Faculty > Professors > WU Kailiang
WU Kailiang
Associate Professor
 Brief Biography
 Research
 Teaching
 Published Works
Employment
◆ 2021.01present: Associate Professor, Department of Mathematics, Southern University of Science and Technology
◆ 2022.03present: Associate Professor, SUSTech International Center for Mathematics, Southern University of Science and Technology
◆ 2022.09present: Associate Professor, National Center for Applied Mathematics Shenzhen
◆ 2016.082020.12: Postdoctoral Scholar, Department of Mathematics, The Ohio State University
◆ 2016.042016.08: Postdoctoral Fellow, Scientific Computing and Imaging Institute, University of Utah
Education
◆ 20112016: Ph.D. School of Mathematical Sciences, Peking University
◆ 20072011: B.Sc. School of Mathematics and Statistics, Huazhong University of Science and Technology
Research Interests
◆ Machine Learning and Datadriven Modeling
◆ Numerical Solutions of Partial Differential Equations
◆ Computational Fluid Dynamics and Astrophysics
◆ Highorder 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" May4th Youth Science Award, PKU (2014)
◆ President Scholarship, PKU (2014–2016) (The biggest scholarship of PKU)
Selected Publications
◆ K. Wu
Positivitypreserving analysis of numerical schemes for ideal magnetohydrodynamics
SIAM Journal on Numerical Analysis, 56(4):21242147, 2018.
◆ K. Wu and C.W. Shu
Geometric quasilinearization framework for analysis and design of boundpreserving schemes
SIAM Review, (Research Spotlight) 65(4): 10311073, 2023.
◆ K. Wu* and C.W. Shu
Provably positive highorder schemes for ideal magnetohydrodynamics: Analysis on general meshes
Numerische Mathematik, 142(4): 9951047, 2019.
◆ K. Wu
Minimum principle on specific entropy and highorder accurate invariant region preserving numerical methods for relativistic hydrodynamics
SIAM Journal on Scientific Computing, 43(6): B1164B1197, 2021.
◆ M. Peng, Z. Sun, and K.Wu*
OEDG: Oscillationeliminating discontinuous Galerkin method for hyperbolic conservation laws
Mathematics of Computation, in press, 2024.
◆ K. Wu
Design of provably physicalconstraintpreserving methods for general relativistic hydrodynamics
Physical Review D, 95, 103001, 2017.
◆ K. Wu and H. Tang
Admissible states and physicalconstraintspreserving schemes for relativistic magnetohydrodynamic equations
Math. Models Methods Appl. Sci. (M3AS), 27(10):18711928, 2017.
◆ K. Wu and D. Xiu
Datadriven 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: 250285, 2023.
◆ Z. Sun, Y. Wei, and K. Wu*
On energy laws and stability of RungeKutta methods for linear seminegative problems
SIAM Journal on Numerical Analysis, 60(5): 24482481, 2022.
◆ S. Cui, S. Ding, and K. Wu*
On optimal cell average decomposition for highorder boundpreserving schemes of hyperbolic conservation laws
SIAM Journal on Numerical Analysis, accepted, 2023.
◆ K. Wu* and C.W. Shu
Provably physicalconstraintpreserving discontinuous Galerkin methods for multidimensional relativistic MHD equations
Numerische Mathematik, 148: 699741, 2021.
◆ K. Wu and C.W. Shu
A provably positive discontinuous Galerkin method for multidimensional ideal magnetohydrodynamics
SIAM Journal on Scientific Computing, 40(5):B1302B1329, 2018.
◆ K. Wu and C.W. Shu
Entropy symmetrization and highorder accurate entropy stable numerical schemes for relativistic MHD equations
SIAM Journal on Scientific Computing, 42(4): A2230A2261, 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):A1811A1833, 2017.
◆ K. Wu and Y. Xing
Uniformly highorder structurepreserving discontinuous Galerkin methods for Euler equations with gravitation: Positivity and wellbalancedness
SIAM Journal on Scientific Computing, 43(1): A472A510, 2021.
◆ K. Wu, T. Qin, and D. Xiu
Structurepreserving method for reconstructing unknown Hamiltonian systems from trajectory data
SIAM Journal on Scientific Computing, 42(6): A3704A3729, 2020.
◆ S. Ding and K.Wu*
A new discretely divergencefree positivitypreserving highorder finite volume method for ideal MHD equations
SIAM Journal on Scientific Computing, accepted, 2023.
◆ S. Cui, A. Kurganov, and K. Wu*
Boundpreserving framework for centralupwind schemes for general hyperbolic conservation laws
SIAM Journal on Scientific Computing, accepted, 2024.
◆ K. Wu and H. Tang
A direct Eulerian GRP scheme for spherically symmetric general relativistic hydrodynamics
SIAM Journal on Scientific Computing, 38(3):B458B489, 2016.
◆ A. Chertock, A. Kurganov, M. Redle, and K. Wu
A new locally divergencefree pathconservative centralupwind scheme for ideal and shallow water magnetohydrodynamics
SIAM Journal on Scientific Computing, accepted, 2024.
◆ K. Wu and H. Tang
Highorder accurate physicalconstraintspreserving finite difference WENO schemes for special relativistic hydrodynamics
Journal of Computational Physics, 298:539564, 2015.
◆ T. Qin, K. Wu, and D. Xiu
Data driven governing equations approximation using deep neural networks
Journal of Computational Physics, 395: 620635, 2019.
◆ S. Cui, S. Ding, and K. Wu*
Is the classic convex decomposition optimal for boundpreserving schemes in multiple dimensions?
Journal of Computational Physics, 476: 111882, 2022.
◆ J. Chen and K. Wu*
DeepOSG: Deep learning of operators in semigroup
Journal of Computational Physics, accepted, 2023.
◆ K. Wu and H. Tang
Physicalconstraintpreserving 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)
◆ S. Ding and K. Wu*
GQLbased boundpreserving and locally divergencefree central discontinuous Galerkin schemes for relativistic magnetohydrodynamics
Journal of Computational Physics, accepted, 2024.
◆ 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 NewtonRaphson methods for recovering primitive variables with applications to physicalconstraintpreserving 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 physicalconstraintpreserving finite volume method for special relativistic hydrodynamics on unstructured meshes
Journal of Computational Physics, 466: 111398, 2022.
◆ H. Jiang, H. Tang, and K. Wu*
Positivitypreserving wellbalanced 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: 200221, 2019.
◆ Y. Shin, K. Wu, and D. Xiu
Sequential function approximation with noisy data
Journal of Computational Physics, 371:363381, 2018.
◆ Y. Ren, K. Wu, J. Qiu, and Y. Xing
On positivitypreserving wellbalanced 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, 354:370386, 2018.
◆ K. Wu and H. Tang
On physicalconstraintspreserving 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 firstorder quasilinear hyperbolic systems with uncertainty
Journal of Computational Physics, 345:224244, 2017.
◆ K. Wu and H. Tang
Finite volume local evolution Galerkin method for twodimensional relativistic hydrodynamics
Journal of Computational Physics, 256:277307, 2014.
◆ K. Wu, Z. Yang, and H. Tang
A thirdorder accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics
Journal of Computational Physics, 264:177208, 2014.
◆ J. Chen and K. Wu*
Positional knowledge is all you need: Positioninduced Transformer (PiT) for operator learning
International Conference on Machine Learning (ICML), 2024.
Professional Services
◆ Editorial Board of Journal on Numerical Methods and Computer Applications
◆ Editorial Board of Frontiers in Applied Mathematics and Statistics (Numerical Analysis and Scientific Computation Section)
◆ Reviewer for AMS Mathematical Reviews
◆ Referee for scientific journals and machine learning conferences including

Annals of Applied Mathematics

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 ( 70+ 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

Numerical Methods for Partial Differential Equations

SIAM Journal on Scientific Computing (SISC)

SIAM/ASA Journal on Uncertainty Quantification

Theoretical and Applied Mechanics Letters

International Conference on Machine Learning (ICML)
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.
Design and Analysis of Structurepreserving Methods: Bound/Positivity, Minimum Entropy Principle, Entropy Stability, Energy Stability, Wellbalance, Asymptotic Preserving, Divergencefree
K. Wu, Positivitypreserving analysis of numerical schemes for ideal magnetohydrodynamics, SIAM Journal on Numerical Analysis, 2018.
K. Wu and C.W. Shu, Geometric quasilinearization framework for analysis and design of boundpreserving schemes, SIAM Review, 2023.
K. Wu* and C.W. Shu, Provably positive highorder schemes for ideal magnetohydrodynamics: Analysis on general meshes, Numerische Mathematik, 2019.
K. Wu, Minimum principle on specific entropy and highorder accurate invariant region preserving numerical methods for relativistic hydrodynamics, SIAM Journal on Scientific Computing, 2021.
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, 2023.
S. Cui, S. Ding, and K. Wu*, On optimal cell average decomposition for highorder boundpreserving schemes of hyperbolic conservation laws, SIAM Journal on Numerical Analysis, 2024.
Z. Sun, Y. Wei, and K. Wu*, On energy laws and stability of RungeKutta methods for linear seminegative problems, SIAM Journal on Numerical Analysis, 2022.
K. Wu* and C.W. Shu, Provably physicalconstraintpreserving discontinuous Galerkin methods for multidimensional relativistic MHD equations, Numerische Mathematik, 2021.
K. Wu and H. Tang, Admissible states and physicalconstraintspreserving schemes for relativistic magnetohydrodynamic equations, Math. Models Methods Appl. Sci. (M3AS), 2017.
K. Wu and Y. Xing, Uniformly highorder structurepreserving discontinuous Galerkin methods for Euler equations with gravitation: Positivity and wellbalancedness, SIAM Journal on Scientific Computing, 2021.
K. Wu and C.W. Shu, Entropy symmetrization and highorder 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 physicalconstraintpreserving methods for general relativistic hydrodynamics, Physical Review D, 2017.
K. Wu and H. Tang, Highorder accurate physicalconstraintspreserving finite difference WENO schemes for special relativistic hydrodynamics, Journal of Computational Physics, 2015.
H. Jiang, H. Tang, and K. Wu*, Positivitypreserving wellbalanced central discontinuous Galekin schemes for the Euler equations under gravitational fields, Journal of Computational Physics, 2022.
S. Cui, S. Ding, and K. Wu*, Is the classic convex decomposition optimal for boundpreserving schemes in multiple dimensions?, Journal of Computational Physics, 2023.
A. Chertock, A. Kurganov, M. Redle, and K. Wu, A new locally divergencefree pathconservative centralupwind scheme for ideal and shallow water magnetohydrodynamics, preprint, 2022.
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, 2023.
Y. Ren, K. Wu, J. Qiu, and Y. Xing, On highorder positivitypreserving wellbalanced finite volume methods for the Euler equations with gravitation, Journal of Computational Physics, 2023.
C. Cai, J. Qiu, and K.Wu*, Provably convergent NewtonRaphson methods for recovering primitive variables with applications to physicalconstraintpreserving Hermite WENO schemes for relativistic hydrodynamics, Journal of Computational Physics, 2024.
L. Xu, S. Ding, and K. Wu*, Highorder accurate entropy stable schemes for relativistic hydrodynamics with a general equation of state, Journal of Scientific Computing, 2024.
S. Ding and K. Wu*, A new discretely divergencefree positivitypreserving highorder finite volume method for ideal MHD equations, SIAM Journal on Scientific Computing, 2024.
W. Chen, K. Wu, and T. Xiong, High order structurepreserving finite difference WENO scheme for MHD equations with gravitation in all sonic Mach numbers, Journal of Scientific Computing, 2024.
S. Cui, A. Kurganov, and K. Wu*, Boundpreserving framework for centralupwind schemes for general hyperbolic conservation laws, preprint, 2024.
C. Cai, J. Qiu, and K. Wu*, Efficient provably convergent NewtonRaphson method for primitive variables in relativistic MHD equations, preprint, 2024.
Deep Learning and Datadriven Modeling
J. Chen and K. Wu*, Positional knowledge is all you need: Positioninduced Transformer (PiT) for operator learning, International Conference on Machine Learning (ICML), 2024.
J. Chen and K. Wu*, DeepOSG: Deep learning of operators in semigroup, Journal of Computational Physics, 2023.
C. Zhang, K. Wu, and Z. He, Critical sampling for robust evolution operator learning of unknown dynamical systems, IEEE Transactions on Artificial Intelligence, 2024.
K.Wu and D. Xiu, Datadriven 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, Structurepreserving 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, 2022.
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 nonintrusive 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.
Mathematical Properties and Highorder Numerical Methods of Relativistic Hydrodynamic Equations
K. Wu, Minimum principle on specific entropy and highorder accurate invariant region preserving numerical methods for relativistic hydrodynamics, SIAM Journal on Scientific Computing, 2021.
K. Wu, Design of provably physicalconstraintpreserving methods for general relativistic hydrodynamics, Physical Review D, 2017.
K. Wu and H. Tang, Highorder accurate physicalconstraintspreserving finite difference WENO schemes for special relativistic hydrodynamics, Journal of Computational Physics, 2015.
K. Wu and H. Tang, Admissible states and physicalconstraintspreserving schemes for relativistic magnetohydrodynamic equations, Math. Models Methods Appl. Sci. (M3AS), 2017.
K. Wu* and C.W. Shu, Provably physicalconstraintpreserving 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, Physicalconstraintpreserving 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 twodimensional relativistic hydrodynamics, Journal of Computational Physics, 2014.
Y. Chen and K. Wu*, A physicalconstraintpreserving finite volume method for special relativistic hydrodynamics on unstructured meshes, Journal of Computational Physics, 2022.
L. Xu, S. Ding, and K. Wu*, Highorder accurate entropy stable schemes for relativistic hydrodynamics with a general equation of state, Journal of Scientific Computing, 2024.
C. Cai, J. Qiu, and K.Wu*, Provably convergent NewtonRaphson methods for recovering primitive variables with applications to physicalconstraintpreserving Hermite WENO schemes for relativistic hydrodynamics, Journal of Computational Physics, 2024.
C. Cai, J. Qiu, and K. Wu*, Efficient provably convergent NewtonRaphson method for primitive variables in relativistic MHD equations, preprint, 2024.
Highdimensional Function Approximation：Big Data, Optimal Sampling, and Polynomial Approximation
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.
Generalized Riemann Problem Solvers and Godunovtype Schemes for Hyperbolic Conservation Laws
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 twodimensional relativistic hydrodynamics, Journal of Computational Physics, 2014.
K. Wu, Z. Yang, and H. Tang, A thirdorder accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics, Journal of Computational Physics, 2014.
Uncertainty Quantification and Stochastic Galerkin Methods
K. Wu, D. Xiu, and X. Zhong, A WENObased 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 firstorder quasilinear hyperbolic systems with uncertainty, Journal of Computational Physics, 2017.
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): Ph.D. from Tulane University; Postdoc at Temple University; VAP at SUSTech. We have a joint article: "Is the classic convex decomposition optimal for boundpreserving schemes in multiple dimensions?" published in 《Journal of Computational Physics》. We have a joint article: "On optimal cell average decomposition for highorder boundpreserving schemes of hyperbolic conservation laws" accepted for publication in 《SIAM Journal on Numerical Analysis》. We have a joint article with Prof. Alexander Kurganov: "Boundpreserving framework for centralupwind schemes for general hyperbolic conservation laws" accepted by 《SIAM Journal on Scientific Computing》. We have a joint article with Prof. Tao Xiong: "Boundpreserving OEDG method for AwRascleZhang traffic models on networks" submitted to SISC.

Dr. Shengrong Ding (2023.12): Ph.D. from University of Science and Technology of China（中科大博士）; Postdoc at SUSTech（南科大博士后）. We have a joint article: "Is the classic convex decomposition optimal for boundpreserving schemes in multiple dimensions?" published in 《Journal of Computational Physics》. We have a joint article: "On optimal cell average decomposition for highorder boundpreserving schemes of hyperbolic conservation laws" accepted for publication in 《SIAM Journal on Numerical Analysis》. We have a joint article "A new discretely divergencefree positivitypreserving highorder finite volume method for ideal MHD equations" published in 《SIAM Journal on Scientific Computing》. We have a joint article: "Highorder accurate entropy stable schemes for relativistic hydrodynamics with a general equation of state" published in《Journal of Scientific Computing》. We have a joint article: "GQLbased boundpreserving and locally divergencefree central discontinuous Galerkin schemes for relativistic magnetohydrodynamics" published in 《Journal of Computational Physics》(A special issue in honor of 俄罗斯科学院院士 Sergei Godunov).
Postdoctoral Fellows（博士后研究员）

Dr. Shengrong Ding (2021.112023.11): 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 boundpreserving schemes in multiple dimensions?" published in 《Journal of Computational Physics》. We have a joint article: "On optimal cell average decomposition for highorder boundpreserving schemes of hyperbolic conservation laws" accepted for publication in 《SIAM Journal on Numerical Analysis》. We have a joint article "A new discretely divergencefree positivitypreserving highorder finite volume method for ideal MHD equations" published in 《SIAM Journal on Scientific Computing》. We have a joint article: "Highorder accurate entropy stable schemes for relativistic hydrodynamics with a general equation of state" published in《Journal of Scientific Computing》. We have a joint article: "GQLbased boundpreserving and locally divergencefree central discontinuous Galerkin schemes for relativistic magnetohydrodynamics" published in 《Journal of Computational Physics》(A special issue in honor of 俄罗斯科学院院士 Sergei Godunov).

Dr. Junfeng Chen (Postdoc Fellow: 2022.10present; Visiting Postdoc Scholar: 2022.032022.09): 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 "DeepOSG: Deep learning of operators in semigroup" published in《Journal of Computational Physics》. We have a joint article "Positional knowledge is all you need: Positioninduced Transformer (PiT) for operator learning" published in 《International Conference on Machine Learning (ICML)》. We have a joint article "DUE: A deep learning framework and library for modeling unknown equations" submitted.

Dr. Ruifang Yan (Postdoc Fellow: 2023.07): Ph.D. from Wuhan University（武汉大学博士）. We are writing a joint article "Uniformly highorder boundpreserving OEDG schemes for twophase flows".

Dr. Huihui Cao (Postdoc Fellow: 2023.07): Ph.D. from Xiangtan University（湘潭大学博士）. We are writing a joint article "Robust OEDG schemes for general relativistic hydrodynamics".

Dr. Chuan Fan (Postdoc Fellow: 2023.09; Visiting Postdoc Scholar: 2023.062023.09): Ph.D. from Xiamen University（厦门大学博士）. We have a joint article "Highorder oscillationeliminating Hermite WENO method for hyperbolic conservation laws" submitted to JCP.

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）. We have a joint article "Structurepreserving oscillationeliminating discontinuous Galerkin schemes for ideal MHD equations: Locally divergencefree and positivitypreserving" submitted to JCP.

Dr. Qinghe Wang (Postdoc Fellow: 2023.12): Ph.D. from the Chinese University of Hong Kong, Shenzhen（香港中文大学深圳分校博士）. We are working on deep learning for differential equations and operator learning.
Graduate Students (研究生)

Haili Jiang (2021.042021.12)，Visiting Ph.D. student from Peking University（北京大学）. We have a joint article with Prof. ChiWang 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: "Positivitypreserving wellbalanced central discontinuous Galerkin schemes for the Euler equations under gravitational fields" published in《Journal of Computational Physics》.

Fang Yan (2021.092023.07)，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）. We have a joint article "Spectral volume from a DG perspective: oscillation elimination, stability, and optimal error estimates" submitted.

Manting Peng (2022.09)，Master student，B.Sc. from SUSTech（南科大）. We have a joint article: "OEDG: Oscillationeliminating discontinuous Galerkin method for hyperbolic conservation laws" published in 《Mathematics of Computation》（计算数学顶级期刊）. We are writing several papers, including one on OECDG, one on "Robust OEDG schemes for general relativistic hydrodynamics", and one on "optimal convergence of ALE DG".

Linfeng Xu (2022.09)，Master student，B.Sc. from SUSTech（南科大）. We have a joint article: "Highorder accurate entropy stable schemes for relativistic hydrodynamics with a general equation of state" published in《Journal of Scientific Computing》. We are writing a joint article "Provably entropybounded highorder schemes for relativistic hydrodynamics with Syngetype equation of state".

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. We are writing a joint article "A secondorder provably positivitypreserving constrainedtransport with globally discrete zerodivergence for ideal MHD".

Miaosen Jiao (2023.09), Master student, B.Sc. from SUSTech（南科大）. We are working on structurepreserving active flux method for hyperbolic conservation laws.

Caiyou Yuan(2023.06.2908.30), Visiting Ph.D. student from Peking University（北京大学）. We are writing a joint article with Prof. Huazhong Tang on "Boundpreserving adaptive moving mesh method for special relativistic hydrodynamics".

Zhihao Zhang (2023.06.2908.30), Visiting Ph.D. student from Peking University（北京大学）. We have a joint article with Prof. Huazhong Tang: "Highorder accurate structurepreserving finite volume schemes on adaptive moving meshes for shallow water equations: Well balancedness and positivity" submitted to JCP.

Jiangfu Wang (2023.06.2908.30), Visiting Ph.D. student from Peking University（北京大学）. We have a joint article with Prof. Huazhong Tang: "Highorder accurate positivitypreserving and wellbalanced discontinuous Galerkin schemes for tenmoment Gaussian closure equations with source terms" submitted to 《Journal of Computational Physics》.

Wei Chen, Visiting Ph.D. student from Xiamen University. We have a joint article with Prof. Tao Xiong: "High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers" published in 《Journal of Computational Physics》. We have a joint article with Prof. Tao Xiong: "High order structurepreserving finite difference WENO scheme for MHD equations with gravitation in all sonic Mach numbers" published in 《Journal of Scientific Computing》. We have a joint article with RAP Shumo Cui and Prof. Tao Xiong: "Boundpreserving OEDG method for AwRascleZhang traffic models on networks" submitted to 《SIAM Journal on Scientific Computing》.

Chaoyi Cai, Visiting Ph.D. student from Xiamen University. We have a joint article with Prof. Jianxian Qiu: "Provably convergent NewtonRaphson methods for recovering primitive variables with applications to physicalconstraintpreserving Hermite WENO schemes for relativistic hydrodynamics" published in 《Journal of Computational Physics》. We have a joint article with Prof. Jianxian Qiu: "Provably convergent and robust NewtonRaphson method: A new dawn in primitive variable recovery for relativistic MHD" submitted to 《SIAM Journal on Numerical Analysis》.
Undergraduate Students (本科生)

Yuanzhe Wei: We have a joint article with Prof. Zheng Sun: "On energy laws and stability of RungeKutta 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/nhlTvmGpdOrXuwZa7v4Tg] . 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 WisconsinMadison（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 (2021.042022.06) 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. He won SUSTech outstanding bachelor thesis (本科毕业论文入选南科大优秀毕业论文).

Yuanji Zhong：He was selected into a joint study program in University of WisconsinMadison（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).
Visiting Postdocs（访问博士后）

Dr. Hao Li (2023.122024.1): Ph.D. from Purdue University；Postdoc at University of Texas at Austin.

Dr. Junming Duan (2023.62023.7): Ph.D. Peking University; Postdoc at EPFL.

Dr. Caiyou Yuan (2024.72024.8): Ph.D. Peking University.
Welcome passionate and highly selfmotivated 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.
Publications List
[64] Z. Zhang, H. Tang, and K. Wu*
Highorder accurate structurepreserving finite volume schemes on adaptive moving meshes for shallow water equations: Well balancedness and positivity
sbumitted, 2024.
[63] S. Cui, K. Wu*, and L. Xu
Provably entropybounded highorder schemes for relativistic hydrodynamics with Syngetype equation of state
preprint, 2024.
[62] M. Peng and K. Wu*
OECDG: Oscillationeliminating central discontinuous Galerkin schemes for hyperbolic conservation laws
preprint, 2024.
[61] J. Chen, K. Wu*, and D. Xiu
DUE: A deep learning framework and library for modeling unknown equations
submitted, 2024.
[60] W. Chen, S. Cui, K. Wu, and T. Xiong
Boundpreserving OEDG method for AwRascleZhang traffic models on networks
submitted, 2024.
[59] C. Fan and K. Wu*
Highorder oscillationeliminating Hermite WENO method for hyperbolic conservation laws
submitted to JCP, 2024.
[58] Z. Li and K. Wu*
Spectral volume from a DG perspective: oscillation elimination, stability, and optimal error estimates
preprint, 2024.
[57] S. Ding, S. Cui, and K. Wu*
Highorder accurate OEDG schemes with rotational invariance for hyperbolic equations on unstructured meshes
preprint, 2024.
[56] M. Liu and K. Wu*
Structurepreserving oscillationeliminating discontinuous Galerkin schemes for ideal MHD equations: Locally divergencefree and positivitypreserving
submitted to JCP, 2024.
[55] L. Y. Win, Y. Chen, Y. Nie, L. Cai, and K. Wu
Physicalconstraintpreserving highorder finite volume WENO method via geometric quasilinearization for Chaplygin gas dynamics
submitted, 2024.
[54] C. Cai, J. Qiu, and K. Wu*
Provably convergent and robust NewtonRaphson method: A new dawn in primitive variable recovery for relativistic MHD
submitted to SIAM Journal on Numerical Analysis, 2024.
[53] J. Wang, H. Tang, K. Wu*
Highorder accurate positivitypreserving and wellbalanced discontinuous Galerkin schemes for tenmoment Gaussian closure equations with source terms
submitted to Journal of Computational Physics, 2024.
[52] S. Ding and K. Wu*
GQLbased boundpreserving and locally divergencefree central discontinuous Galerkin schemes for relativistic magnetohydrodynamics
Journal of Computational Physics, accepted, 2024. A special issue in honor of Sergei Godunov（俄罗斯科学院院士）
[51] S. Cui, A. Kurganov, and K. Wu*
Boundpreserving framework for centralupwind schemes for general hyperbolic conservation laws
SIAM Journal on Scientific Computing, accepted, 2024.
[50] M. Peng, Z. Sun, and K.Wu*
OEDG: Oscillationeliminating discontinuous Galerkin method for hyperbolic conservation laws
Mathematics of Computation, accepted, 2024
[49] J. Chen and K. Wu*
Positional knowledge is all you need: Positioninduced Transformer (PiT) for operator learning
International Conference on Machine Learning (ICML), accepted, 2024.
[48] W. Chen, K. Wu, and T. Xiong
High order structurepreserving finite difference WENO scheme for MHD equations with gravitation in all sonic Mach numbers
Journal of Scientific Computing, 99: 36, 2024.
[47] A. Chertock, A. Kurganov, M. Redle, and K. Wu
A new locally divergencefree pathconservative centralupwind scheme for ideal and shallow water magnetohydrodynamics
SIAM Journal on Scientific Computing, accepted, 2024.
[46] C. Cai, J. Qiu, and K.Wu*
Provably convergent NewtonRaphson methods for recovering primitive variables with applications to physicalconstraintpreserving Hermite WENO schemes for relativistic hydrodynamics
Journal of Computational Physics, 498: 112669, 2024.
[45] C. Zhang, K. Wu, and Z. He
Critical sampling for robust evolution operator learning of unknown dynamical systems
IEEE Transactions on Artificial Intelligence, in press, 2024.
[44] L. Xu, S. Ding, and K. Wu*
Highorder accurate entropy stable schemes for relativistic hydrodynamics with a general equation of state
Journal of Scientific Computing, 98: 43, 2024.
[43] S. Ding and K.Wu*
A new discretely divergencefree positivitypreserving highorder finite volume method for ideal MHD equations
SIAM Journal on Scientific Computing, 46: A50A79, 2024.
[42] S. Cui, S. Ding, and K. Wu*
On optimal cell average decomposition for highorder boundpreserving schemes of hyperbolic conservation laws
SIAM Journal on Numerical Analysis, 62: 775810, 2024.
[41] J. Chen and K. Wu*
DeepOSG: Deep learning of operators in semigroup
Journal of Computational Physics, 493: 112498, 2023.
[40] Y. Ren, K. Wu, J. Qiu, and Y. Xing
On highorder positivitypreserving wellbalanced finite volume methods for the Euler equations with gravitation
Journal of Computational Physics, 492:112429, 2023.
[39] 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.
[38] S. Cui, S. Ding, and K. Wu*
Is the classic convex decomposition optimal for boundpreserving schemes in multiple dimensions?
Journal of Computational Physics, 476: 111882, 2023.
[37] K. Wu*, H. Jiang, and C.W. Shu
Provably positive central DG schemes via geometric quasilinearization for ideal MHD equations
SIAM Journal on Numerical Analysis, 61: 250285, 2023.
[36] K. Wu and C.W. Shu
Geometric quasilinearization framework for analysis and design of boundpreserving schemes
SIAM Review, (Research Spotlight) 65(4): 10311073, 2023.
This paper proposes a general approachGeometric QuasiLinearization (GQL), motivated by our previous boundpreserving works on MHD and RHD systems. GQL equivalently transforms nonlinear constraints into linear ones, through properly introducing free auxiliary variables, i.e., it uses extra auxiliary variables in exchange for linearity.
[35] Z. Sun, Y. Wei, and K. Wu*
On energy laws and stability of RungeKutta methods for linear seminegative problems
SIAM Journal on Numerical Analysis, 60(5): 24482481, 2022.
[34] K. Wu
Minimum principle on specific entropy and highorder accurate invariant region preserving numerical methods for relativistic hydrodynamics
SIAM Journal on Scientific Computing, 43(6): B1164B1197, 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, 449: 110782, 2022.
[32] K. Wu* and C.W. Shu
Provably physicalconstraintpreserving discontinuous Galerkin methods for multidimensional relativistic MHD equations
Numerische Mathematik, 148: 699741, 2021.
[31] Y. Chen and K. Wu*
A physicalconstraintpreserving finite volume WENO method for special relativistic hydrodynamics on unstructured meshes
Journal of Computational Physics, 466: 111398, 2022.
[30] H. Jiang, H. Tang, and K. Wu*
Positivitypreserving wellbalanced central discontinuous Galerkin schemes for the Euler equations under gravitational fields
Journal of Computational Physics, 463: 111297, 2022.
[29] K. Wu and Y. Xing
Uniformly highorder structurepreserving discontinuous Galerkin methods for Euler equations with gravitation: Positivity and wellbalancedness
SIAM Journal on Scientific Computing, 43(1): A472A510, 2021.
[28] K. Wu and D. Xiu
Datadriven deep learning of partial differential equations in modal space
Journal of Computational Physics, 408: 109307, 2020.
[27] K. Wu, T. Qin, and D. Xiu
Structurepreserving method for reconstructing unknown Hamiltonian systems from trajectory data
SIAM Journal on Scientific Computing, 42(6): A3704A3729, 2020.
[26] K. Wu and C.W. Shu
Entropy symmetrization and highorder accurate entropy stable numerical schemes for relativistic MHD equations
SIAM Journal on Scientific Computing, 42(4): A2230A2261, 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 WENObased stochastic Galerkin scheme for ideal MHD equations with random inputs
Communications in Computational Physics, 30: 423447, 2021.
[23] J. Hou, T. Qin, K. Wu and D. Xiu
A nonintrusive correction algorithm for classification problems with corrupted data
Commun. Appl. Math. Comput., 3: 337356, 2021.
[22] K. Wu* and C.W. Shu
Provably positive highorder schemes for ideal magnetohydrodynamics: Analysis on general meshes
Numerische Mathematik, 142(4): 9951047, 2019.
[21] T. Qin, K. Wu, and D. Xiu
Data driven governing equations approximation using deep neural networks
Journal of Computational Physics, 395: 620635, 2019.
[20] K. Wu and D. Xiu
Numerical aspects for approximating governing equations using data
Journal of Computational Physics, 384: 200221, 2019.
[19] K. Wu and D. Xiu
Sequential approximation of functions in Sobolev spaces using random samples
Commun. Appl. Math. Comput., 1: 449466, 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):B1302B1329, 2018.
[17] K. Wu
Positivitypreserving analysis of numerical schemes for ideal magnetohydrodynamics
SIAM Journal on Numerical Analysis, 56(4):21242147, 2018.
[16] Y. Shin, K. Wu, and D. Xiu
Sequential function approximation with noisy data
Journal of Computational Physics, 371:363381, 2018.
[15] K. Wu and D. Xiu
Sequential function approximation on arbitrarily distributed point sets
Journal of Computational Physics, 354:370386, 2018.
[14] K. Wu and H. Tang
On physicalconstraintspreserving 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):A1811A1833, 2017.
[11] K. Wu
Design of provably physicalconstraintpreserving methods for general relativistic hydrodynamics
Physical Review D, 95, 103001, 2017.
[10] K. Wu, H. Tang, and D. Xiu
A stochastic Galerkin method for firstorder quasilinear hyperbolic systems with uncertainty
Journal of Computational Physics, 345:224244, 2017.
[9] K. Wu and H. Tang
Admissible states and physicalconstraintspreserving schemes for relativistic magnetohydrodynamic equations
Math. Models Methods Appl. Sci. (M3AS), 27(10):18711928, 2017.
[8] Y. Kuang, K. Wu, and H. Tang
RungeKutta discontinuous local evolution Galerkin methods for the shallow water equations on the cubedsphere grid
Numer. Math. Theor. Meth. Appl., 10(2):373419, 2017.
[7] K. Wu and H. Tang
Physicalconstraintpreserving 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):B458B489, 2016.
[5] K. Wu and H. Tang
A Newton multigrid method for steadystate shallow water equations with topography and dry areas
Applied Mathematics and Mechanics, 37(11):14411466, 2016.
[4] K. Wu and H. Tang
Highorder accurate physicalconstraintspreserving finite difference WENO schemes for special relativistic hydrodynamics
Journal of Computational Physics, 298:539564, 2015.
[3] K. Wu, Z. Yang, and H. Tang
A thirdorder accurate direct Eulerian GRP scheme for onedimensional relativistic hydrodynamics
East Asian J. Appl. Math., 4(2):95131, 2014.
[2] K. Wu and H. Tang
Finite volume local evolution Galerkin method for twodimensional relativistic hydrodynamics
Journal of Computational Physics, 256:277307, 2014.
[1] K. Wu, Z. Yang, and H. Tang
A thirdorder accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics
Journal of Computational Physics, 264:177208, 2014.