ZHOU, Xiang (周 翔), PhD

http://personal.cityu.edu.hk/~xizhou/index.html

My main  works  are on rare event (transition path, saddle point, importance sampling, application)  as well as the noisy nonlinear dynamics and multiscale method. My current interests are   energy landscape for machine learning, and the interface between optimal control and  machine learning. 

PUBLICATION 

https://www.researchgate.net/profile/Xiang_Zhou26

ORCID

• 2018
  • 
    
  • Two-parameter asymptotic expansions for elliptic equations with small geometric perturbation and high contrast ratio (with J Chen, L Lin, Z Zhang,  submitted in Sept. 2017) 
  • …. . . 
  • Simplified Gentlest Ascent Dynamics for Saddle Points in Non-gradient Systems (ST Gu and X Zhou,, Chaos. 28, 123106,  Dec. 2018)
  • Quasi-Potential Calculation and Minimum Action Method for Limit Cycle (L. Lin,  H. Yu and X Zhou, accepted , JNLS, Oct 2018). 
  • Estimation of exciton diffusion lengths of organic semiconductors in random domains (  J. Chen, L. Lin, Z. Zhang, X. Zhou,   J. Comp. Phys. , accepted  2018)
  • Moderate Deviation For Random Elliptic PDE With Small Noise (  X. Li, J. Liu, J. Lu, X. Zhou  Ann. Appl. Probab., Volume 28, Number 5 (Oct. 2018), 2781-2813.)  
  • Asymptotic Expansion with Boundary Layer Analysis for Strongly Anisotropic Elliptic Equation (L Lin and X Zhou, Comm. Math. Sci. , vol 16, no 3, 636-658, 2018).
  • An Improved Adaptive Minimum Action Method for the Calculation of Transition Path in Non-gradient Systems (  Y. Sun and X. Zhou, Commun. Comput. Phys., vol. 24, No. 1, pp. 44-68,  July 2018)
  • —  — 
  • Asymptotically efficient simulation of elliptic problems with small random forcing.  (with X. Wan, SIAM J. SCI. COMPUT. Vol. 40, No. 1, pp. A548-A572. 2018)   bib
  • Convex Splitting Method for  the  Calculation of  Transition States of Energy Functional  (  ST  Gu and X Zhou,   J. Comp. Phys.  353, pp 417-434, 2018)

• 2017
  • Multiscale gentlest ascent dynamics for saddle point in effective dynamics of slow-fast system (S. Gu and X. Zhou, Comm. Math. Sci. vol 15, no. 8, pp 2279-2302, 2017).
  • — — 
  • Sensitivity analysis and optimization of  reaction rate  (  S. Gu,  L. Lin and X. Zhou, Comm. Math. Sci.  vol.15, No. 6, pp.1507-1525, 2017)
• 2016
  • — — 
  • Explore stochastic instabilities of periodic points  by transition path theory (  Y. Cao, L. Lin and X. Zhou,  J. Nonlinear Sci., vol 26, issue 3, pp755-786,  March 2016.)
  • Finding transition pathways on manifolds  (with T. Li,  X. Li, Multiscale Model Simul., vol 14, pp173-206, Jan. 2016) 
  • Iterative minimization algorithm for efficient calculations of transition states (W. Gao, J. Leng and X. Zhou,  J. Comp. Phys. vol 309, pp 69-87.  Jan. 2016)
• 2010--2015
  
  • An iterative minimization formulation for saddle-point search  (IMF)(  W. Gao,  J. Leng and X. Zhou,  SIAM J. Numer. Anal., vol. 53, no.4, 1786–1805,  July, 2015: typo correction for Eqn4.3a: x^(k+1)\to x^(k))
  • Escaping from an Attractor: Importance Sampling and Rest Points (   P. Dupuis, K. Spiliopoulos and X. Zhou,  Ann. Appl. Prob., Vol 25, No. 5, 2909-2958, 2015)    
  • —  — 
  • Efficient rare event simulation for failure problems in random media (with J. Liu and J. Lu,   SIAM J. Sci. Comput. vol.37, No. 2,  March 2015 )
  • A cross-entropy scheme for mixtures(H. Wang and X. Zhou,  TOMACS, vol. 25, no. 1, 6:1-6:20, Jan. 2015).
  • Extreme analysis of a random ordinary differential equation (  J. Liu and X. Zhou, J. Appl. Probab., vol. 51, no.4, p1021-1036, 2014)
  • On the failure Probability of one dimensional random material under delta external force (  J. Liu and X. Zhou, Comm. Math. Sci., 11, pp. 499-521, 2013) 
  •  Subcritical bifurcation in spatially extended systems ( W. E, X. Zhou and  X. Cheng, Nonlinearity, vol. 25, pp. 761, 2012)
  • The gentlest ascent dynamics  (GAD) (  W. E and X Zhou, Nonlinearity, vol. 24, no. 6, pp. 1831, 2011)
  • Failure of random materials: a large deviation and computational study (with J. Liu et al.) Proceedings of the 2011 Winter Simulation Conference, p3779, Dec. 2011.
•  before 2010
  
  • Study of the noise-induced transition and the exploration of the phase space for the Kuramoto-Sivashinsky equation using the minimum action method. (X. Wan, X Zhou and W. E, Nonlinearity, vol. 23, pp. 475-493, 2010.) 
  • Study of noise-induced transitions in the Lorenz system using the minimum action method. ( X. Zhou and W. E, Comm. Math. Sci., vol.  8,  no. 2, pp. 341-355, 2010.)
  • Time-varying perturbations can distinguish among integrate-to-threshold models for per- ceptual decision-making in reaction time tasks. ( X. Zhou, KongFatt Wong-Lin and Philip Holmes, Neural Computation, vol. 21, pp. 2336-2362, 2009) 
  • Adaptive minimum action method for the study of rare events. ( X. Zhou, W. Ren and W. E, J. Chem. Phys., vol 128, pp. 104111, 2008.) 
  • Analysis of 1+1 dimensional stochastic model of liquid crystal polymer flows. (   T. Li, P.  Zhang and X. Zhou,  Comm. Math. Sci. vol. 2, pp. 295-316, 2004.) 

• https://www.researchgate.net/profile/Xiang_Zhou26
• http://orcid.org/0000-0002-3835-3894

Acknowledgement: My work at CityU is financially supported by

CityU Start-Up  (2012-2014, 200,000 HKD)

ECS 109113     (2013-2016, 710,223 HKD)

GRF 11304314 (2014-2017, 614,810 HKD)

GRF 11304715 (2015-2018, 631,972 HKD) 

GRF 11337216 (2016-2019, 488,501 HKD) 

GRF 11305318 (2019-2021, 456,452 HKD)