Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics. - Kailiang Wu; Huazhong Tang (J. Comput. Phys., 2014)

A third-order accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics. - Kailiang Wu; Zhicheng Yang; Huazhong Tang (J. Comput. Phys., 2014)

High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics. - Kailiang Wu; Huazhong Tang (J. Comput. Phys., 2015)

A Direct Eulerian GRP Scheme for Spherically Symmetric General Relativistic Hydrodynamics. - Kailiang Wu; Huazhong Tang (SIAM J. Sci. Comput., 2016)

A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty. - Kailiang Wu; Huazhong Tang; Dongbin Xiu (J. Comput. Phys., 2017)

A Randomized Tensor Quadrature Method for High Dimensional Polynomial Approximation. - Kailiang Wu; Yeonjong Shin; Dongbin Xiu (SIAM J. Sci. Comput., 2017)

An Explicit Neural Network Construction for Piecewise Constant Function Approximation. - Kailiang Wu; Dongbin Xiu (CoRR, 2018)

Sequential function approximation with noisy data. - Yeonjong Shin; Kailiang Wu; Dongbin Xiu (J. Comput. Phys., 2018)

Sequential function approximation on arbitrarily distributed point sets. - Kailiang Wu; Dongbin Xiu (J. Comput. Phys., 2018)

Positivity-Preserving Analysis of Numerical Schemes for Ideal Magnetohydrodynamics. - Kailiang Wu (SIAM J. Numer. Anal., 2018)

A Provably Positive Discontinuous Galerkin Method for Multidimensional Ideal Magnetohydrodynamics. - Kailiang Wu; Chi-Wang Shu (SIAM J. Sci. Comput., 2018)

Data driven governing equations approximation using deep neural networks. - Tong Qin 002; Kailiang Wu; Dongbin Xiu (J. Comput. Phys., 2019)

Numerical aspects for approximating governing equations using data. - Kailiang Wu; Dongbin Xiu (J. Comput. Phys., 2019)

Provably positive high-order schemes for ideal magnetohydrodynamics: analysis on general meshes. - Kailiang Wu; Chi-Wang Shu (Numerische Mathematik, 2019)

A Non-Intrusive Correction Algorithm for Classification Problems with Corrupted Data. - Jun Hou; Tong Qin 002; Kailiang Wu; Dongbin Xiu (CoRR, 2020)

Data-driven deep learning of partial differential equations in modal space. - Kailiang Wu; Dongbin Xiu (J. Comput. Phys., 2020)

Methods to Recover Unknown Processes in Partial Differential Equations Using Data. - Zhen Chen; Kailiang Wu; Dongbin Xiu (J. Sci. Comput., 2020)

Structure-Preserving Method for Reconstructing Unknown Hamiltonian Systems From Trajectory Data. - Kailiang Wu; Tong Qin 002; Dongbin Xiu (SIAM J. Sci. Comput., 2020)

Entropy Symmetrization and High-Order Accurate Entropy Stable Numerical Schemes for Relativistic MHD Equations. - Kailiang Wu; Chi-Wang Shu (SIAM J. Sci. Comput., 2020)

Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations. - Kailiang Wu; Chi-Wang Shu (Numerische Mathematik, 2021)

Minimum Principle on Specific Entropy and High-Order Accurate Invariant-Region-Preserving Numerical Methods for Relativistic Hydrodynamics. - Kailiang Wu (SIAM J. Sci. Comput., 2021)

Uniformly High-Order Structure-Preserving Discontinuous Galerkin Methods for Euler Equations with Gravitation: Positivity and Well-Balancedness. - Kailiang Wu; Yulong Xing (SIAM J. Sci. Comput., 2021)

Provably Positive Central DG Schemes via Geometric Quasilinearization for Ideal MHD Equations. - Kailiang Wu; Haili Jiang; Chi-Wang Shu (CoRR, 2022)

Deep neural network modeling of unknown partial differential equations in nodal space. - Zhen Chen; Victor Churchill; Kailiang Wu; Dongbin Xiu (J. Comput. Phys., 2022)

A physical-constraint-preserving finite volume WENO method for special relativistic hydrodynamics on unstructured meshes. - Yaping Chen; Kailiang Wu (J. Comput. Phys., 2022)

Positivity-preserving well-balanced central discontinuous Galerkin schemes for the Euler equations under gravitational fields. - Haili Jiang; Huazhong Tang; Kailiang Wu (J. Comput. Phys., 2022)

On Energy Laws and Stability of Runge-Kutta Methods for Linear Seminegative Problems. - Zheng Sun 004; Yuanzhe Wei; Kailiang Wu (SIAM J. Numer. Anal., 2022)

Deep-OSG: A deep learning approach for approximating a family of operators in semigroup to model unknown autonomous systems. - Junfeng Chen; Kailiang Wu (CoRR, 2023)

OEDG: Oscillation-eliminating discontinuous Galerkin method for hyperbolic conservation laws. - Manting Peng; Zheng Sun 004; Kailiang Wu (CoRR, 2023)

Provably Positive Central Discontinuous Galerkin Schemes via Geometric Quasilinearization for Ideal MHD Equations. - Kailiang Wu; Haili Jiang; Chi-Wang Shu (SIAM J. Numer. Anal., 2023)

Is the classic convex decomposition optimal for bound-preserving schemes in multiple dimensions? - Shumo Cui; Shengrong Ding; Kailiang Wu (J. Comput. Phys., 2023)

High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers. - Wei Chen; Kailiang Wu; Tao Xiong (J. Comput. Phys., 2023)

Deep-OSG: Deep learning of operators in semigroup. - Junfeng Chen; Kailiang Wu (J. Comput. Phys., 2023)

On high order positivity-preserving well-balanced finite volume methods for the Euler equations with gravitation. - Yupeng Ren; Kailiang Wu; Jianxian Qiu; Yulong Xing (J. Comput. Phys., 2023)

Geometric Quasilinearization Framework for Analysis and Design of Bound-Preserving Schemes. - Kailiang Wu; Chi-Wang Shu (SIAM Rev., 2023)

Positional Knowledge is All You Need: Position-induced Transformer (PiT) for Operator Learning. - Junfeng Chen; Kailiang Wu (ICML, 2024)

Provably Convergent and Robust Newton-Raphson Method: A New Dawn in Primitive Variable Recovery for Relativistic MHD. - Chaoyi Cai; Jianxian Qiu; Kailiang Wu (CoRR, 2024)

Spectral Volume from a DG perspective: Oscillation Elimination, Stability, and Optimal Error Estimates. - Zhuoyun Li; Kailiang Wu (CoRR, 2024)

Provably Positivity-Preserving Constrained Transport (PPCT) Second-Order Scheme for Ideal Magnetohydrodynamics. - Dongwen Pang; Kailiang Wu (CoRR, 2024)

Bound preserving Point-Average-Moment PolynomiAl-interpreted (PAMPA) scheme: one-dimensional case. - Rémi Abgrall; Miaosen Jiao; Yongle Liu; Kailiang Wu (CoRR, 2024)

A Novel and Simple Invariant-Domain-Preserving Framework for PAMPA Scheme: 1D Case. - Rémi Abgrall; Miaosen Jiao; Yongle Liu; Kailiang Wu (CoRR, 2024)

GQL-based bound-preserving and locally divergence-free central discontinuous Galerkin schemes for relativistic magnetohydrodynamics. - Shengrong Ding; Kailiang Wu (J. Comput. Phys., 2024)

High-order oscillation-eliminating Hermite WENO method for hyperbolic conservation laws. - Chuan Fan; Kailiang Wu (J. Comput. Phys., 2024)

High-order accurate positivity-preserving and well-balanced discontinuous Galerkin schemes for ten-moment Gaussian closure equations with source terms. - Jiangfu Wang; Huazhong Tang; Kailiang Wu (J. Comput. Phys., 2024)

On Optimal Cell Average Decomposition for High-Order Bound-Preserving Schemes of Hyperbolic Conservation Laws. - Shumo Cui; Shengrong Ding; Kailiang Wu (SIAM J. Numer. Anal., 2024)

A New Locally Divergence-Free Path-Conservative Central-Upwind Scheme for Ideal and Shallow Water Magnetohydrodynamics. - Alina Chertock; Alexander Kurganov; Michael Redle; Kailiang Wu (SIAM J. Sci. Comput., 2024)

Bound-Preserving Framework for Central-Upwind Schemes for General Hyperbolic Conservation Laws. - Shumo Cui; Alexander Kurganov; Kailiang Wu (SIAM J. Sci. Comput., 2024)

Provably convergent Newton-Raphson methods for recovering primitive variables with applications to physical-constraint-preserving Hermite WENO schemes for relativistic hydrodynamics. - Chaoyi Cai; Jianxian Qiu; Kailiang Wu (J. Comput. Phys., 2024)

High-Order Accurate Entropy Stable Schemes for Relativistic Hydrodynamics with General Synge-Type Equation of State. - Linfeng Xu; Shengrong Ding; Kailiang Wu (J. Sci. Comput., 2024)

A New Discretely Divergence-Free Positivity-Preserving High-Order Finite Volume Method for Ideal MHD Equations. - Shengrong Ding; Kailiang Wu (SIAM J. Sci. Comput., 2024)

High Order Structure-Preserving Finite Difference WENO Schemes for MHD Equations with Gravitation in all Sonic Mach Numbers. - Wei Chen; Kailiang Wu; Tao Xiong (J. Sci. Comput., 2024)

Critical Sampling for Robust Evolution Operator Learning of Unknown Dynamical Systems. - Ce Zhang 009; Kailiang Wu; Zhihai He (IEEE Trans. Artif. Intell., 2024)

Robust discontinuous Galerkin methods maintaining physical constraints for general relativistic hydrodynamics. - Huihui Cao; Manting Peng; Kailiang Wu (J. Comput. Phys., 2025)

Bound-preserving OEDG schemes for Aw-Rascle-Zhang traffic models on networks. - Wei Chen; Shumo Cui; Kailiang Wu; Tao Xiong (J. Comput. Phys., 2025)

Positivity-preserving new low-dissipation central-upwind schemes for compressible Euler equations. - Shumo Cui; Yaguang Gu; Alexander Kurganov; Kailiang Wu; Ruixiao Xin (J. Comput. Phys., 2025)

Robust DG schemes on unstructured triangular meshes: Oscillation elimination and bound preservation via optimal convex decomposition. - Shengrong Ding; Shumo Cui; Kailiang Wu (J. Comput. Phys., 2025)

Structure-preserving oscillation-eliminating discontinuous Galerkin schemes for ideal MHD equations: Locally divergence-free and positivity-preserving. - Mengqing Liu; Kailiang Wu (J. Comput. Phys., 2025)

Provably positivity-preserving constrained transport scheme for 2D and 3D ideal magnetohydrodynamics. - Dongwen Pang; Kailiang Wu (J. Comput. Phys., 2025)

High-order accurate structure-preserving finite volume schemes on adaptive moving meshes for shallow water equations: Well-balancedness and positivity. - Zhihao Zhang; Huazhong Tang; Kailiang Wu (J. Comput. Phys., 2025)

Provably Convergent Newton-Raphson Method: Theoretically Robust Recovery of Primitive Variables in Relativistic MHD. - Chaoyi Cai; Jianxian Qiu; Kailiang Wu (SIAM J. Numer. Anal., 2025)

Spectral Volume from a Discontinuous Galerkin Perspective: Oscillation Elimination, Stability, and Optimal Error Estimates. - Zhuoyun Li; Kailiang Wu (SIAM J. Sci. Comput., 2025)

On Local Minimum Entropy Principle of High-Order Schemes for Relativistic Euler Equations. - Shumo Cui; Kailiang Wu; Linfeng Xu (CoRR, 2025)

Oscillation-eliminating central DG schemes for hyperbolic conservation laws. - Manting Peng; Kailiang Wu; Caiyou Yuan (CoRR, 2025)

DUE: A Deep Learning Framework and Library for Modeling Unknown Equations. - Junfeng Chen; Kailiang Wu; Dongbin Xiu (CoRR, 2025)

Provably positivity-preserving, globally divergence-free central DG methods for ideal MHD system. - Ruifang Yan; Huihui Cao; Kailiang Wu (CoRR, 2025)