DeepSpace Comput Flow (DSCF) Group

Where Math Meets AI, Fluids, and Astrophysics

Exploring Nature through Intelligent Computation......


PI---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 


Employment


Education



Research Interests



Publications 



80. J. Chen, Q. Wang, and K. Wu*

Continuous Memory Neural Networks for Learning Complex Dynamical Systems

preprint2025


79. Y. Huang and K. Wu*

Constraint-preserving high-order schemes with oscillation elimination for spherically symmetric Einstein-Euler system

preprint2025


78. C. Yuan, Z. Zhang, H. Tang, and K. Wu*

High-order accurate bound-preserving adaptive moving mesh finite volume methods for 2D and 3D special relativistic hydrodynamics

submitted2025


77. M. Peng, Z. Li, and K. Wu*

Superconvergence of nonlinear oscillation-eliminating DG methods for linear hyperbolic equations

preprint2025


76. M. Liu, D. Pang, R. Abgrall, and K. Wu*,

An active-flux-type scheme for ideal MHD with provable positivity and discrete divergence-free property

preprint2025


75. H. Cao, Y. Huang (Yunqing Huang), Z. Li, and K. Wu*

COS(DG): Convex Oscillation-Suppressing Discontinuous Galerkin Method with Provable High-Order Accuracy

submitted2025


74. R. Yan, H. Cao, and K. Wu*

Provably positivity-preserving and globally divergence-free central DG methods for ideal MHD

submitted2025


73. K. Wu, X. Zhang, and C.-W. Shu

High order numerical methods preserving invariant domain for hyperbolic and related systems

submitted2025.     


72. M. Peng, K. Wu*, and C. Yuan

Oscillation-eliminating central DG schemes for hyperbolic conservation laws

submitted2025


71. R. Abgrall, M. Jiao, Y. Liu, and K. Wu*

A novel and simple invariant-domain-preserving framework for PAMPA scheme: 1D case

submitted2024. 


70. D. Pang and K. Wu*

Provably positivity-preserving constrained transport scheme for 2D and 3D ideal magnetohydrodynamics

sbumitted2024. 


69. 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.




68. S. Cui, K. Wu*, and L. Xu

On local minimum entropy principle of high-order schemes for relativistic Euler equations

Mathematics of Computation,     accepted,  2025.    



67. R. Abgrall, M. Jiao, Y. Liu, and K. Wu

Bound-preserving Point-Average-Moment PolynomiAl-interpreted (PAMPA) scheme: One-dimensional case

Communications in Computational Physics,   accepted,  2025



66. C. Cai, J. Qiu, and K. Wu*

Provably Convergent Newton–Raphson Method: Theoretically Robust Recovery of Primitive Variables in Relativistic MHD

SIAM Journal on Numerical Analysis,   63: 1128-1159,   2025.



65. J. Chen, K. Wu*, and D. Xiu

DUE: A deep learning framework and library for modeling unknown equations

SIAM to appear,  2025.



64. Z. Li and K. Wu*

Spectral volume from a DG perspective: oscillation elimination, stability, and optimal error estimates

SIAM Journal on Scientific Computing,    47: A1304-A1333,  2025.



63. H. Cao, M. Peng, and K. Wu*

Robust discontinuous Galerkin methods maintaining physical constraints for general relativistic hydrodynamics

Journal of Computational Physics,   526: 113770, 2025. 



62. M. Liu and K. Wu*

Structure-preserving oscillation-eliminating discontinuous Galerkin schemes for ideal MHD equations: Locally divergence-free and positivity-preserving

Journal of Computational Physics,   527: 1137952025.



61. S. Cui, Y. Gu, A. Kurganov, K. Wu, and R. Xin

Positivity-preserving new low-dissipation central-upwind schemes for compressible Euler equations

Journal of Computational Physics,   538: 114189,  2025. 



60. S. Ding, K. Wu*, and C. Yuan

Divergence-free finite volume WENO scheme for relativistic magnetohydrodynamics preserving positivity and subluminal velocity

Monthly Notices of the Royal Astronomical Society (MNRAS) 538:  1167-1190,   2025. 



59. W. Chen, S. Cui, K. Wu, and T. Xiong

Bound-preserving OEDG method for Aw-Rascle-Zhang traffic models on networks

Journal of Computational Physics,   520: 113507,   2025.



58. S. Ding, S. Cui, and K. Wu*

Robust DG schemes on unstructured triangular meshes: Oscillation elimination and bound preservation via optimal convex decomposition

Journal of Computational Physics,   526: 113769,   2025.



57. 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

Journal of Computational Physics,   527: 113801,   2025.



56. R. Yan, R. Abgrall, and K. Wu*

Uniformly high-order bound-preserving OEDG schemes for two-phase flows

Math. Models Methods Appl. Sci. (M3AS),   34: 2537-2610,  2024. 



55. J. Du, C. Fan, and K. Wu

Oscillation-eliminating discontinuous Galerkin methods for multicomponent chemically reacting flows

Annals of Applied Mathematics,  40: 412-444,   2024. 



54. J. Chen and K. Wu*

Positional knowledge is all you need: Position-induced Transformer (PiT) for operator learning

International Conference on Machine Learning (ICML),   7526-7552,  2024.



53. C. Fan and K. Wu*

High-order oscillation-eliminating Hermite WENO method for hyperbolic conservation laws

Journal of Computational Physics,   519: 113435,   2024.



52. M. Peng, Z. Sun, and K. Wu*

OEDG: Oscillation-eliminating discontinuous Galerkin method for hyperbolic conservation laws

Mathematics of Computation,     94: 1147-1198,  2025.    Published online on July 30, 2024     

  ( arXiv:2310.04807,  October 7, 2023 )



51. 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 Computing46: A1998-A2024, 2024



50. 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-A792024



49. S. Cui, A. Kurganov, and K. Wu*

Bound-preserving framework for central-upwind schemes for general hyperbolic conservation laws

SIAM Journal on Scientific Computing,    46: A2899-A2924,  2024.



48. S. Cui, S. Ding, and K. Wu*

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

SIAM Journal on Numerical Analysis,   62: 775-810,  2024



47. S. Ding and K. Wu*

GQL-based bound-preserving and locally divergence-free central discontinuous Galerkin schemes for relativistic magnetohydrodynamics

Journal of Computational Physics,   514: 113208,   2024.   A special issue in honor of Prof. Sergei Godunov(俄罗斯科学院院士)



46. C. Zhang, K. Wu, and Z. He

Critical sampling for robust evolution operator learning of unknown dynamical systems

IEEE Transactions on Artificial Intelligence,   5: 2856-2871,  2024.    



45. 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

      Journal of Computational Physics,   519: 113451,   2024.



44. 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.



43. 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



42. 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




41. 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.



40. 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 



39. J. Chen and K. Wu*

Deep-OSG: Deep learning of operators in semigroup

Journal of Computational Physics493: 112498, 2023.



38. 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 Physics492: 112429, 2023.



37. 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 Physics488: 112240, 2023.



36. 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.



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 (PCP) 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.




Funding & Honors


Group Members

  ◆  Dr. Shumo Cui (2023.02.01-present):  Ph.D. from Tulane University;  Postdoc at Temple University. 

  ◆  Dr. Shengrong Ding (2023.12.29-2025.6):  Ph.D. from USTC;  Postdoc at SUSTech

First job after leaving our group: Associate Professor at Sun Yat-sen University (Shenzhen). 

  ◆  Dr. Huihui Cao (2025.7-present):  Ph.D. from Xiangtan University;  Postdoc at SUSTech. 

  ◆  Dr. Shengrong Ding (2021.11-2023.12):  Ph.D. from University of Science and Technology of China.  

First job after postdoc: Research Assistant Professor at SUSTech

  ◆  Dr. Junfeng Chen ( 2022.10-2025.7.24 ):  B.Sc. from Tsinghua University, Ph.D. from Paris Sciences et Lettres – PSL Research University. 

First job after postdoc: Assistant Professor (tenure-track) at Hong Kong University of Science and Technolog (HKUST)

  ◆  Dr. Huihui Cao (2023.7-2025.6):  Ph.D. from Xiangtan University.

First job after postdoc: Research Assistant Professor at SUSTech. 

  ◆  Dr. Ruifang Yan (2023.7-):  Ph.D. from Wuhan University.

  ◆  Dr. Chuan Fan (2023.9-):  Ph.D. from Xiamen University.

  ◆  Dr. Mengqing Liu (2023.9-):  Ph.D. from University of Chinese Academy of Sciences.

  ◆  Dr. Qinghe Wang (2023.12-):  Ph.D. from Chinese University of Hong Kong, Shenzhen.

  ◆  Dr. Caiyou Yuan (2024.9-): B.Sc. from Zhejiang University, Ph.D. from Peking University.

  ◆  Dr. Jie Xu (2025.7-): Ph.D. from Ocean University of China.

  ◆  Dr. Jun Fang (2025.9-): Ph.D. from IAPCM.

  (1) Ph.D. Students:

  ◆  Zhuoyun Li (2022.9-),  Ph.D. Student,  B.Sc. from Southern University of Science and Technology.

  ◆  Manting Peng (2022.9-),  Ph.D. Student,  B.Sc. from Southern University of Science and Technology.

  ◆  Linfeng Xu (2022.9-),  Ph.D. Student,  B.Sc. from Southern University of Science and Technology.

  ◆  Dongwen Pang (2023.9-),  Ph.D. Student,  B.Sc. from Wuhan University of Technology, M.Sc. from Xiangtan University. 

  ◆  Jiahe Yue (2024.09-),  Ph.D. Student,  B.Sc. from NUAA.

  ◆  Miaosen Jiao (2025.9-),  Ph.D Student,  B.Sc. from Southern University of Science and Technology.

  ◆  Zongda He (2025.9-),  Ph.D Student,  B.Sc. from Southern University of Science and Technology.

 (2) Master Students:

  ◆  Fang Yan (2021.9-2023.7), Master Student,B.Sc. from South China University of Technology.

  ◆  Miaosen Jiao (2023.9-2025.7),  Master Student,  B.Sc. from Southern University of Science and Technology.

  ◆  Yuchen Huang (2024.09-),  Master Student,  B.Sc. from Southern University of Science and Technology.

  ◆  Haoxiang Yang (2025.09-),  Master Student,  B.Sc. from Southern University of Science and Technology.

  ◆  Fangyu Du (2025.09-),  Master Student,  B.Sc. from Southern University of Science and Technology.

  ◆  Dr. Junfeng Chen ( 2022.3-2022.9 ):  B.Sc. from Tsinghua University, Ph.D. from Paris Sciences et Lettres – PSL Research University. 

  ◆  Dr. Chuan Fan (2023.6-2023.9):  Ph.D. from Xiamen University.

  ◆  Dr. Hao Li (2023.12-2024.1): Ph.D. from Purdue University;Postdoc at University of Texas at Austin. 

      ◆  Dr. Junming Duan (2023.6-2023.7): Ph.D. Peking University; Postdoc at EPFL. 

      ◆  Dr. Caiyou Yuan (2024.7-2024.8): Ph.D. Peking University.

  ◆  Dr. Jun Fang (2025.7-2025.8): Ph.D. from IAPCM.

  ◆  Haili Jiang (2021.4-2021.12), Visiting Ph.D. Student from Peking University.

  ◆  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.

  ◆  Wei Chen (2024/2025), Visiting Ph.D. student from Xiamen University.

  ◆  Chaoyi Cai (2024/2025), Visiting Ph.D. student from Xiamen University.

  ◆  Hao Wang (2025.7-2025.8), Visiting undergraduate student from Zhejiang University.


Professional Services



Some Links