrators)
Geometric Estimation and Filtering (for Robot Systems & Flexible Systems)
Physics-Informed Learning on Manifolds
Selected Research
 |
Variational Principle for Stochastic Nonholonomic Systems Part II: Stochastic Nonholonomic Integrator International Conference on Geometric Science of Information (GSI 2025), Saint-Malo, France. Lecture Notes in Computer Science, vol 16034, pp. 225-233. Springer, Cham, 2026. We propose stochastic discrete variational principles for stochastic nonholonomic systems and construct the associated stochastic nonholonomic integrator. |
 |
Variational Unscented Kalman Filter on Matrix Lie Groups Automatica, 172: 111995, 2025 (Regular Paper). We propose a family of computationally efficient unscented Kalman filters (UKF-Vs) for mechanical systems on matrix Lie groups. |
 |
Reduced Dynamics and Geometric Optimal Control of Nonequilibrium Thermodynamics: Gaussian Case Automatica, 164: 111626, 2024 (Regular Paper). We study the geometric structures of n-DOF Gaussian distributions, and we propose a geometric optimal control algorithm for minimum-energy optimal control problem of Gaussian distributions. |
 |
Physics-Informed Gaussian Process Learning on Lie Groups Journal of Guidance, Control, and Dynamics, 48 (11), pp. 2654-2662, 2025. We introduce a physics-informed Gaussian process learning method for mechanical systems on Lie groups and on a special class of homogeneous manifolds based on discrete mechanics theory. |
News
Sep 2025: I am so happy and excited to recieve the National Scholarship (top 1%) from Chinese Ministry of Education!
Aug 2025: Our paper Structure-Preserving Unscented Kalman Filter for Planar Mobile Robots has been accepted to IEEE Control Systems Letters (IEEE L-CSS).
Aug 2025: Our paper Physics-Informed Gaussian Process Learning on Lie Groups has been accepted to Journal of Guidance, Control, and Dynamics (JGCD).
Jul 2025: Our two papers Variational Principle for Stochastic Nonholonomic Systems Part I & Part II (joint work with Professors François Gay-Balmaz, Donghua Shi, and Jinzhi Wang) have been accepted by the International Conference on Geometric Science of Information (GSI 2025).
Jun 2025: I am humbled and beyond grateful to recieve the PKU Presidential Doctoral Scholarship (2025-2026)!
Dec 2024: I am so happy and excited to be a visiting student under the supervision of Prof. François Gay-Balmaz at Nanyang Technological University (NTU) in Singapore!
Nov 2024: I am very honored to recieve the PKU-CoE Dean's Scholarship-First Prize, 2024-2025!
Sep 2024: Our paper Variational Unscented Kalman Filter on Matrix Lie Groups has been accepted to Automatica.
Jul 2024: I was thrilled to present “Stochastic Nonholonomic Variational Principle” at the Geometric Mechanics & Control Seminar (BIT) organized by Prof. Donghua Shi. The discussion with Prof. Hiroaki Yoshimura and Prof. Linyu Peng was very insightful and interesting!
Jul 2024: I am so happy to announce that I am awarded the CSC Scholarship! I will be a visiting student of Prof. François Gay-Balmaz at Nanyang Technological University (NTU) for a 12-month academic visit.
Apr 2024: I was thrilled to give a talk about my PhD work at Beijing Institute of Technology (BIT) invited by Prof. Qiang Tian and Prof. Ju Chen. The discussion was very insightful and interesting!
Feb 2024: Our paper Reduced Dynamics and Geometric Optimal Control of Nonequilibrium Thermodynamics: Gaussian Case has been accepted by Automatica.
Aug 2023: I was thrilled to present “Multisymplectic Unscented Kalman Filter for Geometrically Exact Beams” at the 6th International Conference on Geometric Science of Information (GSI)! I am very grateful to Prof. Hiroaki Yoshimura and Dr. Christian Offen for their valuable comments and suggestions on my work! Also, I was very lucky to meet Stephanie Chen, Daiying Yin, and Takemi Nakamura. We had some happy time at Saint-Malo, France!
Jul 2023: I was honored to present ’'Variational Unscented Kalman Filter on Lie Groups’’ at the Geometric Mechanics & Control Seminar (BIT) organized by Prof. Donghua Shi and Prof. Dmitry Zenkov.