Machine Learning and Data-Driven Modeling | 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
Machine Learning and Data-Driven Modeling
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, 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}
}
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}
}
International Conference on Machine Learning (ICML), 2024.
arXiv
BibTeX
@inproceedings{pub2024positionalknowledgeisallyouneedpositioninducedtransformer,
author = {Junfeng Chen and Kailiang Wu},
title = {{Positional knowledge is all you need: Position-induced Transformer (PiT) for operator learning}},
booktitle = {International Conference on Machine Learning (ICML)},
year = {2024},
eprint = {2405.09285},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2405.09285}
}
Journal of Computational Physics, 2023.
Paper
arXiv
BibTeX
@article{pub2023deeposgdeeplearningofoperatorsinsemigroup,
author = {Junfeng Chen and Kailiang Wu},
title = {{Deep-OSG: Deep learning of operators in semigroup}},
journal = {Journal of Computational Physics},
year = {2023},
volume = {493},
pages = {112498},
doi = {10.1016/j.jcp.2023.112498},
eprint = {2302.03358},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2023.112498}
}
SIAM Journal on Scientific Computing, 2020.
arXiv
BibTeX
@article{pub2020structurepreservingmethodforreconstructingunknownhamiltoniansystemsfrom,
author = {Kailiang Wu and Tong Qin and Dongbin Xiu},
title = {{Structure-preserving method for reconstructing unknown Hamiltonian systems from trajectory data}},
journal = {SIAM Journal on Scientific Computing},
year = {2020},
volume = {42},
number = {6},
pages = {A3704--A3729},
eprint = {1905.10396},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1905.10396}
}
Journal of Computational Physics, 2019.
Paper
arXiv
BibTeX
@article{pub2019datadrivengoverningequationsapproximationusingdeepneuralnetworks,
author = {Tong Qin and Kailiang Wu and Dongbin Xiu},
title = {{Data driven governing equations approximation using deep neural networks}},
journal = {Journal of Computational Physics},
year = {2019},
volume = {395},
pages = {620--635},
doi = {10.1016/j.jcp.2019.06.042},
eprint = {1811.05537},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2019.06.042}
}
Journal of Computational Physics, 2022.
arXiv
BibTeX
@article{pub2022deepneuralnetworkmodelingofunknownpartialdifferentialequations,
author = {Zhen Chen and Victor Churchill and Kailiang Wu and Dongbin Xiu},
title = {{Deep neural network modeling of unknown partial differential equations in nodal space}},
journal = {Journal of Computational Physics},
year = {2022},
volume = {449},
pages = {110782},
eprint = {2106.03603},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2106.03603}
}
IEEE Transactions on Artificial Intelligence, 2024.
arXiv
BibTeX
@article{pub2024criticalsamplingforrobustevolutionoperatorlearningofunknowndynamicalsystems,
author = {Ce Zhang and Kailiang Wu and Zhihai He},
title = {{Critical sampling for robust evolution operator learning of unknown dynamical systems}},
journal = {IEEE Transactions on Artificial Intelligence},
year = {2024},
volume = {5},
pages = {2856-2871},
eprint = {2304.07485},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2304.07485}
}
Journal of Scientific Computing, 2020.
arXiv
BibTeX
@article{pub2020methodstorecoverunknownprocessesinpartialdifferentialequations,
author = {Zhen Chen and Kailiang Wu and Dongbin Xiu},
title = {{Methods to recover unknown processes in partial differential equations using data}},
journal = {Journal of Scientific Computing},
year = {2020},
volume = {85},
pages = {23},
eprint = {2003.02387},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2003.02387}
}
Journal of Computational Physics, 2019.
arXiv
BibTeX
@article{pub2019numericalaspectsforapproximatinggoverningequationsusingdata,
author = {Kailiang Wu and Dongbin Xiu},
title = {{Numerical aspects for approximating governing equations using data}},
journal = {Journal of Computational Physics},
year = {2019},
volume = {384},
pages = {200--221},
eprint = {1809.09170},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1809.09170}
}
Commun. Appl. Math. Comput., 2021.
arXiv
BibTeX
@article{pub2021anonintrusivecorrectionalgorithmforclassificationproblemswithcorrupteddata,
author = {Jun Hou and Tong Qin and Kailiang Wu and Dongbin Xiu},
title = {{A non-intrusive correction algorithm for classification problems with corrupted data}},
journal = {Commun. Appl. Math. Comput.},
year = {2021},
volume = {3},
pages = {337--356},
eprint = {2002.04658},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2002.04658}
}
Commun. Appl. Math. Comput., 2019.
Paper
BibTeX
@article{pub2019sequentialapproximationoffunctionsinsobolevspacesusingrandomsamples,
author = {K. Wu and D. Xiu},
title = {{Sequential approximation of functions in Sobolev spaces using random samples}},
journal = {Commun. Appl. Math. Comput.},
year = {2019},
volume = {1},
pages = {449--466},
doi = {10.1007/s42967-019-00028-7},
url = {https://doi.org/10.1007/s42967-019-00028-7}
}
Journal of Computational Physics, 2018.
Paper
BibTeX
@article{pub2018sequentialfunctionapproximationwithnoisydata,
author = {Y. Shin and K. Wu and D. Xiu},
title = {{Sequential function approximation with noisy data}},
journal = {Journal of Computational Physics},
year = {2018},
volume = {371},
pages = {363--381},
doi = {10.1016/j.jcp.2018.05.042},
url = {https://doi.org/10.1016/j.jcp.2018.05.042}
}
Journal of Computational Physics, 2018.
Paper
BibTeX
@article{pub2018sequentialfunctionapproximationonarbitrarilydistributedpointsets,
author = {K. Wu and D. Xiu},
title = {{Sequential function approximation on arbitrarily distributed point sets}},
journal = {Journal of Computational Physics},
year = {2018},
volume = {354},
pages = {370--386},
doi = {10.1016/j.jcp.2017.10.020},
url = {https://doi.org/10.1016/j.jcp.2017.10.020}
}
SIAM Journal on Scientific Computing, 2017.
Paper
BibTeX
@article{pub2017arandomizedtensorquadraturemethodforhighdimensionalpolynomial,
author = {K. Wu and Y. Shin and D. Xiu},
title = {{A randomized tensor quadrature method for high dimensional polynomial approximation}},
journal = {SIAM Journal on Scientific Computing},
year = {2017},
volume = {39},
number = {5},
pages = {A1811--A1833},
doi = {10.1137/16M1081695},
url = {https://doi.org/10.1137/16M1081695}
}