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WU Kailiang

Associate Professor  

https://faculty.sustech.edu.cn/wukl/en/

  • Brief Biography
  • Research
  • Teaching
  • Published Works

Employment

◆ 2021.01-present: Associate Professor, Department of 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

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


Awards

◆ 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 Ph.D. Graduates Award, PKU (2016)

◆ 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 (see [Published Works] for Full Publications List)


◆ 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

Provably positive high-order schemes for ideal magnetohydrodynamics: Analysis on general meshes

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


◆ 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* and C.-W. Shu

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

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


◆ K. Wu 

Minimum principle on specific entropy and high-order accurate invariant region preserving numerical methods for relativistic hydrodynamics

SIAM Journal on Scientific Computing,   accepted for publication, 2021.


◆ 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,    accepted for publication, 2021.


◆ 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


◆ Y. Chen and K. Wu*

A physical-constraint-preserving finite volume method for special relativistic hydrodynamics on unstructured meshes

Journal of Computational Physics,     submitted for publication, 2021.


◆ 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,     submitted for publication, 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. 


◆ 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. 


◆ 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, D. Xiu, and X. Zhong

A WENO-based stochastic Galerkin scheme for ideal MHD equations with random inputs 

Communications in Computational Physics,    30: 423--447, 2021.


◆ T. Qin, K. Wu, and D. Xiu

Data driven governing equations approximation using deep neural networks

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


◆ K. Wu and D. Xiu

Numerical aspects for approximating governing equations using data

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


◆ 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.


◆ Y. Shin, K. Wu, and D. Xiu

Sequential function approximation with noisy data

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


◆ 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, 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

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

Physical Review D,   95, 103001, 2017. 


◆ 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

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 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)


◆ 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.


◆ 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

◆ Referee for scientific journals including

  • Communications in Computational Physics
  • Computer Methods in Applied Mechanics and Engineering
  • East Asian Journal on Applied Mathematics
  • Engineering Optimization
  • Journal of Computational and Applied Mathematics
  • Journal of Computational Physics
  • Journal of Scientific Computing
  • Journal of Applied Mathematics and Computing
  • Mathematical Models and Methods in Applied Sciences (M3AS)
  • Mathematica Numerica Sinica
  • SIAM Journal on Scientific Computing
  • SIAM/ASA Journal on Uncertainty Quantification


2 postdoc positions available

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




保结构数值方法及其理论:保持正性、物理约束、平衡性、熵稳定、最小熵原理等结构

K. Wu, Positivity-preserving analysis of numerical schemes for ideal magnetohydrodynamics, SIAM Journal on Numerical Analysis, 2018.

K. Wu and C.-W. Shu, Provably positive high-order schemes for ideal magnetohydrodynamics: Analysis on general meshes, Numerische Mathematik, 2019.

K. Wu, Minimum principle on specific entropy and high-order accurate invariant region preserving numerical methods for relativistic hydrodynamics, SIAM Journal on Scientific Computing,  2021.

K. Wu and C.-W. Shu, Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations, Numerische Mathematik, 2021.

K. Wu and H. Tang, Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations, Math. Models Methods Appl. Sci. (M3AS), 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,  2021.

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, 2020.

K. Wu and C.-W. Shu, A provably positive discontinuous Galerkin method for multidimensional ideal magnetohydrodynamics, SIAM Journal on Scientific Computing, 2018.

K. Wu, Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics, Physical Review D, 2017.

K. Wu and H. Tang, High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics, Journal of Computational Physics, 2015.


深度学习、数据驱动建模


K.Wu and D. Xiu, Data-driven deep learning of partial differential equations in modal space, Journal of Computational Physics, 2020.

T. Qin, K. Wu, and D. Xiu, Data driven governing equations approximation using deep neural networks, Journal of Computational Physics, 2019.

K.Wu, T. Qin, and D. Xiu, Structure-preserving method for reconstructing unknown Hamiltonian systems from trajectory data, SIAM Journal on Scientific Computing, 2020.

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, 2021.

Z. Chen, K. Wu, and D. Xiu, Methods to recover unknown processes in partial differential equations using data, Journal of Scientific Computing, 2020.

J. Hou, T. Qin, K. Wu and D. Xiu,  A non-intrusive correction algorithm for classification problems with corrupted data, Commun. Appl. Math. Comput., 2020.

K. Wu and D. Xiu, Numerical aspects for approximating governing equations using data, Journal of Computational Physics, 2019.




相对论流体力学方程的数学性质与高阶精度数值方法

K. WuMinimum principle on specific entropy and high-order accurate invariant region preserving numerical methods for relativistic hydrodynamics, SIAM Journal on Scientific Computing,  2021.

K. Wu, Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics, Physical Review D, 2017.

K. Wu and H. Tang, High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics, Journal of Computational Physics, 2015.

K. Wu and H. Tang, Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations, Math. Models Methods Appl. Sci. (M3AS), 2017.

K. Wu and C.-W. Shu, Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations, Numerische Mathematik, 2021.

K. Wu and H. Tang, A direct Eulerian GRP scheme for spherically symmetric general relativistic hydrodynamics, SIAM Journal on Scientific Computing, 2016.

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), 2017.

K. Wu and H. Tang, Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics, Journal of Computational Physics, 2014.


高维函数逼近:大数据样本、最优采样、多项式逼近

K. Wu, Y. Shin, and D. Xiu, A randomized tensor quadrature method for high dimensional polynomial approximation, SIAM Journal on Scientific Computing, 2017.

K. Wu and D. Xiu, Sequential function approximation on arbitrarily distributed point sets, Journal of Computational Physics, 2018.

Y. Shin, K. Wu, and D. Xiu, Sequential function approximation with noisy data, Journal of Computational Physics, 2018.

K. Wu and D. Xiu,  Sequential approximation of functions in Sobolev spaces using random samples, Commun. Appl. Math. Comput., 2019.


双曲守恒律方程的(广义)黎曼解算子与Godunov型数值方法

K. Wu and H. Tang, A direct Eulerian GRP scheme for spherically symmetric general relativistic hydrodynamics, SIAM Journal on Scientific Computing, 2016.

K. Wu and H. Tang, Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics, Journal of Computational Physics, 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, 2014.


随机Galerkin方法、不确定性量化

K. Wu, D. Xiu, and X. Zhong, A WENO-based stochastic Galerkin scheme for ideal MHD equations with random inputs, Communications in Computational Physics, 2021.

K. Wu, H. Tang, and D. Xiu, A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty, Journal of Computational Physics, 2017.

Publications List  


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

SIAM Journal on Scientific Computing,   accepted for publication, 2021.


[33] 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,   accepted for publication, 2021.


[32] Y. Chen and K. Wu*
A physical-constraint-preserving finite volume method for special relativistic hydrodynamics on unstructured meshes
submitted for publication, 2021.


[31] H. Jiang, H. Tang, and K. Wu*

Positivity-preserving well-balanced central discontinuous Galerkin schemes for the Euler equations under gravitational fields

submitted for publication, 2021.


[30] K. Wu* and C.-W. Shu

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

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


[29] 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.


[28] K. Wu and D. Xiu

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

Journal of Computational Physics,  408: 109307, 2020. 


[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] 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. 


[24] 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: 423--447, 2021.


[23] 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.


[22] 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.


[21] T. Qin, K. Wu, and D. Xiu

Data driven governing equations approximation using deep neural networks

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


[20] K. Wu and D. Xiu

Numerical aspects for approximating governing equations using data

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


[19] K. Wu and D. Xiu

Sequential approximation of functions in Sobolev spaces using random samples
Commun. Appl. Math. Comput.,  1: 449--466, 2019.


[18] 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.


[17] K. Wu

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

Sequential function approximation on arbitrarily distributed point sets

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


[14] 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.


[13] K. Wu and D. Xiu

An explicit neural network construction for piecewise constant function approximation

arXiv preprint arXiv:1808.07390, 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.