吴开亮
副教授  

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

简历
科研
教学
发表论著
吴开亮，男，籍贯安徽省安庆市，理学博士，南方科技大学数学系副教授、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工作；2021年1月加入南方科技大学、任副教授。研究方向包括计算流体力学与数值相对论、机器学习与数据驱动建模、微分方程数值解、高维逼近与不确定性量化等。研究成果发表在SINUM，SISC，Numer. Math.，M3AS，J. Comput. Phys.，JSC，ApJS，Phys. Rev. D等期刊上。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）。

研究领域
微分方程数值解、计算流体力学与数值相对论、机器学习与数据科学、计算物理、高维逼近论与不确定性量化

荣誉及获奖
◆ 2019：中国数学会 钟家庆数学奖
◆ 2016：北京大学 优秀毕业生
◆ 2015：中国数学会计算数学分会优秀青年论文奖一等奖
◆2014：北京大学 “挑战杯”五四青年科学奖一等奖

代表性论文（全部文章列表见【发表论著】）

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

◆K. Wuand C.-W. Shu
Provably positive high-order schemes for ideal magnetohydrodynamics: Analysis on general meshes
Numerische Mathematik, 142(4): 995--1047, 2019.

◆K. Wuand D. Xiu
Data-driven deep learning of partial differential equations in modal space
Journal of Computational Physics, 408: 109307, 2020.

◆K. Wuand C.-W. Shu
Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations
Numerische Mathematik, accepted for publication,2021.

◆K. Wu
Minimum principle on specific entropy and high-order accurate invariant region preserving numerical methods for relativistic hydrodynamics
submitted for publication,arXiv:2102.03801, 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, submitted for publication, 2021.

◆K. Wuand 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.

◆K. Wuand 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, accepted for publication, 2020.
◆J. Hou, T. Qin,K. Wuand D. Xiu
A non-intrusive correction algorithm for classification problems with corrupted data
Commun. Appl. Math. Comput., in press, 2020.
◆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. Wuand D. Xiu
Numerical aspects for approximating governing equations using data
Journal of Computational Physics, 384: 200--221, 2019.
◆K. Wuand 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. Wuand D. Xiu
Sequential function approximation on arbitrarily distributed point sets
Journal of Computational Physics, 354:370--386, 2018.
◆K. Wuand 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. Wuand H. Tang
Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations
Math. Models Methods Appl. Sci. (M3AS), 27(10):1871--1928, 2017.
◆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.
◆K. Wuand 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. Wuand H. Tang
A direct Eulerian GRP scheme for spherically symmetric general relativistic hydrodynamics
SIAM Journal on Scientific Computing, 38(3):B458--B489, 2016.
◆K. Wuand 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.
◆K. Wuand 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. Wuand 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.

学术服务
◆美国《数学评论》评论员
◆ 下列期刊审稿人
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


课题组正在招聘博士后1-2名，计划招收博士生1名、硕士生1名。
详情请见：https://faculty.sustech.edu.cn/?cat=11&tagid=wukl&orderby=date&iscss=1&snapid=1
有意者请将相关应聘或申请材料发送至：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 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 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, 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, Minimum principle on specific entropy and high-order accurate invariant region preserving numerical methods for relativistic hydrodynamics, preprint, 2021.

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.
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, K. Wu, and D. Xiu, Methods to recover unknown processes in partial differential equations using data, Journal of Scientific Computing, 2020.
T. Qin, K. Wu, and D. Xiu, Data driven governing equations approximation using deep neural networks, Journal of Computational Physics, 2019.
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.
Z. Chen, V. Churchill, K. Wu, and D. Xiu, Deep neural network modeling of unknown partial differential equations in nodal space, preprint, 2021.


相对论流体力学方程的数学性质与高阶精度数值方法
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.
K. Wu, Minimum principle on specific entropy and high-order accurate invariant region preserving numerical methods for relativistic hydrodynamics, preprint, 2021.

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


[32]K. Wu
Minimum principle on specific entropy and high-order accurate invariant region preserving numerical methods for relativistic hydrodynamics
submitted for publication, arXiv:2102.03801, 2021.


[31] Z. Chen, V. Churchill, K. Wu, and D. Xiu
Deep neural network modeling of unknown partial differential equations in nodal space
submitted for publication, 2021.


[30]K. Wuand C.-W. Shu
Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations
Numerische Mathematik, accepted for publication, 2021.

[29]K. Wuand 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. Wuand 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. Wuand 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, accepted for publication, 2020.
[23] J. Hou, T. Qin,K. Wuand D. Xiu
A non-intrusive correction algorithm for classification problems with corrupted data
Commun. Appl. Math. Comput., in press, 2020.

[22]K. Wuand 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. Wuand D. Xiu
Numerical aspects for approximating governing equations using data
Journal of Computational Physics, 384: 200--221, 2019.

[19]K. Wuand D. Xiu
Sequential approximation of functions in Sobolev spaces using random samples
Commun. Appl. Math. Comput., 1: 449--466, 2019.

[18]K. Wuand 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. Wuand D. Xiu
Sequential function approximation on arbitrarily distributed point sets
Journal of Computational Physics, 354:370--386, 2018.
[14]K. Wuand 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. Wuand 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. Wuand 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. Wuand 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. Wuand 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. Wuand 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. Wuand 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. Wuand 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.