Home / People / Faculty / Kailiang WU
Kailiang WU
Associate Professor
Research interest: ◆ 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 ◆ Approximation Theory and Unce

Employment

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

◆ 2022.03-present: Associate Professor, SUSTech International Center for Mathematics, Southern University of Science and Technology

◆ 2022.09-present: Associate Professor, National Center for Applied Mathematics Shenzhen

◆ 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

Education

◆ 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

 

Research Interests

◆ 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

◆ Approximation Theory and Uncertainty Quantification

 

Honors & Awards

◆ Distinguished Young Scholar, Shenzhen Science and Technology Program, PI (2023)

◆ National Excellent 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, PKU (2014–2016) (The biggest scholarship of PKU)

 

Selected Publications

 

 

 

 

◆ K. Wu

Positivity-preserving analysis of numerical schemes for ideal magnetohydrodynamics
SIAM Journal on Numerical Analysis,   56(4):2124--2147, 2018.

 

◆ K. Wu and C.-W. Shu
Geometric quasilinearization framework for analysis and design of bound-preserving schemes
SIAM Review,    (Research Spotlight)   65(4): 1031--1073, 2023.  

 

 

 

◆ 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.

 

◆ K. Wu

Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics

Physical Review D,   95, 103001, 2017. 

 

◆ 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.

 

◆ K. Wu and D. Xiu

Data-driven deep learning of partial differential equations in modal space

Journal of Computational Physics,   408: 109307, 2020.

 

◆ K. Wu*, H. Jiang, and C.-W. Shu
Provably positive central discontinuous Galerkin schemes via geometric quasilinearization for ideal MHD equations
SIAM Journal on Numerical Analysis,   61: 250--285, 2023.

 

◆ 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.

 

◆ 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,   60(5): 2448--2481, 2022.

 

 

◆ S. Cui, S. Ding, and K. Wu*

On optimal cell average decomposition for high-order bound-preserving schemes of hyperbolic conservation laws

SIAM Journal on Numerical Analysis,   accepted,  2023.

 

◆ K. Wu* and C.-W. Shu

Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations

Numerische Mathematik,   148: 699--741, 2021.

 

◆ 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.

 

 

◆ 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. 

 

◆ 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.

 

◆ 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,    43(1): A472--A510, 2021.

 

◆ 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. 

 

 

◆ S. Ding and K.Wu*

A new discretely divergence-free positivity-preserving high-order finite volume method for ideal MHD equations

SIAM Journal on Scientific Computing,   aceepted, 2023.

 

◆ 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. 

 

◆ 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.

 

◆ T. Qin, K. Wu, and D. Xiu

Data driven governing equations approximation using deep neural networks

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

 

◆ S. Cui, S. Ding, and K. Wu*
Is the classic convex decomposition optimal for bound-preserving schemes in multiple dimensions?
Journal of Computational Physics,   476: 111882,  2022.

 

◆  J. Chen and K. Wu*
Deep-OSG: Deep learning of operators in semigroup
Journal of Computational Physics,   accepted, 2023.

 

◆ 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)

 

◆ W. Chen, K. Wu, and T. Xiong
High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers
Journal of Computational Physics,    488: 112240, 2023.

 

 

 

◆ C. Cai, J. Qiu, and K.Wu*

Provably convergent Newton-Raphson methods for recovering primitive variables with applications to physical-constraint-preserving Hermite WENO schemes for relativistic hydrodynamics

Journal of Computational Physics,   accepted, 2023.

 

 

◆ 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,     449: 110782, 2022.

 

 

◆ 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.

 

◆ 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.

 

◆ 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. 


◆ K. Wu and D. Xiu

Numerical aspects for approximating governing equations using data

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


◆ Y. Shin, K. Wu, and D. Xiu

Sequential function approximation with noisy data

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

 

◆ Y. Ren, K. Wu, J. Qiu, and Y. Xing 

On positivity-preserving well-balanced finite volume methods for the Euler equations with gravitation

Journal of Computational Physics,  accepted, 2023.

 

◆ K. Wu and D. Xiu

Sequential function approximation on arbitrarily distributed point sets

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


◆ 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.

 

◆ 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. 

 

◆ K. Wu and H. Tang

Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics

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


◆ 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. 

 

 

 

Professional Services

◆ Reviewer for AMS Mathematical Reviews

◆ Editorial Board of Numerical Analysis and Scientific Computation (specialty section of Frontiers in Applied Mathematics and Statistics)

◆ Referee for scientific journals including

 

  • Applied Mathematics and Computation
  • Applied Numerical Mathematics
  • Chinese Journal of Theoretical and Applied Mechanics
  • Communications in Computational Physics
  • Computer Methods in Applied Mechanics and Engineering
  • Computers and Mathematics with Applications
  • East Asian Journal on Applied Mathematics
  • Electronic Research Archive
  • Engineering Optimization
  • Journal of Computational and Applied Mathematics
  • Journal of Computational Physics   ( > 60 times )
  • Journal of Numerical Mathematics
  • Journal of Scientific Computing
  • Journal of Mathematical Biology
  • Journal of Applied Mathematics and Computing
  • Mathematical Models and Methods in Applied Sciences (M3AS)
  • Mathematica Numerica Sinica
  • Mathematics of Computation
  • SIAM Journal on Scientific Computing (SISC)
  • SIAM/ASA Journal on Uncertainty Quantification
  • Theoretical and Applied Mechanics Letters

 

2 extra Postdoc or RAP positions available

The candidates should have a Ph.D. degree in Mathematics, Computational Physics, Fluid Mechanics, Computer Science, or Astrophysics. Research 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.

 

 

Teaching（授课课程）

 

Fall Semester：Mathematical Experiments 数学实验（本科生）Spring Semester：Computational Fluid Dynamics and Deep Learning 计算流体力学与深度学习（本研）2021 Spring Semester：Calculus II 高等数学II（本科生）2022 Spring Semester：Advanced Topics in Modern Computational Mathematics （本科生）

Group Members (课题组成员)


Research Assistant Professor（研究助理教授）

  • Dr. Shumo Cui (2023.2.1-) We have a joint article: "Is the classic convex decomposition optimal for bound-preserving schemes in multiple dimensions?" published in 《Journal of Computational Physics》. We have a joint article: "On optimal cell average decomposition for high-order bound-preserving schemes of hyperbolic conservation laws" accepted for publication in 《SIAM Journal on Numerical Analysis》.


Postdoctoral Fellows（博士后研究员）

  • Dr. Shengrong Ding (2021.11-present): Ph.D. from University of Science and Technology of China（中科大博士）. We have a joint article: "Is the classic convex decomposition optimal for bound-preserving schemes in multiple dimensions?" published in 《Journal of Computational Physics》. We have a joint article: "On optimal cell average decomposition for high-order bound-preserving schemes of hyperbolic conservation laws" accepted for publication in 《SIAM Journal on Numerical Analysis》. We have a joint article "A new discretely divergence-free positivity-preserving high-order finite volume method for ideal MHD equations" accepted for publication in 《SIAM Journal on Scientific Computing》. We have a joint article: "High-order accurate entropy stable schemes for relativistic hydrodynamics with a general equation of state" submitted to JSC.

  • Dr. Junfeng Chen (Postdoc Fellow: 2022.10-present; Visiting Postdoc Scholar: 2022.03-2022.09): B.Sc. from Tsinghua University（清华大学本科），Ph.D. from Paris Sciences et Lettres – PSL Research University（法国巴黎文理研究大学博士）. We have a joint article "Deep-OSG: Deep learning of operators in semigroup" published in《Journal of Computational Physics》.

  • Dr. Ruifang Yan (Postdoc Fellow: 2023.07-): Ph.D. from Wuhan University（武汉大学博士）.

  • Dr. Huihui Cao (Postdoc Fellow: 2023.07-): Ph.D. from Xiangtan University（湘潭大学博士）.

  • Dr. Chuan Fan (Postdoc Fellow: 2023.09-; Visiting Postdoc Scholar: 2023.06-2023.09): Ph.D. from Xiamen University（厦门大学博士）.

  • Dr. Mengqing Liu (Postdoc Fellow: 2023.09-): Ph.D. from University of Chinese Academy of Sciences（中国科学院大学博士）.


Graduate Students (研究生)

  • Haili Jiang (2021.04-2021.12)，Visiting Ph.D. student from Peking University（北京大学）. We have a joint article with Prof. Chi-Wang Shu: "Provably positive central DG schemes via geometric quasilinearization for ideal MHD equations" published in《SIAM Journal on Numerical Analysis》. We have a joint article with Prof. Huazhong Tang: "Positivity-preserving well-balanced central discontinuous Galerkin schemes for the Euler equations under gravitational fields" published in《Journal of Computational Physics》.

  • Fang Yan (2021.09-2023.07)，Master student，B.Sc. from South China University of Technology（华南理工）.

  • Zhuoyun Li (2022.09-)，Ph.D. student，B.Sc. from SUSTech（南科大）.

  • Manting Peng (2022.09-)，Master student，B.Sc. from SUSTech（南科大）. We have a joint article: "OEDG: Oscillation-eliminating discontinuous Galerkin method for hyperbolic conservation laws" submitted.

  • Linfeng Xu (2022.09-)，Master student，B.Sc. from SUSTech（南科大）. We have a joint article: "High-order accurate entropy stable schemes for relativistic hydrodynamics with a general equation of state" submitted to JSC.

  • Dongwen Pang (2023.09-), Ph.D. student, B.Sc. from Wuhan University of Technology（武汉理工）, M.Sc. from Xiangtan University（湘潭大学）. He is a visiting master student from 2023.03 to 2023.08.

  • Miaosen Jiao (2023.09-), Master student, B.Sc. from SUSTech（南科大）.

  • Caiyou Yuan(2023.06.29-08.30), Visiting Ph.D. student from Peking University（北京大学）.

  • Zhihao Zhang (2023.06.29-08.30), Visiting Ph.D. student from Peking University（北京大学）.

  • Jiangfu Wang (2023.06.29-08.30), Visiting Ph.D. student from Peking University（北京大学）.


Undergraduate Students (本科生)

  • Yuanzhe Wei: We have a joint article with Prof. Zheng Sun: "On energy laws and stability of Runge-Kutta methods for linear seminegative problems" published in 《SIAM Journal on Numerical Analysis》（计算数学方向的顶级期刊，南科大本科生首次）。He was selected to an exchange study program in MIT（麻省理工）南科大数学系第一位入选MIT交流项目的学生，见报道 [https://mp.weixin.qq.com/s/nhlTvmGpdOrXuwZ-a7v4Tg] . He won SUSTech outstanding bachelor thesis (本科毕业论文入选南科大优秀毕业论文). He received two offers from MIT and one offer from Brown University（收获麻省理工的2个offer和布朗大学的1个offer）; He chooses to pursue his Ph.D. at Brown University（布朗大学）since Sep. 2023.

  • Yunhao Jiang: He was selected into a joint study program in University of Wisconsin-Madison（威斯康星大学麦迪逊分校）. He won 3rd class prize in the 2022 International Mathematics Competition for University Students (国际大学生数学竞赛).

  • Zhuoyun Li: 推免研究生（GPA排名并列第一）. He won SUSTech outstanding bachelor thesis (本科毕业论文入选南科大优秀毕业论文).

  • Zepei Liu：推免研究生. He became a master student of Prof. Alexander KURGANOV in Sep. 2022.

  • Manting Peng：推免研究生. She won SUSTech outstanding bachelor thesis (本科毕业论文入选南科大优秀毕业论文).

  • Mingrui Wang: He pursues his master degree in electronic information at Peking University（北京大学）.

  • Linfeng Xu：推免研究生. He won SUSTech outstanding bachelor thesis (本科毕业论文入选南科大优秀毕业论文).

  • Luowei Yin：He worked on summer research and his bachelor thesis in our group (2021.04-2022.06) and after graduation pursues his Ph.D. at CUHK（香港中文）since Sep. 2022.

  • Zijun Jia：推免研究生. 

  • Yuchen Huang：推免研究生. 

  • Yuanji Zhong：He was selected into a joint study program in University of Wisconsin-Madison（威斯康星大学麦迪逊分校）. He won 1st class prize (Guangdong) and 3rd class prize (National) in the 13th Chinese Mathematics Competitions for University Students（全国大学生数学竞赛）. He won Silver Award in the 2nd Winter National Mathematical Olympiad for University Students（全国大学生奥林匹克数学竞赛-冬季赛）in 2023.

  • Zhihua Li：He won SUSTech outstanding bachelor thesis (本科毕业论文入选南科大优秀毕业论文). He pursues his Ph.D. at University of Iowa（爱荷华大学）since Sep. 2023.

  • Miaosheng Jiao：推免研究生. He won SUSTech outstanding bachelor thesis (本科毕业论文入选南科大优秀毕业论文).

 

 

Welcome passionate and highly self-motivated students to join our group! If you are interested in our research, please feel free to contact me by email: WUKL@sustech.edu.cn.

 

 

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. Research 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.