My research focuses on the numerical and mathematical aspects of computational algorithms for scientific computing problems in complex dynamical systems arising in natural science and engineering. My work integrates tools from probability theory, stochastic processes, dynamical systems, numerical analysis, optimization, optimal control, and machine learning to design efficient methods for better understanding complex phenomena such as rare events.
The major research works include (1) the transition-state/saddle-point calculation on energy landscape; (2) optimal transition pathways in stochastic dynamical systems; (3) rare-event Monte Carlo simulation. More recent projects explore the interplay between machine learning and dynamical systems, with applications to longstanding challenges in rare events, generative approaches for sampling, learning, and models related to data and probility distribution.
I received the BSc from Peking University (School of Mathematical Sciences) and PhD from Princeton University (PACM). Before joining the Department of Mathematics City University of Hong Kong in 2012, he worked as a research associate at Princeton University and Brown University. I also joined the School of Data Science concurrently as one of founding memebers from 2018.
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.
Journal
- (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
- (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
- 2020 - 2025, Undergraduate , SDSC2002 Convex Optimization.
- 2018 - Now, Postgraduate , MA6630 Introduction to Statistical Learning .
- 2013 - 2018, Undergraduate , MA4546 Introduction to Stochastic Process.
Last update date :
15 Feb 2025
