Kailiang Wu
Associate Professor of Mathematics, Southern University of Science and Technology
E-mail: WUKL [AT] sustech [DOT] edu [DOT] cn
Address: M613, SUSTech College of Science Building, 1088 Xueyuan Avenue, Xili, Nanshan District, Shenzhen, Guangdong 518055, P.R. China
Website: English Version , 中文版本
Join us: A postdoc position 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 about￥380,000 per year for postdocs. If you are interested, please send your CV to WUKL [AT] sustech [DOT] edu [DOT] cn.
Employment
2021.01-present: Associate Professor, Department of Mathematics, Southern University of Science and Technology
2022.03-present: Associate Professor, Shenzhen 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
Editorial Board
Journal on Numerical Methods and Computer Applications
Frontiers in Applied Mathematics and Statistics (Numerical Analysis and Scientific Computation Section)
Research Interests
Machine Learning and Data-driven Modeling
Numerical Solutions of Partial Differential Equations
Hyperbolic Conservation Laws
Computational Fluid Dynamics
High-order Accurate Numerical Methods
Structure-preserving Methods: Design and Analysis
Approximation Theory and Uncertainty Quantification
Publications
64. S. Ding, S. Cui, and K. Wu*
High-order accurate OEDG schemes with rotational invariance for hyperbolic equations on unstructured meshes
preprint, 2024.
63. Z. Zhang, H. Tang, and K. Wu*
High-order accurate structure-preserving finite volume schemes on adaptive moving meshes for shallow water equations: Well-balancedness and positivity
submitted, 2024.
62. S. Cui, K. Wu*, and L. Xu
Provably entropy-bounded high-order schemes for relativistic hydrodynamics with Synge-type equation of state
preprint, 2024.
61. M. Peng and K. Wu*
OECDG: Oscillation-eliminating central discontinuous Galerkin schemes for hyperbolic conservation laws
preprint, 2024.
60. W. Chen, S. Cui, K. Wu, and T. Xiong
Bound-preserving OEDG method for Aw-Rascle-Zhang traffic models on networks
submitted, 2024.
59. C. Fan and K. Wu*
High-order oscillation-eliminating Hermite WENO method for hyperbolic conservation laws
submitted, 2024.
58. Z. Li and K. Wu*
Spectral volume from a DG perspective: oscillation elimination, stability, and optimal error estimates
preprint, 2024.
57. J. Chen, K. Wu*, and D. Xiu
DUE: A deep learning framework and library for modeling unknown equations
submitted, 2024.
56. M. Liu and K. Wu*
Structure-preserving oscillation-eliminating discontinuous Galerkin schemes for ideal MHD equations: Locally divergence-free and positivity-preserving
submitted, 2024.
55. L. Y. Win, Y. Chen, Y. Nie, L. Cai, K. Wu
Physical-constraint-preserving high-order 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 Newton-Raphson 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*
High-order accurate positivity-preserving and well-balanced discontinuous Galerkin schemes for ten-moment Gaussian closure equations with source terms
submitted to Journal of Computational Physics, 2024.
52. S. Ding and K. Wu*
GQL-based bound-preserving and locally divergence-free central discontinuous Galerkin schemes for relativistic magnetohydrodynamics
Journal of Computational Physics, accepted, 2024. A special issue in honor of Prof. Sergei Godunov（俄罗斯科学院院士）
51. S. Cui, A. Kurganov, and K. Wu*
Bound-preserving framework for central-upwind schemes for general hyperbolic conservation laws
SIAM Journal on Scientific Computing, accepted, 2024.
50. M. Peng, Z. Sun, and K. Wu*
OEDG: Oscillation-eliminating discontinuous Galerkin method for hyperbolic conservation laws
Mathematics of Computation, accepted, 2024. (arXiv:2310.04807)
This paper proposes a novel approach for eliminating spurious oscillations in DG methods for hyperbolic equations;
The idea is to eliminate oscillations by evolving a damping equation with the DG solution as the "initial value";
Oscillation-Eliminating (OE) procedure is non-intrusive, highly efficient, very easy to implement, scale-invariant, evolution-invariant, and linearity-invariant;
This work first reveals the damping technique's role as a modal filter, bridging the damping and spectral viscosity (filtering) techniques.
49. J. Chen and K. Wu*, Positional knowledge is all you need: Position-induced Transformer (PiT) for operator learning
International Conference on Machine Learning (ICML), accepted, 2024.
48. W. Chen, K. Wu, and T. Xiong
High order structure-preserving 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 divergence-free path-conservative central-upwind scheme for ideal and shallow water magnetohydrodynamics
SIAM Journal on Scientific Computing, accepted, 2024.
46. L. Xu, S. Ding, and K. Wu*, High-order accurate entropy stable schemes for relativistic hydrodynamics with a general equation of state
Journal of Scientific Computing, 98: 43, 2024.
45. 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, 498: 112669, 2024.
44. 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.
43. 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, 46: A50-A79, 2024.
42. 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, 62: 775-810, 2024.
It remained unknown for a decade what CAD is optimal for general polynomial spaces, especially in multiple dimensions;
This work proved the classical 1D cell average decomposition (CAD) is optimal for designing high-order BP schemes;
It is discovered that the classical 2D CAD is not optimal for P^k space;
A general theory is estalbished for seeking the optimal 2D CAD, involving convex geometry and symmetric group techniques;
We develop a generic approach to find out the genuine OCAD, which gives much milder BP CFL than the classic CAD yet requires much fewer nodes.
These findings notably improve the efficiency of general high-order BP methods for a large class of hyperbolic equations while requiring only a minor adjustment of the implementation code.
41. J. Chen and K. Wu*, Deep-OSG: Deep learning of operators in semigroup
Journal of Computational Physics, 493: 112498, 2023.
40. 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, 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 bound-preserving schemes in multiple dimensions?
Journal of Computational Physics, 476: 111882, 2023.
37. 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.
36. K. Wu and C.-W. Shu*, Geometric Quasilinearization (GQL) Framework for Analysis and Design of Bound-Preserving Schemes
SIAM Review, (Research Spotlight) 65(4): 1031--1073, 2023.
This paper proposes a general framework, motivated by our previous bound-preserving works [10,16,18,22,30,32] 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 Runge--Kutta methods for linear seminegative problems
SIAM Journal on Numerical Analysis, 60(5): 2448--2481, 2022.
34. Y. Chen and K. Wu*, A physical-constraint-preserving finite volume WENO method for special relativistic hydrodynamics on unstructured meshes
Journal of Computational Physics, 466: 111398, 2022.
33. H. Jiang, H. Tang, and K. Wu*, Positivity-preserving well-balanced central discontinuous Galekin schemes for the Euler equations under gravitational fields
Journal of Computational Physics, 463: 111297, 2022.
32. 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. arXiv:2102.03801
31. 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. arXiv:2106.03603
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. arXiv:2002.03371
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. arXiv:2005.07166.
28. 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. arXiv:1905.10396.
27. K. Wu and D. Xiu, Data-driven deep learning of partial differential equations in modal space
Journal of Computational Physics, 408: 109307, 2020. arXiv:1910.06948 (15 Oct 2019).
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. arXiv:1907.07467 (17 July 2019).
25. K. Wu, D. Xiu, and X. Zhong, A WENO-based stochastic Galerkin scheme for ideal MHD equations with random inputs
Communications in Computational Physics, 30(2): 423--447, 2021.
24. Z. Chen, K. Wu, and D. Xiu, Methods to recover unknown processes in partial differential equations using data
Journal of Scientific Computing, 85:23, 2020. arXiv:2003.02387.
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. arXiv:2002.04658.
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. Y. Shin, K. Wu, and D. Xiu, Sequential function approximation with noisy data
Journal of Computational Physics, 371:363--381, 2018.
16. K. Wu, Positivity-preserving analysis of numerical schemes for ideal magnetohydrodynamics
SIAM Journal on Numerical Analysis, 56(4):2124--2147, 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, 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.
12. K. Wu, Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics
Physical Review D, 95, 103001, 2017.
11. 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.
10. 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.
9. 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. A special issue dedicated to Prof. Zhenhuan Teng's 80th birthday
8. 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)
7. 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.
6. 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.
5. 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.
4. 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.
3. K. Wu and H. Tang, Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics
Journal of Computational Physics, 256:277--307, 2014.
2. 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.
RESEARCH REPORT
1. K. Wu and D. Xiu, An explicit neural network construction for piecewise constant function approximation, arXiv preprint arXiv:1808.07390.
Awards & Funding
National Natural Science Foundation of China (NSFC), Major Program, PI (国家自然科学基金 重大研究计划培育项目，主持) (2023) (Funding: 0.7 million)
Distinguished Young Scholar, Shenzhen Science and Technology Program, PI (深圳市杰青项目，主持) (2023) (Funding: 4 million)
National Natural Science Foundation of China (NSFC), General Program, PI (国家自然科学基金 面上项目，主持) (2021) (Funding: 0.5 million)
National Excellent Young Scholar Program, PI (国家高层次人才计划 青年项目，主持) (2020) (Funding: 2 million)
Zhong Jiaqing Mathematics Award, the Chinese Mathematical Society (中国数学会 钟家庆数学奖) (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 (中国数学会计算数学分会 优秀青年论文奖一等奖) (2015)
First Prize of “Challenge Cup” May-4th Youth Science Award, PKU (2014)
Group Members
Principal Investigator: Prof. Dr. Kailiang Wu
Research Assistant Professor
◆ Dr. Shumo Cui (2023.02.01-present): Ph.D. from Tulane University; Postdoc at Temple University.
◆ Dr. Shengrong Ding (2023.12.29-present): Ph.D. from USTC; Postdoc at SUSTech.
Postdoctoral Fellows
◆ Dr. Shengrong Ding (2021.11-2023.12): Ph.D. from University of Science and Technology of China.
◆ Dr. Junfeng Chen ( Postdoc Fellow: 2022.10-present; Visiting Postdoc Scholar: 2022.03-2022.09): B.Sc. from Tsinghua University, Ph.D. from Paris Sciences et Lettres – PSL Research University.
◆ Dr. Ruifang Yan (Postdoc Fellow: 2023.07-): Ph.D. from Wuhan University.
◆ Dr. Huihui Cao (Postdoc Fellow: 2023.07-): Ph.D. from Xiangtan University.
◆ Dr. Chuan Fan (Postdoc Fellow: 2023.09-; Visiting Postdoc Scholar: 2023.06-2023.09): Ph.D. from Xiamen University.
◆ Dr. Mengqing Liu (Postdoc Fellow: 2023.09-): Ph.D. from University of Chinese Academy of Sciences.
◆ Dr. Qinghe Wang (Postdoc Fellow: 2023.12-): Ph.D. from Chinese University of Hong Kong, Shenzhen.
Graduate Students
◆ Haili Jiang (2021.04-2021.12), Visiting Ph.D. Student from Peking University.
◆ Fang Yan (2021.09-2023.07), Master Student，B.Sc. from South China University of Technology.
◆ Zhuoyun Li (2022.09-), Ph.D. Student, B.Sc. from Southern University of Science and Technology.
◆ Manting Peng (2022.09-), Master Student, B.Sc. from Southern University of Science and Technology.
◆ Linfeng Xu (2022.09-), Master Student, B.Sc. from Southern University of Science and Technology.
◆ Dongwen Pang (2023.09-), Ph.D. Student, B.Sc. from Wuhan University of Technology, M.Sc. from Xiangtan University.
◆ Miaosen Jiao (2023.09-), Master Student, B.Sc. from Southern University of Science and Technology.
◆ Caiyou Yuan(2023.06.29-08.30), Visiting Ph.D. student from Peking University.
◆ Zhihao Zhang (2023.06.29-08.30), Visiting Ph.D. student from Peking University.
◆ Jiangfu Wang (2023.06.29-08.30), Visiting Ph.D. student from Peking University.
Professional Services
Reviewer for AMS Mathematical Reviews (Invited)
Referee for scientific journals including
Annals of Applied Mathematics
Applied Mathematics and Computation
Applied Numerical Mathematics
Chinese Journal of Computational Physics
Electronic Research Archive
Journal of Computational Physics ( 70+ times )
Journal of Mathematical Biology
Journal of Numerical Mathematics
Journal of Applied Mathematics and Computing
Mathematics of Computation
Numerical Methods for Partial Differential Equations
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