* Uncertainty Quantification: "uncertainty is anywhere", UQ aims to include uncertainty in mathematical models and quantify its effect on output of interest used in decision making. UQ has a variety of applications, including hydrology, fluid mechanics, data assimilation, and weather forecasting. I study this topic with collaborators including: Akil Narayan (Utah), Fabio Nobile (EPFL), John Jakeman (Sandia), Tao Tang (SUSTech), Dongbin Xiu (Utah), Zhiqiang Xu (CAS). In case you are interested in this topic, you are welcome to take a look at my review paper (PDF in Chinese), and the paper is written in honor of Prof. Qun Lin's 80th birthday.
* Forward backward stochastic differential equations (FBSDEs): which have comprehensive applications in stochastic optimal control, computational finance, nonlinear filtering, etc. Prof. Weidong Zhao from Shandong University is an international expert in this area. I study this topic also with Yu Fu (SDU), Bo Gong (HKBU), Wenbin Liu (Kent) , and Tao Tang (SUSTech).
* Spectral methods, Parareal, Fractional PDEs, ect.
* Mini-symposia Organizer: ICOSAHOM18, 9--13 July, 2018, London, UK.
* Mini-symposia Organizer & Invited Mini-symposia Speaker: SIAM UQ18, Apr. 16--19, 2018, CA, USA.
* Starting from Jan. 2018, I will be one of the Managing Editors for E. Asian J. Appl. Math.
Editorial Board and Awards:
* Top 10 Scientific Research Achievement by AMSS, 2017. (十大科研进展)
* Member of Youth Innovation Promotion Association by CAS, 2017. (中科院青年创新促进会会员)
* Chen Jingrun Future Star by AMSS, 2017. (陈景润未来之星)
* Excellent Young Scholar Prize by CSIAM, 2016. (中国工业与应用数学学会优秀青年学者奖)
* Associate Editor: Commun. Comput. Phys. (CUP, IF: 2.004)
* Editorial Board: Int. J. Uncertainty Quantification. (Begellhouse, IF: 1.007)
* Associate Editor: Numer. Math: Theor. Meth. Appl. (CUP, IF: 0.509)
-- Mar.2017 -- Now, Associate professor, Institute of Computational Mathematics and Scientific/Engineering Computing , Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, China.
-- Jul.2011-- Mar.2017, Assistant professor, Institute of Computational Mathematics and Scientific/Engineering Computing , Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, China.
-- Sep.2011-Sep.2012, Postdoc research fellow, CSQI, Department of Mathematics, Ecole Polytechnique Fédérale de Lausanne ( EPFL), Switzerland.
* Jan.2012-Dec.2015, High-performance numerical algorithms for stochastic differential equations and their applications, NSFC, No.91130003 (Co-PI, RMB 4 Million 重大研究计划重点项目)
* Jan.2013-Dec.2015, Numerical methods for non-linear hyperbolic equations with random parameters, NSFC, No.11201461 (PI, RMB 220, 000, 青年基金)
* Jan.2016-Dec.2016, Muti-symplectic methods and uncertainty quantification for SPDEs. , NSFC, No.91530118 (Co-PI, RMB 1 Million, 重大研究计划重点项目延续).
* Jan.2016-Dec.2019, Efficient stochastic collocation methods with applications to uncertainty quantification NSFC, No.11571351 (PI, RMB 532,000, 面上基金).
* Jan.2017-Dec.2019, Efficient numerical methods for stochastic Hamiltonian PDEs, NSFC, No.91630312 (Co-PI, RMB 3 Million, 重大研究计划集成项目).
* Jan.2017-Dec.2019, Theory and algorithms for the recovery of signals using incomplete measurements, NSFC, No.91630203 (Co-PI, RMB 2 Million, 重大研究计划重点项目).
* Jan.2018-Dec.2022, High order methods for UQ with applications to environement sciences, NSFC, No. 11731006 (Co-PI, RMB 2.8 Million, 重点项目).
* Jan.2018-Dec.2021, Science challenge project by COSTIND, No. TZ2016001 (Group leader, RMB 20 Million, 国防科工委挑战计划, UQ方向负责人, 领域总经费1.11亿).
38, Shulin Wu, and Tao Zhou, Analysis of the diagonalization-based parallel coarse-grid correction in parareal algorithms, submitted to J. Sci. Comput., 2017.
37, Shulin Wu, Tao Zhou, and Xiaojun Chen, Iterative algorithms for dynamic nonlinear complementarity problems with applications to random nonlinear switch circuits, submitted to SINUM, 2017.
36, Shulin Wu and Tao Zhou, Analysis of a periodic-like waveform relaxation method for initial value problems via diagonalization, submitted to Numer. Math., 2017
35, Yabing Sun, Weidong Zhao, Tao Zhou, An explicit \theta-scheme for mean field forward backward stochastic differential equations, submitted to SINUM, 2017.
34, Shulin Wu and Tao Zhou, Parareal algorithms with multi-fidelity propagators for acoustic wave propagation in random medium, preprint, 2017.
33, Yu Fu, Weidong Zhao, and Tao Zhou, A second order numerical scheme for stochastic optimal control via FBSDEs, submitted to SIAM J. Sci. Comput., 2017.
32, Zhiqiang Xu and Tao Zhou, A gradient enhanced L^1 recovery for sparse Fourier expansions, submitted to Commun. Comput. Phys., 2017.
31, Ling Guo, Akil Narayan, Dongbin Xiu, and Tao Zhou, A gradient enhanced L^1 mininization for sparse approximation of polynomial chaos expansions, preprint, 2017.
30, Akil Narayan, Liang Yan, and Tao Zhou, Quasi-optimal meshes for RBF interpolation with applications to uncertainty quantification, preprint, 2017.
29, Shulin Wu and Tao Zhou, Parareal algorithms with local time-integrators for time fractional differential equations, J. Comput. Phys., 358:135-149, 2018.
28, Ling Guo, Akil Narayan, Liang Yan, and Tao Zhou, Weighted approximate Fekete points: sampling for least-squares polynomial approximation, to appear in SIAM J. Sci. Comput., 2018.
27, Tao Tang, Huifang Yuan, and Tao Zhou, Hermite spectral collocation methods for fractional PDEs in unbounded domain, to appear in Commun. Comput. Phys., 2018. (Special issue for Prof. Houde Han's 80th birthday)
26, Bo Gong, Wenbin Liu, Tao Tang, Weidong Zhao, and Tao Zhou, An Efficient gradient projection methods for stochastic optimal control problems, SIAM J. Numer. Anal., 55(6), 2982–3005.2017.
25, Yu Fu, Weidong Zhao and Tao Zhou, Efficient sparse grid approximations for multi-dimensional coupled forward backward stochastic differential equations, DCDS-B, 22(9), pp. 3439-3458, 2017.
24, John Jakeman, Akil Narayan, and Tao Zhou, A generalized sampling and preconditioner scheme for sparse approximation of polynomial chaos expansions, SIAM J. Sci. Comput., 39-3, pp. A 1114 -1144, 2017.
23, Tao Tang, Weidong Zhao, and Tao Zhou, Deferred correction methods for forward backward stochastic differential equations, Numer. Math. Theor. Meth. Appl., 10(2), pp. 222-242, 2017. (Special issue for Prof Zhenhuan Teng's 80th birthday)
22, Akil Narayan, John Jakeman, and Tao Zhou, A Christoffel function weighted least squares algorithm for collocation approximations, Math. Comput., (86)2017, pp.1913-1947.
21, Ling Guo, Akil Narayan, Tao Zhou, and Yuhang Chen, Stochastic collocation methods via l^1 minimization using randomized quadratures, SIAM J. Sci. Comput., 39-1, pp. A333-A359, 2017.
20, Shulin Wu and Tao Zhou, Fast parareal iterations for fractional diffusion equations, J. Comput. Phys., 329:210-226, 2017.
19, Tao Kong, Weidong Zhao, and Tao Zhou, High order numerical schemes for second order FBSDEs with applications to stochastic optimal control, Commun. Comput. Phys., (21)2017, pp. 808-834.
18, Yu Fu, Weidong Zhao, and Tao Zhou, Multistep schemes for forward backward stochastic differential equations with jumps, J. Sci. Comput., Volume 69, Issue 2, pp 651–672, 2016.
17, Hehu Xie and Tao Zhou, A multilevel finite element method for Fredholm integral eigenvalue problems, J. Comput. Phys., 303(2015), pp. 173-184.
16, Tao Kong, Weidong Zhao, and Tao Zhou, High order probabilistic numerical schemes for fully nonlinear parabolic PDEs, Commun. Comput. Phys., (18)2015, pp. 1482-1503.
15, Eleonora Musharbash, Fabio Nobile and Tao Zhou, Error analysis of the dynamically orthogonal approximation of time dependent random PDEs, SIAM J. Sci. Comput., 37-2, pp. A776–A810, 2015.
14, Akil Narayan and Tao Zhou, Stochastic collocation methods on unstructured meshes, Commun. Comput. Phys., 18(2015), pp. 1-36.
13, Tao Zhou, Akil Narayan, and Dongbin Xiu, Weighted discrete least-squares polynomial approximation using randomized quadratures, J. Comput. Phys., (298)2015, pp. 787-800.
12, Shulin Wu and Tao Zhou, Convergence analysis for three parareal solvers, SIAM J. Sci. Comput. 37-2 (2015), pp. A970-A992.
11, Tao Tang and Tao Zhou, Discrete least square projection in unbounded domain with random evaluations and its application to parametric uncertainty quantification, SIAM J. Sci. Comput., 36(5), pp. A2272–A2295, 2014.
10, Zhiqiang Xu and Tao Zhou, On sparse interpolation and the design of deterministic interpolation points, SIAM J. Sci. Comput. 36-4 (2014), pp. A1752-A1769.
9, Tao Zhou, Akil Narayan and Zhiqiang Xu, Multivariate discrete least-squares approximations with a new type of collocation grid, SIAM J. Sci. Comput., 36-5 (2014), pp. A2401–A2422.
8, Weidong Zhao, Yu Fu and Tao Zhou, New kinds of high-order multi-step schemes for forward backward stochastic differential equations, SIAM J. Sci. Comput. 36-4 (2014), pp. A1731-A1751.
7, Tao Zhou, A stochastic collocation method for delay differential equations with random input, Adv. Appl. Math. Mech., (6)2014, pp. 403-418,
6, Zhen Gao and Tao Zhou, Choice of nodal sets for least square polynomial chaos method with application to uncertainty quantification, Commun. Comput. Phys., 16:365–381, 2014.
5, Tao Zhou and Tao Tang, Galerkin methods for stochastic hyperbolic problems using bi-orthogonal polynomials, J. Sci. Comput. 51 (2012), pp.274-292.
4, Tao Zhou and Tao Tang, Convergence analysis for spectral approximation to a scalar transport equation with a random wave speed, J. Comput. Math., 30 (2012), pp.643-656.
3, Tao Zhou, Stochastic Galerkin methods for elliptic interface problems with random input, J. Comput. & App. Math., 236(2011) , pp.782-792.
2, Tao Tang and Tao Zhou, Convergence analysis for stochastic collocation methods to scalar hyperbolic equations, Commun. Comput. Phys., 8(2010), pp.226-248.
1, Tao Zhou and Tao Tang, Note on coefficient matrices from stochastic Galerkin methods for random diffusion equations, J. Comput. Phys., 229 (2010), pp.8225-8230.
* Mini-symposia Organizer: ICOSAHOM 2018, 9-13 July, 2018, London, UK.
* Mini-symposia Organizer & Invited Mini-symposia Speaker: SIAM UQ18, Apr. 16-19, 2018, CA, USA.
* Plenary Speaker： International Conference on Recent Advances in Computational and Applied Mathematics, Dec.14--17, 2017, Wuhan University, China
* Invited Speaker： From approximation theory to real world applications, TSIMF Workshop, Dec.11--15, 2017, Sanya, China
* Invited Speaker: HKUST IAS Focused Program on Scientific Computing, Dec.04 --08, 2017, HKUST, Hongkong.
* Mini-symposia Organizer: 15th Annual Meeting of CSIAM (中国工业与应用数学学会第15届年会), Oct. 12-14, 2017，Qingdao, China.
* Invited Speaker: 最优控制与反问题研讨会，Linyi University, July 28--30, 2017, Shandong, China
* Invited Speaker：Uncertainty quantification in CFD, Shanghai Jiao Tong University, July 24--27, 2017, China.
* Invited Speaker：Workshop on "UQ and stochastic methods", CSRC, June 19--21, Beijing, 2017.
* Invited Speaker：航天工业与数学---哈工大航天学院建院三十年，June 11, 哈尔滨, 2017.
* Invited Participants：Workshop on "Probablistic scientific computing: statistical inference approaches to numerical analysis and algorithm design"，ICERM, Brown University, June 5-9, 2017
* Invited Speaker：International Workshop on PDEs: Theory and Numerics，May 11--13, Zhejiang University, Hangzhou, China.
* Invited Speaker：Recent advances in Scientific and Engineering Computation, Shanghai Jiao Tong University, May 3--7, 2017, China.
* Invited Participants：第十届中科院--德国洪堡基金会前沿科学研讨会，2017年5月18--21日，德国波茨坦。
* Invited Mini-symposium Speaker：SIAM CSE, Feb.27--Mar. 3, 2017, Altlante, USA.
* Invited Speaker: Chinese Mathematical Society 2016 Annual meeting (中国数学会2016学术年会), Sep. 23-26, 2016, Neimeng, China.
* Prize Lecture: 14th Annual Meeting of CSIAM (中国工业与应用数学学会第14届年会), Aug. 12-14, 2016，Xiangtan, China.
* Invited Speaker: 最优控制与反问题研讨会，Wuhan University，Aug.5-7, 2016.
* Invited Speaker: NSFC-RGC Joint Conference for Young Chinese Mathematician, July 6-8, 2016. (国家自然科学基金委和香港资助计划局联合青年学者论坛)
* Invited Speaker: The Tenth International Conference on Scientific Computing and Applications (ICSCA2016), June 6-10, 2016, at the Fields Institute, Toronto, Canada.
* Invited Mini-symposia Speaker: 15th International Conference on Approximation Theory (AT15) (San Antonio, TX, USA, May 22-26, 2016)
* Invited Speaker: Workshop on Stochastic Numerics (by Prof. Peter Kloeden), HUST, Wuhan，April.16-17, 2016.
* Invited Mini-symposia Speaker: "Mathematical advances in high-dimensional approximation and integration" at SIAM conference on Uncertainty Quantification (UQ16) , by Albert Cohen and Clayton Webster. (EPFL, Lausanne, Switzerland, April 5-8, 2016)
* Mini-symposia Organizer: "Theoretical and computational advances in collocation approximations for high-dimensional problems" at SIAM conference on Uncertainty Quantification (UQ16) . Joint with John Jackman and Akil Narayan. (EPFL, Lausanne, Switzerland, April 5-8, 2016)
* Invited Participants: Workshop on "Numerical methods for nonlinear problems" (Tsinghua Sanya International Mathematics Forum (TSIMF) , Jan 11-15, 2016)
* Invited Speaker: 计算数学与应用数学青年研讨会 (The 8th Workshop for Young Chinese Computational Mathematicians)，Tsinghua University, Beijing, Nov. 21-22, 2015.
* Organizer & speaker: Workshop on computation methods and stochastic modelling, Hunan University, Nov 14-15, 2015 (Joint with Prof. L. Jiang).
* Invited Speaker: International Workshop on Computational Mathematics and Scientific Computing to honor Max Gunzburger's 70th birthday, Jeju Island, South Korea, August 19-21, 2015.
* Mini-symposia Organizer: Mini-symposium on "Numerical Analysis for Forward-Backward Stochastic Differential Equations and Related Problems" at the 8th International Congress on Industrial and Applied Mathematics (ICIAM2015). Joint With Prof. Weidong Zhao from Shandong University. (Beijing, China, August 10-14, 2015)
* Invited Mini-symposium Speaker: Mini-symposium on "Reduced-order modeling in uncertainty quantification and computational fluid dynamics" at The 8th International Congress on Industrial and Applied Mathematics (ICIAM2015). Mini-symposium organized by A. Quarteroni et al. (Beijing, China, August 10-14, 2015)
* Invited Participants: Uncertainty quantification in kinetic and hyperbolic problems (KI-Net Conference), University of Wisconsin-Madison, Mar 28-31, 2015 .
* Invited Mini-symposium Speaker: Mini-symposiums on "Numerical Methods for High-Dimensional Stochastic and Parametric Problems" and "Sparse and compressible representations: Theory, Algorithms and Applications" (two talks) at the SIAM CSE Conference. Mini-symposiums organized by A. Doostan et al. for numerical methods and J. Jackman et al. for compressed sensing. (Salt Lake City, Utah, USA, March 14-18, 2015)
* Mini-symposia Organizer: Mini-symposium on "Numerical Methods for the Stochastic Differential Equations" at the 9th International Conference on Computational Physics (ICCP9). Joint With Prof. Tiejun Li from Peking University. ( Singapore January 7-11, 2015)
* Invited Speaker: Workshop on "Recent Advances in Numerical Analysis". (Shanghai Jiao Tong University, China, November 15-16, 2014)
* Invited Speaker: International conference on “Recent Advances in Computational Mathematics & Applications”. (Tsinghua Sanya International Mathematics Forum (TSIMF) , December 8-12, 2014)
* Invited Speaker: 计算数学与应用数学青年研讨会 (The 7th Workshop for Young Chinese Computational Mathematicians.) (Wuhan University, China, Dec.12-15, 2014)
* Invited Speaker: The third International conference on interdisciplinary applied and computational mathematics. (Zhejiang University, China, June 7-10, 2014)
* Invited Mini-symposium Speaker: Mini-symposium on "High order methods for high-dimensional problems: applications in UQ" at the international conference on spectral and high order methods (ICOSAHOM14). (Salt Lake City, Utah, USA, June 23-27, 2014)
* Invited Mini-symposium Speaker: Mini-symposium on "Theoretical and numerical analysis for forward-backward stochastic differential equations and stochastic optimal control" at the SIAM conference on UQ. (Savannah, Georgia, USA, Mar.31-Apr.3, 2014)
* Invited Mini-symposium Speaker: 25th Biennial Conference on Numerical Analysis, University of Strathdyde, UK, June 25-28, 2013.
* Invited speaker: The International Conference on Stochastic Model and Numerical Simulation, Wuhan, Nov. 8-11, 2012
* Invited Mini-symposium Speaker: Third Chinese-German Workshop on Computational and Applied Mathematics, Sep.28 - Oct.5 2009, University of Heidelberg, Germany.