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Kailiang WU
Associate Professor
Research interest: ◆ Machine Learning and Data-driven Modeling ◆ Numerical Solutions of Partial Differential Equations ◆ Computational Fluid Dynamics and Astrophysics ◆ High-order Accurate Numerical Methods ◆ Hyperbolic Conservation Laws ◆ Approximation Theory and Unce

Employment

◆ 2021.01-present: Associate Professor, Department of Mathematics, Southern University of Science and Technology

 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


Research Interests

◆ Machine Learning and Data-driven Modeling

◆ Numerical Solutions of Partial Differential Equations

◆ Computational Fluid Dynamics and Astrophysics

◆ High-order Accurate Numerical Methods

◆ Hyperbolic Conservation Laws

◆ Approximation Theory and Uncertainty Quantification


Honors & Awards

◆ National Distinguished Young Scholar (2020)

◆ Zhong Jiaqing Mathematics Award, the Chinese Mathematical Society (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  (2015)

◆ First Prize of "Challenge Cup" May-4th Youth Science Award, PKU (2014)

◆ President Scholarship, PKU (2014–2016) (The biggest scholarship of PKU)


Selected Publications (see [Published Works] for Full Publications List)


◆ K. Wu

Positivity-preserving analysis of numerical schemes for ideal magnetohydrodynamics
SIAM Journal on Numerical Analysis,    56(4):2124--2147, 2018.


◆ 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.


◆ K. Wu and D. Xiu*

Data-driven deep learning of partial differential equations in modal space

Journal of Computational Physics,    408: 109307, 2020. 


◆ K. Wu and C.-W. Shu*

Geometric quasilinearization framework for analysis and design of bound-preserving schemes
submitted for publication, 2021.  arXiv:2111.04722.  8 Nov 2021


◆ K. Wu* and C.-W. Shu

Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations

Numerische Mathematik,    148: 699--741, 2021.


◆ 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.


◆ Z. Sun, Y. Wei, and K. Wu*

On energy laws and stability of Runge--Kutta methods for linear seminegative problems

submitted to SIAM Journal on Numerical Analysis,   2022.


◆ 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.


◆ 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


◆ Y. Chen and K. Wu*

A physical-constraint-preserving finite volume method for special relativistic hydrodynamics on unstructured meshes

Journal of Computational Physics,     submitted for publication, 2021.


◆ H. Jiang, H. Tang, and K. Wu*

Positivity-preserving well-balanced central discontinuous Galerkin schemes for the Euler equations under gravitational fields

Journal of Computational Physics,     submitted for publication, 2021.


◆ 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. 


◆ 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. 


◆ 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. 


◆ 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: 423--447, 2021.


◆ T. Qin, K. Wu, and D. Xiu

Data driven governing equations approximation using deep neural networks

Journal of Computational Physics,    395: 620--635, 2019.


◆ K. Wu and D. Xiu

Numerical aspects for approximating governing equations using data

Journal of Computational Physics,    384: 200--221, 2019.


◆ 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.


◆ Y. Shin, K. Wu, and D. Xiu

Sequential function approximation with noisy data

Journal of Computational Physics,    371:363--381, 2018.


◆ K. Wu and D. Xiu

Sequential function approximation on arbitrarily distributed point sets

Journal of Computational Physics,    354:370--386, 2018.


◆ 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.


◆ 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. 


◆ K. Wu

Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics

Physical Review D,   95, 103001, 2017. 


◆ 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. 


◆ 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. 


◆ 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)


◆ 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. 


◆ 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.


◆ K. Wu and H. Tang

Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics

Journal of Computational Physics,   256:277--307, 2014. 


◆ 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.


Professional Services

◆ Reviewer for AMS Mathematical Reviews

◆ Referee for scientific journals including

  • Communications in Computational Physics

  • Computer Methods in Applied Mechanics and Engineering

  • East Asian Journal on Applied Mathematics

  • Engineering Optimization

  • Journal of Computational and Applied Mathematics

  • Journal of Computational Physics

  • Journal of Scientific Computing

  • Journal of Applied Mathematics and Computing

  • Mathematical Models and Methods in Applied Sciences (M3AS)

  • Mathematica Numerica Sinica

  • SIAM Journal on Scientific Computing

  • SIAM/ASA Journal on Uncertainty Quantification