Prof. ZHOU Xiang (周翔博士)

PhD(Princeton University)
B.Sc. (Peking University)

Associate Professor

Contact Information

Office:	YEUNG-B-5102 Department of Mathematics, City University of Hong Kong
Phone:	(+852) 3442-6421
Fax:	(+852) 3442-0515
Email:	xizhou@cityu.edu.hk
Web:	Researchgate

Research Interests

applied and computational mathematics
rare event
stochastic dynamical system and machine learning.

My research focuses on the mathematical foundations and numerical analysis of computational methods for complex stochastic dynamical systems arising in the natural sciences and engineering. My work integrates tools from computational mathematics, applied stochastic processes, numerical analysis, optimal control, and machine learning to build mathematical models, design efficient algorithms, and conduct rigorous analysis for understanding complex phenomena such as rare transition events.

My major research contributions include (1) transition-state (saddle-point) computation on energy landscapes; (2) optimal transition pathways in stochastic dynamical systems; and (3) Monte Carlo simulation of rare events. My more recent projects explore the interplay between machine learning and dynamical systems, addressing longstanding challenges in rare-event studies as well as generative approaches to sampling, learning, and the modelling of probability distributions from data.

I received my BSc from Peking University (School of Mathematical Sciences) and my PhD from Princeton University (Program in Applied and Computational Mathematics). Before joining the Department of Mathematics at City University of Hong Kong in 2012, I worked as a research associate at Princeton University and Brown University. From 2018 to 2024, I also served concurrently in the School of Data Science.

For PhD studentship applicants, please refer to the researchgate link at the right panel for details. https://www.researchgate.net/publication/377305937_Openings

Previous Experience

2 Jan 2025 - Now, Associate Professor, Department of Mathematics, City University of Hong Kong.
2 Jan 2025 - Now, Associate Professor, Department of Data Science, City University of Hong Kong. (Affiliated).
1 Aug 2018 - 31 Aug 2024, Associate Professor, School of Data Science, City University of Hong Kong.
May 2012 - Jul 2018, Assistant Professor, Department of Mathematics, City University of Hong Kong.

Patents

ZHOU, Xiang (Inventor); XIAO, Bo (Inventor); PENG, Xianhua (Inventor)., 一種基於機器學習的金融衍生品對沖方法, China Patent No. 202410179678.4.

Publications Show All Publications Show Prominent Publications

Journal

Cai, Zhiqiang. , Cao, Yu. , Huang, Yuanfei. & Zhou, Xiang. (Jul 2026). Weak generative sampler to efficiently sample invariant distribution of stochastic differential equation. SIAM Scientific Computing. 48/4. C708 - C735. doi:10.1137/24M1665271
Huang, Yuanfei. , Liu, Chengyu. & Zhou, Xiang. (May 2026). Lévy Score Function and Score-Based Particle Algorithm for Nonlinear Lévy–Fokker–Planck Equations. SIAM Numerical Analysis. doi:10.1137/24M1721311
(Spring 11 Feb 2026). Entropy Production in Non-Gausian Active Matter: A Unified Fluctuation Theorem and Deep Learning Framework. Physics Review Letter. 136, 068302. doi:10.1103/y94p-4qcz
(Nov 2022). Active Learning for Transition State Calculation. J. Sci. Comput. .
(Oct 2022). Value-Gradient based Formulation of Optimal Control Problem and Machine Learning Algorithm. SIAM J. Numer. Anal. .
(Jan 2022). Learn Quasi-Stationary Distributions of Finite State Markov Chain. Entropy. 24(1). 133 doi:10.3390/e24010133
(May 2020). Stochastic dynamics of an active particle escaping from a potential well. Chaos. 30. 053133 doi:10.1063/1.5140853
(June 2019). Quasi-potential calculation and minimum action method for limit cycle. Journal of Nonlinear Science. 29. 961 - 991. doi:10.1007/s00332-018-9509-3
(March 2016). Iterative minimization algorithm for efficient calculations of transition states. Journal of Computational Physics. 309. 69 - 87. doi:10.1016/j.jcp.2015.12.056
(January 2015). A cross-entropy scheme for mixtures. ACM Transactions on Modeling and Computer Simulation. 25. doi:10.1145/2685030
(June 2011). The gentlest ascent dynamics. Nonlinearity. 24. 1831 - 1842. doi:10.1088/0951-7715/24/6/008

Conference Paper

Tepakbong, Nathanael. , Hu, Hanyu. , Liu, Chengyu. & Zhou, Xiang. (2026). Taming the Loss Landscape of PINNs with Noisy Feynman–Kac Supervision: Operator Preconditioning and Non-Asymptotic Error Bounds. 43rd International Conference on Machine Learning. Seoul. South Korea: .
(22 Sep 2023). Exploring the Optimal Choice for Generative Processes in Diffusion Models: Ordinary vs Stochastic Differential Equations. NeurIPS 2023 poster.
(December 2023). Roughness Index for Loss Landscapes of Neural Network Models of Partial Differential Equations. 2023 IEEE International Conference on Big Data.
(Dec 2022). Residual-Quantile Adjustment for Adaptive Training of Physics-informed Neural Network. IEEE International Conference on Big Data.

Service in CityUHK

Teaching Service

2025 - Now, Postgraduate, MA6635: Mathematical Foundations of Data Science.
2020 - 2025, Undergraduate , SDSC2002 Convex Optimization.
2018 - Now, Postgraduate , MA6630 Introduction to Statistical Learning .
2013 - 2018, Undergraduate , MA4546 Introduction to Stochastic Process.