Kailiang Wu | DeepAI

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Wei Chen
332 publications
Ce Zhang
133 publications
Zhen Chen
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Zhihai He
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Zheng Sun
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Dongbin Xiu
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Jianxian Qiu
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Tao Xiong
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Chi-Wang Shu
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Tong Qin
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Yulong Xing
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∙ 05/24/2023

A new discretely divergence-free positivity-preserving high-order finite volume method for ideal MHD equations

This paper proposes and analyzes a novel efficient high-order finite vol...

0 Shengrong Ding, et al. ∙

∙ 05/24/2023

Provably convergent Newton-Raphson methods for recovering primitive variables with applications to physical-constraint-preserving Hermite WENO schemes for relativistic hydrodyn

The relativistic hydrodynamics (RHD) equations have three crucial intrin...

0 Chaoyi Cai, et al. ∙

∙ 04/15/2023

Critical Sampling for Robust Evolution Operator Learning of Unknown Dynamical Systems

Given an unknown dynamical system, what is the minimum number of samples...

0 Ce Zhang, et al. ∙

∙ 02/07/2023

Deep-OSG: A deep learning approach for approximating a family of operators in semigroup to model unknown autonomous systems

This paper proposes a novel deep learning approach for approximating evo...

0 Junfeng Chen, et al. ∙

∙ 12/09/2022

On Optimal Cell Average Decomposition for High-Order Bound-Preserving Schemes of Hyperbolic Conservation Laws

This paper presents the first systematic study on the fundamental proble...

0 Shumo Cui, et al. ∙

∙ 12/06/2022

A New Locally Divergence-Free Path-Conservative Central-Upwind Scheme for Ideal and Shallow Water Magnetohydrodynamics

We develop a new second-order unstaggered path-conservative central-upwi...

0 Alina Chertock, et al. ∙

∙ 11/30/2022

High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers

In this paper, a high-order semi-implicit (SI) asymptotic preserving (AP...

0 Wei Chen, et al. ∙

∙ 07/19/2022

Positivity-Preserving Well-Balanced Central Discontinuous Galerkin Schemes for the Euler Equations under Gravitational Fields

This paper designs and analyzes positivity-preserving well-balanced (WB)...

0 Haili Jiang, et al. ∙

∙ 07/19/2022

A Physical-Constraint-Preserving Finite Volume WENO Method for Special Relativistic Hydrodynamics on Unstructured Meshes

This paper presents a highly robust third-order accurate finite volume w...

0 Yaping Chen, et al. ∙

∙ 07/18/2022

Is the Classic Convex Decomposition Optimal for Bound-Preserving Schemes in Multiple Dimensions?

Since proposed in [X. Zhang and C.-W. Shu, J. Comput. Phys., 229: 3091–3...

0 Shumo Cui, et al. ∙

∙ 03/28/2022

Provably Positive Central DG Schemes via Geometric Quasilinearization for Ideal MHD Equations

In the numerical simulation of ideal MHD, keeping the pressure and densi...

0 Kailiang Wu, et al. ∙

∙ 01/17/2022

On Energy Laws and Stability of Runge–Kutta Methods for Linear Seminegative Problems

This paper presents a systematic theoretical framework to derive the ene...

0 Zheng Sun, et al. ∙

∙ 11/08/2021

Geometric Quasilinearization Framework for Analysis and Design of Bound-Preserving Schemes

Solutions to many partial differential equations satisfy certain bounds ...

0 Kailiang Wu, et al. ∙

∙ 06/07/2021

Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Space

We present a numerical framework for deep neural network (DNN) modeling ...

0 Zhen Chen, et al. ∙

∙ 02/07/2021

Minimum Principle on Specific Entropy and High-Order Accurate Invariant Region Preserving Numerical Methods for Relativistic Hydrodynamics

This paper explores Tadmor's minimum entropy principle for the relativis...

0 Kailiang Wu, et al. ∙

∙ 05/14/2020

Uniformly High-Order Structure-Preserving Discontinuous Galerkin Methods for Euler Equations with Gravitation: Positivity and Well-Balancedness

This paper presents a class of novel high-order accurate discontinuous G...

0 Kailiang Wu, et al. ∙

∙ 03/05/2020

Methods to Recover Unknown Processes in Partial Differential Equations Using Data

We study the problem of identifying unknown processes embedded in time-d...

13 Zhen Chen, et al. ∙

∙ 02/11/2020

A Non-Intrusive Correction Algorithm for Classification Problems with Corrupted Data

A novel correction algorithm is proposed for multi-class classification ...

0 Jun Hou, et al. ∙

∙ 02/09/2020

Provably Physical-Constraint-Preserving Discontinuous Galerkin Methods for Multidimensional Relativistic MHD Equations

We propose and analyze a class of robust, uniformly high-order accurate ...

0 Kailiang Wu, et al. ∙

∙ 10/15/2019

Data-Driven Deep Learning of Partial Differential Equations in Modal Space

We present a framework for recovering/approximating unknown time-depende...

0 Kailiang Wu, et al. ∙

∙ 07/17/2019

Entropy Symmetrization and High-Order Accurate Entropy Stable Numerical Schemes for Relativistic MHD Equations

This paper presents entropy symmetrization and high-order accurate entro...

0 Kailiang Wu, et al. ∙

∙ 05/24/2019

Structure-preserving Method for Reconstructing Unknown Hamiltonian Systems from Trajectory Data

We present a numerical approach for approximating unknown Hamiltonian sy...

0 Kailiang Wu, et al. ∙

∙ 11/13/2018

Data Driven Governing Equations Approximation Using Deep Neural Networks

We present a numerical framework for approximating unknown governing equ...

0 Tong Qin, et al. ∙

∙ 09/24/2018

Numerical Aspects for Approximating Governing Equations Using Data

We present effective numerical algorithms for locally recovering unknown...

0 Kailiang Wu, et al. ∙

∙ 08/22/2018

An Explicit Neural Network Construction for Piecewise Constant Function Approximation

We present an explicit construction for feedforward neural network (FNN)...

0 Kailiang Wu, et al. ∙

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