Uncertainty Quantification and Approximation Theory | Kailiang Wu

Uncertainty Quantification and Approximation Theory

A randomized tensor quadrature method for high dimensional polynomial approximation

K. Wu, Y. Shin, and D. Xiu

SIAM Journal on Scientific Computing, 2017.

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}
}

Sequential approximation of functions in Sobolev spaces using random samples

K. Wu and D. Xiu

Commun. Appl. Math. Comput., 2019.

Paper

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@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}
}

Sequential function approximation on arbitrarily distributed point sets

K. Wu and D. Xiu

Journal of Computational Physics, 2018.

Paper

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@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}
}

Sequential function approximation with noisy data

Y. Shin, K. Wu, and D. Xiu

Journal of Computational Physics, 2018.

Paper

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@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}
}

A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty

K. Wu, H. Tang, and D. Xiu

Journal of Computational Physics, 2017.

Paper arXiv

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@article{pub2017astochasticgalerkinmethodforfirstorderquasilinearhyperbolic,
  author = {Kailiang Wu and Huazhong Tang and Dongbin Xiu},
  title = {{A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty}},
  journal = {Journal of Computational Physics},
  year = {2017},
  volume = {345},
  pages = {224--244},
  doi = {10.1016/j.jcp.2017.05.027},
  eprint = {1601.04121},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1016/j.jcp.2017.05.027}
}

A WENO-based stochastic Galerkin scheme for ideal MHD equations with random inputs

K. Wu, D. Xiu, and X. Zhong

Communications in Computational Physics, 2021.

Paper

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@article{pub2021awenobasedstochasticgalerkinschemeforidealmhdequationswithrandom,
  author = {K. Wu and D. Xiu and X. Zhong},
  title = {{A WENO-based stochastic Galerkin scheme for ideal MHD equations with random inputs}},
  journal = {Communications in Computational Physics},
  year = {2021},
  volume = {30},
  number = {2},
  pages = {423--447},
  doi = {10.4208/cicp.OA-2020-0167},
  url = {https://doi.org/10.4208/cicp.OA-2020-0167}
}

Numerical aspects for approximating governing equations using data

K. Wu and D. Xiu

Journal of Computational Physics, 2019.

arXiv

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@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}
}

Critical sampling for robust evolution operator learning of unknown dynamical systems

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

IEEE Transactions on Artificial Intelligence, 2024.

arXiv

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@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}
}

Provably realizability-preserving finite volume method for quadrature-based moment models of kinetic equations

C. Fan, Q. Huang, and K. Wu*

arXiv, 2025. Preprint

arXiv

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@misc{pubarxiv251018380,
  author = {Chuan Fan and Qian Huang and Kailiang Wu},
  title = {{Provably realizability-preserving finite volume method for quadrature-based moment models of kinetic equations}},
  year = {2025},
  eprint = {2510.18380},
  archivePrefix = {arXiv},
  note = {Preprint},
  url = {https://arxiv.org/abs/2510.18380}
}