Hao Liu

Orcid: 0000-0002-7504-9859

Affiliations:
  • Hong Kong Baptist University, Department of Mathematics, Hong Kong
  • Georgia Institute of Technology, Department of Mathematics, Atlanta, GA, USA (former)
  • Hong Kong University of Science and Technology, Department of Mathematics, Hong Kong (former)


According to our database1, Hao Liu authored at least 36 papers between 2017 and 2024.

Collaborative distances:
  • Dijkstra number2 of four.
  • Erdős number3 of four.

Timeline

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Bibliography

2024
PottsMGNet: A Mathematical Explanation of Encoder-Decoder Based Neural Networks.
SIAM J. Imaging Sci., March, 2024

Learning Functions Varying along a Central Subspace.
SIAM J. Math. Data Sci., 2024

Operator-Splitting/Finite Element Methods for the Minkowski Problem.
SIAM J. Sci. Comput., 2024

Double-Well Net for Image Segmentation.
Multiscale Model. Simul., 2024

Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces.
J. Mach. Learn. Res., 2024

A Mathematical Explanation of UNet.
CoRR, 2024

Deep Convolutional Neural Networks Meet Variational Shape Compactness Priors for Image Segmentation.
CoRR, 2024

Deep Neural Networks are Adaptive to Function Regularity and Data Distribution in Approximation and Estimation.
CoRR, 2024

Generalization Error Guaranteed Auto-Encoder-Based Nonlinear Model Reduction for Operator Learning.
CoRR, 2024

2023
Group Projected subspace pursuit for IDENTification of variable coefficient differential equations (GP-IDENT).
J. Comput. Phys., December, 2023

Elastica Models for Color Image Regularization.
SIAM J. Imaging Sci., March, 2023

Fourier Features for Identifying Differential Equations (FourierIdent).
CoRR, 2023

Connections between Operator-splitting Methods and Deep Neural Networks with Applications in Image Segmentation.
CoRR, 2023

Deep Nonparametric Estimation of Intrinsic Data Structures by Chart Autoencoders: Generalization Error and Robustness.
CoRR, 2023

2022
An Operator-Splitting Method for the Gaussian Curvature Regularization Model with Applications to Surface Smoothing and Imaging.
SIAM J. Sci. Comput., 2022

Robust Identification of Differential Equations by Numerical Techniques from a Single Set of Noisy Observation.
SIAM J. Sci. Comput., 2022

High Dimensional Binary Classification under Label Shift: Phase Transition and Regularization.
CoRR, 2022

Numerical Identification of Nonlocal Potential in Aggregation.
CoRR, 2022

An Efficient Operator-Splitting Method for the Eigenvalue Problem of the Monge-Ampère Equation.
CoRR, 2022

Benefits of Overparameterized Convolutional Residual Networks: Function Approximation under Smoothness Constraint.
Proceedings of the International Conference on Machine Learning, 2022

2021
A Color Elastica Model for Vector-Valued Image Regularization.
SIAM J. Imaging Sci., 2021

An Operator-Splitting Method for the Gaussian Curvature Regularization Model with Applications in Surface Smoothing and Imaging.
CoRR, 2021

Besov Function Approximation and Binary Classification on Low-Dimensional Manifolds Using Convolutional Residual Networks.
Proceedings of the 38th International Conference on Machine Learning, 2021

2020
Reinforcement Learning Tracking Control for Robotic Manipulator With Kernel-Based Dynamic Model.
IEEE Trans. Neural Networks Learn. Syst., 2020

Curvature Regularized Surface Reconstruction from Point Clouds.
SIAM J. Imaging Sci., 2020

Doubly Robust Off-Policy Learning on Low-Dimensional Manifolds by Deep Neural Networks.
CoRR, 2020

On the Numerical Solution of Nonlinear Eigenvalue Problems for the Monge-Ampère Operator.
CoRR, 2020

Robust PDE Identification from Noisy Data.
CoRR, 2020

An Alternating Direction Explicit Method for Time Evolution Equations with Applications to Fractional Differential Equations.
CoRR, 2020

Curvature Regularized Surface Reconstruction from Point Cloud.
CoRR, 2020

2019
A Finite Element/Operator-Splitting Method for the Numerical Solution of the Three Dimensional Monge-Ampère Equation.
J. Sci. Comput., 2019

Correction to: A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge-Ampère Equation.
J. Sci. Comput., 2019

A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge-Ampère Equation.
J. Sci. Comput., 2019

Fast Algorithms for Surface Reconstruction from Point Cloud.
CoRR, 2019

Robotic Tracking Control with Kernel Trick-based Reinforcement Learning.
Proceedings of the 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2019

2017
A Level Set Based Variational Principal Flow Method for Nonparametric Dimension Reduction on Riemannian Manifolds.
SIAM J. Sci. Comput., 2017


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