Selected publications | Kailiang Wu
Kailiang Wu
Professor of Mathematics
Southern University of Science and Technology (SUSTech)
Email: wukl@sustech.edu.cn
Mailing address
Department of Mathematics, School of Science
Southern University of Science and Technology
1088 Xueyuan Avenue, Nanshan District
Shenzhen, Guangdong 518055, China
Selected publications
A selection of work in numerical analysis and scientific machine learning.
Nature Communications, 2026.
Paper
Code
BibTeX
@article{pub2026learningmissingphysicsfromlegacysimulatorswithalternatingneural,
author = {H. Wang and Q. Wang and C. Yuan and K. Wu},
title = {{Learning missing physics from legacy simulators with alternating neural integrators}},
journal = {Nature Communications},
year = {2026},
doi = {10.1038/s41467-026-74002-2},
url = {https://doi.org/10.1038/s41467-026-74002-2}
}
SIAM Review, 2026. In press
PDF
arXiv
BibTeX
@article{pub2026highordernumericalmethodspreservinginvariantdomainforhyperbolicandrelatedsystems,
author = {Kailiang Wu and Xiangxiong Zhang and Chi-Wang Shu},
title = {{High order numerical methods preserving invariant domain for hyperbolic and related systems}},
journal = {SIAM Review},
year = {2026},
eprint = {2512.09116},
archivePrefix = {arXiv},
note = {In press},
url = {https://arxiv.org/abs/2512.09116}
}
SIAM Review, 2025.
Paper
PDF
arXiv
Code
BibTeX
@article{pub2025dueadeeplearningframeworkandlibraryformodeling,
author = {Junfeng Chen and Kailiang Wu and Dongbin Xiu},
title = {{DUE: A deep learning framework and library for modeling unknown equations}},
journal = {SIAM Review},
year = {2025},
volume = {67},
number = {4},
pages = {873--902},
doi = {10.1137/24M1671827},
eprint = {2504.10373},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/24M1671827}
}
Mathematics of Computation, 2025.
Paper
PDF (arXiv version)
arXiv
BibTeX
@article{pub2025oedgoscillationeliminatingdiscontinuousgalerkinmethodforhyperbolicconservation,
author = {Manting Peng and Zheng Sun and Kailiang Wu},
title = {{OEDG: Oscillation-eliminating discontinuous Galerkin method for hyperbolic conservation laws}},
journal = {Mathematics of Computation},
year = {2025},
volume = {94},
pages = {1147--1198},
doi = {10.1090/mcom/3998},
eprint = {2310.04807},
archivePrefix = {arXiv},
url = {https://doi.org/10.1090/mcom/3998}
}
SIAM Journal on Numerical Analysis, 2024.
arXiv
BibTeX
@article{pub2024onoptimalcellaveragedecompositionforhighorderbound,
author = {Shumo Cui and Shengrong Ding and Kailiang Wu},
title = {{On optimal cell average decomposition for high-order bound-preserving schemes of hyperbolic conservation laws}},
journal = {SIAM Journal on Numerical Analysis},
year = {2024},
eprint = {2212.05045},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2212.05045}
}
SIAM Review, Research Spotlight, 2023.
Paper
PDF
arXiv
BibTeX
@article{pub2023geometricquasilinearizationframeworkforanalysisanddesignofbound,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{Geometric quasilinearization framework for analysis and design of bound-preserving schemes}},
journal = {SIAM Review},
year = {2023},
volume = {65},
number = {4},
pages = {1031--1073},
doi = {10.1137/21M1458247},
eprint = {2111.04722},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/21M1458247}
}
SIAM Journal on Scientific Computing, 2021.
arXiv
BibTeX
@article{pub2021minimumprincipleonspecificentropyandhighorderaccurate,
author = {Kailiang Wu},
title = {{Minimum principle on specific entropy and high-order accurate invariant region preserving numerical methods for relativistic hydrodynamics}},
journal = {SIAM Journal on Scientific Computing},
year = {2021},
volume = {43},
number = {6},
pages = {B1164--B1197},
eprint = {2102.03801},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2102.03801}
}
Journal of Computational Physics, 2020.
arXiv
BibTeX
@article{pub2020datadrivendeeplearningofpartialdifferentialequationsin,
author = {Kailiang Wu and Dongbin Xiu},
title = {{Data-driven deep learning of partial differential equations in modal space}},
journal = {Journal of Computational Physics},
year = {2020},
volume = {408},
pages = {109307},
eprint = {1910.06948},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1910.06948}
}
Numerische Mathematik, 2019.
arXiv
BibTeX
@article{pub2019provablypositivehighorderschemesforidealmagnetohydrodynamicsanalysis,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{Provably positive high-order schemes for ideal magnetohydrodynamics: Analysis on general meshes}},
journal = {Numerische Mathematik},
year = {2019},
volume = {142},
number = {4},
pages = {995--1047},
eprint = {1807.11467},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1807.11467}
}
SIAM Journal on Numerical Analysis, 2018.
Paper
PDF
arXiv
BibTeX
@article{pub2018positivitypreservinganalysisofnumericalschemesforidealmagnetohydrodynamics,
author = {Kailiang Wu},
title = {{Positivity-preserving analysis of numerical schemes for ideal magnetohydrodynamics}},
journal = {SIAM Journal on Numerical Analysis},
year = {2018},
volume = {56},
number = {4},
pages = {2124--2147},
doi = {10.1137/18M1168017},
eprint = {1802.02278},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/18M1168017}
}
Math. Models Methods Appl. Sci. (M3AS), 2017.
Paper
arXiv
BibTeX
@article{pub2017admissiblestatesandphysicalconstraintspreservingschemesforrelativistic,
author = {Kailiang Wu and Huazhong Tang},
title = {{Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations}},
journal = {Math. Models Methods Appl. Sci. (M3AS)},
year = {2017},
volume = {27},
number = {10},
pages = {1871--1928},
doi = {10.1142/S0218202517500348},
eprint = {1603.06660},
archivePrefix = {arXiv},
url = {https://doi.org/10.1142/S0218202517500348}
}