Employment

◆ 2026.06-present: Professor, Department of Mathematics, Southern University of Science and Technology

◆ 2021.01-2026.05: 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:  xk星空官方网站D.  School of Mathematical Sciences, Peking University

◆ 2007-2011:  B.xk星空官方网站.  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

◆ xk星空官方网站 Accurate Numerical Methods

◆ Hyperbolic Conservation Laws

◆ Approximation Theory and Uncertainty Quantification

Awards

◆ 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 xk星空官方网站D. Graduates Award, PKU (2016)

◆ 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 (latest update: May 2021)

◆ K. xk星空官方网站

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

◆ K. xk星空官方网站 and C.-W. Shu

Provably positive xk星空官方网站 schemes for ideal magnetohydrodynamics: Analysis on general meshes

Numerische Mathematik,    142(4): 995--1047, 2019.

◆ K. xk星空官方网站 and D. Xiu

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

Journal of Computational Physics,    408: 109307, 2020. 

◆ K. xk星空官方网站 and C.-W. Shu

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

Numerische Mathematik,    accepted for publication, 2021.

◆ K. xk星空官方网站 

Minimum principle on specific entropy and xk星空官方网站 accurate invariant region preserving numerical methods for relativistic hydrodynamics

submitted for publication, arXiv:2102.03801, 2021.

◆ Z. Chen, V. Churchill, K. xk星空官方网站, and D. Xiu
Deep neural network modeling of unknown partial differential equations in nodal space
Journal of Computational Physics,    submitted for publication, 2021.

◆ K. xk星空官方网站 and Y. Xing

Uniformly xk星空官方网站 structure-preserving discontinuous Galerkin methods for Euler equations with gravitation: Positivity and well-balancedness

SIAM Journal on Scientific Computing,    accepted for publication, 2020.

◆ K. xk星空官方网站, 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. xk星空官方网站 and C.-W. Shu

Entropy symmetrization and xk星空官方网站 accurate entropy stable numerical schemes for relativistic MHD equations

SIAM Journal on Scientific Computing,    42(4): A2230--A2261, 2020. 

◆ Z. Chen, K. xk星空官方网站, and D. Xiu

Methods to recover unknown processes in partial differential equations using data

Journal of Scientific Computing,    85:23, 2020. 

◆ K. xk星空官方网站, D. Xiu, and X. Zhong

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

Communications in Computational Physics,    accepted for publication, 2020.

◆ J. Hou, T. Qin, K. xk星空官方网站 and D. Xiu

A non-intrusive correction algorithm for classification problems with corrupted data

Commun. Appl. Math. Comput.,   in press, 2020.

◆ T. Qin, K. xk星空官方网站, and D. Xiu

Data driven governing equations approximation using deep neural networks

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

◆ K. xk星空官方网站 and D. Xiu

Numerical aspects for approximating governing equations using data

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

◆ K. xk星空官方网站 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. xk星空官方网站, and D. Xiu

Sequential function approximation with noisy data

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

◆ K. xk星空官方网站 and D. Xiu

Sequential function approximation on arbitrarily distributed point sets

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

◆ K. xk星空官方网站 and H. Tang

On physical-constraints-preserving schemes for special relativistic magnetohydrodynamics with a general equation of state

Z. Angew. Math. xk星空官方网站.,    69:84(24pages), 2018.

◆ K. xk星空官方网站, 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. xk星空官方网站

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

Physical Review D,   95, 103001, 2017. 

◆ K. xk星空官方网站, 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. xk星空官方网站 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. 

◆ Y. Kuang, K. xk星空官方网站, 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. 

◆ K. xk星空官方网站 and H. Tang

Physical-constraint-preserving central discontinuous Galerkin methods for special relativistic hydrodynamics with a general equation of state

Astrophys. J. Suppl. xk星空官方网站. (ApJS),   228(1):3(23pages), 2017. (2015 Impact Factor of ApJS: 11.257)

◆ K. xk星空官方网站 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. xk星空官方网站 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. 

◆ K. xk星空官方网站 and H. Tang

xk星空官方网站 accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics

Journal of Computational Physics,   298:539--564, 2015.

◆ K. xk星空官方网站 and H. Tang

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

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

◆ K. xk星空官方网站, 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