Kailiang WU

Associate Professor Department of Mathematics, International Center for Mathematics


• 2021.01-present: Associate Professor, Department of Mathematics, Southern University of Science and Technology

• 2022.01-present: Associate Professor, SUSTech International Center for Mathematics, Southern University of Science and Technology

• 2016.08-2020.12: Postdoctoral Scholar, Department of Mathematics, The Ohio State University

• 2016.04-2016.08: Postdoctoral Fellow, Scientific Computing and Imaging Institute, University of Utah



• 2011-2016: Ph.D. School of Mathematical Sciences, Peking University

• 2007-2011: B.Sc. School of Mathematics and Statistics, Huazhong University of Science and Technology


Honors & Awards:

• National Distinguished Young Scholar (2020)

• Zhong Jiaqing Mathematics Award, the Chinese Mathematical Society (2019) One of the three major mathematics awards of the Chinese Mathematical Society (4 per 2 years)

• Outstanding Youth Paper Award (First Prize), the China Society for Computational Mathematics (2015)

• First Prize of "Challenge Cup" May-4th Youth Science Award, PKU (2014)

• President Scholarship of PKU (2014–2016)

Personal Profile


Machine Learning and Data-driven Modeling

Numerical Solutions of Partial Differential Equations

Computational Fluid Dynamics and Astrophysics

High-order Accurate Numerical Methods

Hyperbolic Conservation Laws

Structure-preserving Methods: Design and Analysis

Approximation Theory and Uncertainty Quantification

Publications Read More

Selected Publications:

36. K. Wu, H. Jiang, and C.-W. Shu, Provably positive central DG schemes via geometric quasilinearization for ideal MHD equations

    submitted for publication, 2022.

35. Z. Sun, Y. Wei, and K. Wu*, On energy laws and stability of Runge–Kutta methods for linear seminegative problems

     SIAM Journal on Numerical Analysis,  accepted  for publication, 2022.

34. K. Wu and C.-W. Shu*, Geometric quasilinearization framework for analysis and design of bound-preserving schemes

    submitted for publication, 2021. arXiv:2111.04722. 8 Nov 2021.

33.  K. Wu, Minimum principle on specific entropy and high-order accurate invariant region preserving numerical methods for relativistic hydrodynamics

    SIAM Journal on Scientific Computing, 43(6): B1164–B1197, 2021.

32. Z. Chen, V. Churchill, K. Wu, and D. Xiu, Deep neural network modeling of unknown partial differential equations in nodal space

    Journal of Computational Physics, 110782, 2022.

31. H. Jiang, H. Tang, and K. Wu*, Positivity-preserving well-balanced central discontinuous Galerkin schemes for the Euler equations under gravitational fields

    Journal of Computational Physics, 463: 111297, 2022.

30. Y. Chen and K. Wu*, A physical-constraint-preserving finite volume method for special relativistic hydrodynamics on unstructured meshes

    Journal of Computational Physics, 466: 111398, 2022.

29. K. Wu* and C.-W. Shu, Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations

    Numerische Mathematik,  148: 699–741, 2021.

28. K. Wu and Y. Xing, Uniformly high-order structure-preserving discontinuous Galerkin methods for Euler equations with gravitation: Positivity and well-balancedness

    SIAM Journal on Scientific Computing, A472–A510, 2021.

27. K. Wu, T. Qin, and D. Xiu, Structure-preserving method for reconstructing unknown Hamiltonian systems from trajectory data

    SIAM Journal on Scientific Computing, 42(6): A3704–A3729, 2020.

26. K. Wu and C.-W. Shu, Entropy symmetrization and high-order accurate entropy stable numerical schemes for relativistic MHD equations

    SIAM Journal on Scientific Computing, 42(4): A2230–A2261, 2020.

25. K. Wu and D. Xiu, Data-driven deep learning of partial differential equations in modal space

    Journal of Computational Physics, 408: 109307, 2020.

24. Z. Chen, K. Wu, and D. Xiu, Methods to recover unknown processes in partial differential equations using data

    Journal of Scientific Computing, 85:23, 2020.

23. K. Wu, D. Xiu, and X. Zhong, A WENO-based stochastic Galerkin scheme for ideal MHD equations with random inputs

    Communications in Computational Physics, 30(2): 423–447, 2021.

22. J. Hou, T. Qin, K. Wu and D. Xiu, A non-intrusive correction algorithm for classification problems with corrupted data

    Commun. Appl. Math. Comput., 3: 337–356, 2021.

21. K. Wu and C.-W. Shu, Provably positive high-order schemes for ideal magnetohydrodynamics: Analysis on general meshes

    Numerische Mathematik, 142(4): 995–1047, 2019.

20. T. Qin, K. Wu, and D. Xiu, Data driven governing equations approximation using deep neural networks

    Journal of Computational Physics, 395: 620–635, 2019.

19. K. Wu and D. Xiu, Numerical aspects for approximating governing equations using data

    Journal of Computational Physics, 384: 200–221, 2019.

18. K. Wu and D. Xiu, Sequential approximation of functions in Sobolev spaces using random samples

    Commun. Appl. Math. Comput., 1: 449–466, 2019.

17. K. Wu and C.-W. Shu, A provably positive discontinuous Galerkin method for multidimensional ideal magnetohydrodynamics

   SIAM Journal on Scientific Computing, 40(5):B1302–B1329, 2018.

16. Y. Shin, K. Wu, and D. Xiu, Sequential function approximation with noisy data

    Journal of Computational Physics, 371:363–381, 2018.

15. K. Wu, Positivity-preserving analysis of numerical schemes for ideal magnetohydrodynamics

    SIAM Journal on Numerical Analysis, 56(4):2124–2147, 2018.

14. K. Wu and D. Xiu, Sequential function approximation on arbitrarily distributed point sets

    Journal of Computational Physics, 354:370–386, 2018.

13. K. Wu and H. Tang, On physical-constraints-preserving schemes for special relativistic magnetohydrodynamics with a general equation of state

    Z. Angew. Math. Phys., 69:84(24pages), 2018.

12. K. Wu, Y. Shin, and D. Xiu, A randomized tensor quadrature method for high dimensional polynomial approximation

    SIAM Journal on Scientific Computing, 39(5):A1811–A1833, 2017.

11. K. Wu, Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics

    Physical Review D, 95, 103001, 2017.

10. K. Wu, H. Tang, and D. Xiu, A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty

    Journal of Computational Physics, 345:224–244, 2017.

9. K. Wu and H. Tang, Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations

    Math. Models Methods Appl. Sci. (M3AS), 27(10):1871–1928, 2017.

8. Y. Kuang, K. Wu, and H. Tang, Runge-Kutta discontinuous local evolution Galerkin methods for the shallow water equations on the cubed-sphere grid

    Numer. Math. Theor. Meth. Appl., 10(2):373–419, 2017.

7. K. Wu and H. Tang, Physical-constraint-preserving central discontinuous Galerkin methods for special relativistic hydrodynamics with a general equation of state

    Astrophys. J. Suppl. Ser. (ApJS), 228(1):3(23pages), 2017. (2015 Impact Factor of ApJS: 11.257)

6. K. Wu and H. Tang, A direct Eulerian GRP scheme for spherically symmetric general relativistic hydrodynamics

    SIAM Journal on Scientific Computing, 38(3):B458–B489, 2016.

5. K. Wu and H. Tang, A Newton multigrid method for steady-state shallow water equations with topography and dry areas

    Applied Mathematics and Mechanics, 37(11):1441–1466, 2016.

4. K. Wu and H. Tang, High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics

    Journal of Computational Physics, 298:539–564, 2015.

3. K. Wu, Z. Yang, and H. Tang, A third-order accurate direct Eulerian GRP scheme for one-dimensional relativistic hydrodynamics

    East Asian J. Appl. Math., 4(2):95–131, 2014.

2. K. Wu and H. Tang, Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics

    Journal of Computational Physics, 256:277–307, 2014.

1. K. Wu, Z. Yang, and H. Tang, A third-order accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics

    Journal of Computational Physics, 264:177–208, 2014.

Lab members Read More

Join us

Join us: 2 extra postdoc/RAP(research assistant professor) positions available.
The candidates should have a Ph.D. degree in Mathematics, Computational Physics, Fluid Mechanics, Computer Science, or Astrophysics. R esearch experience in numerical schemes for PDEs, CFD, machine learning, and/or data science is desirable. Salary package is competitive. If you are interested, please send your CV to WUKL@sustech.edu.cn.
招聘博士后研究员、研究助理教授(RAP); 每年计划招收博士生/硕士生 1-2名。
有意者请将相关应聘或申请材料发送至:WUKL@sustech.edu.cn 邮件主题为“应聘岗位-应聘人姓名”(如,应聘博士后-张三)。
博士后申请人应具有博士学位和学历,品学兼优、身心健康、年龄不超过35 岁;获得博士学位不超过3 年;能够保证全职在站从事博士后研究工作。
1) 数学、计算物理、流体力学、计算机或其他相关专业,已获得或即将获得博士学位;
2) 有计算数学、计算流体力学(特别是可压缩流体)、机器学习或数据科学相关的研究经验者优先;
3) 具有良好的数学基础,精通至少一种计算机编程语言(C/C++、Python 或FORTRAN);
4) 具有良好的英文阅读、写作和交流能力;
5) 博士期间至少发表过1 篇高水平学术论文;
6) 对科学研究有非常浓厚的兴趣,敢于探索挑战性的科学问题;
7) 有上进心、独立思考精神、工作勤奋踏实、具有良好的团队合作精神。
1) 博士后聘用期两年,年薪33.4万元起(含广东省生活补助15万元及深圳市生活补助6万元),并按深圳市有关规定参加社会保险及住房公积金。
2) 福利费(过节费、餐补、高温补贴等)约12000元/年(按节日,分月合并工资发放),另有各项工会实物福利等。
3) 特别优秀候选人可以申请校长卓越博士后,年薪可达50万元以上。(含广东省及深圳市在站生活补贴;每年有两次申请“校长卓越博士后”机会)。
4) 住房补贴33600元/年(分月合并工资发放):在站期间,可依托学校申请深圳市公租房,未依托学校使用深圳市公租房的博士后,可享受两年税前2800元/月的住房补贴。
5) 拥有优良的工作环境和境内外合作交流机会,博士后在站期间享受两年共计2.5万学术交流经费资助。
6) 课题组协助符合条件的博士后申请“广东省海外青年博士后引进项目”。即在世界排名前200名的高校(不含境内,排名以上一年度泰晤士、USNEWS、QS和上海交通大学的世界大学排行榜为准)获得博士学位,在广东省博士后设站单位从事博士后研究,并承诺在站2年以上的博士后,申请成功后省财政给予每名进站博士后资助60万元生活补贴(与广东省每年15万生活补助不同时享受,与深圳市每年6万元生活补助同时享受情况以深圳市规定为准);对获得本项目资助,出站后与广东省用人单位签订工作协议或劳动合同,并承诺连续在粤工作3年以上的博士后,省财政给予每人40万元住房补贴。
7) 博士后出站选择留深从事科研工作,且与本市企事业单位签订3年以上劳动(聘用)合同的,可以申请深圳市博士后留深来深科研资助。深圳市政府给予每人每年10万元科研资助,共资助3年(以深圳市最新申报要求为准)。
8) 根据《深圳市新引进博士人才生活补贴工作实施办法》规定,新引进博士人才生活补贴(10万元)与省市博士后在站生活补贴不同时享受。
1) 个人详细简历,包括出生年月、联系方式、预计到岗时间、从本科起教育背景、工作经历等;
2) 能充分反映本人学术水平的有关材料,例如,学术成果总结、已发表论著列表、代表性论著全文、成果获奖情况等;
3) 提供至少2名推荐人的姓名及其有效联系方式。
学制:硕士 2 年;非硕士起点博士 5 年,硕士起点博士 4 年;境外联培博士 4 年。
住宿:目前硕士为两人间宿舍,博士单人间宿舍,住宿费 1300元/ 年,住宿条件在全国高校领先。
学校将为研究生提供充足的资助(目前博士生最高 8+2 万/年, 硕士生最高 4+1 万/年),以及学术交流(包括海外交流)的机会。
与境外大学联合培养的博士生有约 2 年的时间在境外学习,享受对方博士生同等待遇,由双方教授共同指导,发对方学校的学位证书。
课题组负责人吴开亮,现任南方科技大学数学系和杰曼诺夫国际数学中心副教授、研究员、博士生导师。2011年获华中科技大学数学学士学位;2016年获北京大学计算数学博士学位;2016-2020年先后在美国犹他大学和美国俄亥俄州立大学从事博士后研究;2021年1月加入南方科技大学。研究方向包括偏微分方程数值解、计算流体力学、机器学习与数据驱动建模、高维逼近与不确定性量化等。研究成果发表在SIAM系列期刊SINUM/SISC (9篇)、J. Comput. Phys. (12篇)、M3AS、Numer. Math. (2篇)、JSC、天体物理权威期刊ApJS、Phys. Rev. D等。曾获中国数学会计算数学分会 优秀青年论文奖一等奖(2015)和中国数学会 钟家庆数学奖(2019);入选国家高层次人才计划(青年)、深圳市孔雀计划;主持国家自然科学基金面上项目。
研究内容:课题组负责人和合作者在流体力学方程的高精度保结构(包括保界/保正、保平衡、保最小熵原理、熵稳定、保双曲性等)数值方法及其理论分析方面取得了一系列重要进展;首创“以辅助变量换取线性”的几何拟线性化理论框架,为研究强非线性的复杂保界问题开辟了新途径;发展严谨理论,揭示了可压缩磁流体数值方法的保界性与磁场的零散度条件之间的深层联系,解决了关于磁流体保正数值方法的公开性难题,被美国《数学评论》评价为“a highly desirable task”、“a challenge”;独立发现了弯曲时空中可容许状态集依赖于时空度规,系统地发展了狭义和广义相对论流体力学的保界方法,填补了该领域长达50年的空白,广义相对论情形的方法被著名天体物理学家L. Rezzolla等称为“在一般时空中,确保流体变量物理性的一种通用方法”。发展了一套适合大数据的高维函数逼近算法及其分析,并提出用随机张量求积和最优抽样提升算法效率及临近替换法处理分布极不规则的数据。基于可解释的深度学习方法构建了智能推演大数据中蕴藏的未知数学方程/模型的新框架。
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