Liu, Hailiang
- 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
- Gaussian Beam Methods for the Helmholtz Equation
2013/04/04 by Hailiang Liu, James Ralston, Liu, Hailiang +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, Liu, Hailiang, Zhongming Wang +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, Bhatnagar, Manas, Hailiang Liu +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
- Radially symmetric solutions of the ultra-relativistic Euler equations
2020/02/04 by Kunik, Matthias, Liu, Hailiang, Warnecke, Gerald · 1 citation
#35L45 #35L60 #35L65 #35L67 #FOS: Mathematics #Numerical Analysis (math.NA)
- Critical thresholds in a nonlocal Euler system with relaxation
2020/10/05 by Bhatnagar, Manas, Liu, Hailiang · 1 citation
#35B30 (Secondary) #35L65 (Primary) #Analysis of PDEs (math.AP) #FOS: Mathematics
- Critical thresholds in the Euler-Poisson-alignment system
2021/11/23 by Bhatnagar, Manas, Liu, Hailiang, Tan, Changhui · 1 citation
#35B30 #35L65 #35L67 #35Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics
- 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
- Positivity-preserving and energy-dissipating discontinuous Galerkin methods for nonlinear nonlocal Fokker-Planck equations
2024/03/22 by Carrillo, José A., Liu, Hailiang, Yu, Hui · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA)
- 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
- AEGD: Adaptive Gradient Descent with Energy
2020/10/10 by Liu, Hailiang, Tian, Xuping · 1 citation
#65K10 (Primary) 90C15 #68Q25 (Secondary) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Numerical Analysis (math.NA) #Optimization and Control (math.OC)
- Variational structure of Fokker-Planck equations with variable mobility
2025/05/15 by Liu, Hailiang, Tzavaras, Athanasios E. · 1 citation
#35A15 #35K55 #60J60 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)
- Anderson acceleration of gradient methods with energy for optimization problems
2022/11/15 by Hailiang Liu, Jiahao He, Liu, Hailiang +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