Hailiang Liu
- The Direct Discontinuous Galerkin (DDG) Methods for Diffusion Problems
2009/01/01 by Hailiang Liu, Jue Yan · 3 citations
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #Computational Fluid Dynamics and Aerodynamics
- Optimal error estimates of the direct discontinuous Galerkin method for convection-diffusion equations
2015/02/17 by Hailiang Liu · 3 citations
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #Computational Fluid Dynamics and Aerodynamics
- Wide Neural Networks as Gaussian Processes: Lessons from Deep Equilibrium Models
2023/10/16 by Tianxiang Gao, Xiaokai Huo, Gao, Tianxiang +5 · 4 citations
Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Neural Networks and Applications
- Critical Thresholds in Euler-Poisson Equations
2001/12/03 by Shlomo Engelberg, Hailiang Liu, Eitan Tadmor · 1 citation
Mathematics · #math.AP #msc:35Q35 #msc:35B30
- Gaussian Beam Methods for the Helmholtz Equation
2013/04/04 by Hailiang Liu, Liu, Hailiang, James Ralston +5 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #35B45 #35J05 #35Q60 #78A40 #Advanced Mathematical Modeling in Engineering #Electromagnetic Scattering and Analysis #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems
- An entropy satisfying discontinuous Galerkin method for nonlinear Fokker-Planck equations
2016/01/11 by Hailiang Liu, Zhongming Wang, Liu, Hailiang +1 · 1 citation
Engineering · Physics and Astronomy · #35B40 #65M60 #92D15 #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Numerical Analysis (math.NA) #Statistical Mechanics and Entropy
- Critical Thresholds in One Dimensional Damped Euler-Poisson Systems
2019/07/21 by Manas Bhatnagar, Hailiang Liu, Bhatnagar, Manas +1 · 1 citation
Engineering · Mathematics · #35L65(Primary) #35L67(Secondary) #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions
- A note to paper: Axial symmetry and classification of stationary solutions of Doi-Onsager equation on the sphere with Maier-Saupe potential
2019/09/29 by Hailiang Liu, Hui Zhang, Liu, Hailiang +3 · 1 citation
Physics and Astronomy · Mathematics · #Quantum chaos and dynamical systems #Nonlinear Waves and Solitons #Algebraic and Geometric Analysis
- The Onsager principle and structure preserving numerical schemes
2024/06/18 by Huangxin Chen, Hailiang Liu, Chen, Huangxin +3 · 2 citations
Computer Science · Mathematics · #65M12 #65M22 #76M30 #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations
- A global convergence theory for deep ReLU implicit networks via over-parameterization
2021/10/11 by Tianxiang Gao, Hailiang Liu, Gao, Tianxiang +7 · 1 citation
Computer Science · #Stochastic Gradient Optimization Techniques #Machine Learning and ELM #Domain Adaptation and Few-Shot Learning
- Anderson acceleration of gradient methods with energy for optimization problems
2022/11/15 by Hailiang Liu, Liu, Hailiang, Jiahao He +3 · 1 citation
Computer Science · Mathematics · #Stochastic Gradient Optimization Techniques #Matrix Theory and Algorithms #Advanced Optimization Algorithms Research
- Adaptive Preconditioned Gradient Descent with Energy
2023/10/10 by Hailiang Liu, Levon Nurbekyan, Liu, Hailiang +5 · 1 citation
Computer Science · Mathematics · #Matrix Theory and Algorithms #Advanced Optimization Algorithms Research #Stochastic Gradient Optimization Techniques
- A Unified Variational Framework for Optimal Transport with Lagrangian Costs
2026/07/16 by Hailiang Liu
#math.OC