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Current Research Interests
My research focuses on deep learning theory, PDE learning, numerical PDEs and image processing.
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Deep learning theory: I develope approximation theories and statistical learning theories of deep neural networks on various problems, especially when data have some low-dimensional structures.
- PDE learning: I design efficient and robust algorithms for PDE learning from noisy data sets.
- Numerical PDEs: I focus on using the level set method and operator-splitting method to solve various problems and nonlinear PDEs. My recent works proposed operator-splitting method based numerical solvers for the Monge-Ampère type equations.
- Image processing: I design image regularization models and efficient algorithms by operator-splitting methods.
Selected Publications
- Minshuo Chen, Hao Liu, Wenjing Liao, Tuo Zhao.
Doubly Robust Off-Policy Learning on Low-Dimensional Manifolds by Deep Neural Networks.
Submitted, 2021.
- Yuchen He, Sung Ha Kang, Wenjing Liao, Hao Liu, Yingjie Liu. Robust PDE Identification from Noisy Data.
Submitted, 2021.
- Yuchen He, Martin Huska, Sung Ha Kang, Hao Liu. Fast Algorithms for Surface Reconstruction from Point Cloud.
Accepted by Proceeding of International Workshop On Image Processing and Inverse Problems, 2021.
- Hao Liu, Minshuo Chen, Tuo Zhao, Wenjing Liao.
Besov Function Approximation and Binary Classification on Low-Dimensional Manifolds Using Convolutional Residual Networks.
International Conference on Machine Learning, 6770-6780, 2021.
- Hao Liu, Xue-Cheng Tai, Ron Kimmel, Roland Glowinski. A Color Elastica Model for Vector-Valued Image Regularization.
SIAM Journal on Imaging Sciences 14 (2), 717-748, 2021.
- Roland Glowinski, Shingyu Leung, Hao Liu, Jianliang Qian.
On the Numerical Solution of Nonlinear Eigenvalue Problems for the Monge-Ampère Operator.
ESAIM: Control, Optimisation and Calculus of Variations, 26, 118, 2020.
- Yuchen He, Sung Ha Kang, Hao Liu. Curvature Regularized Surface Reconstruction from Point Cloud.
SIAM Journal on Imaging Sciences, 13(4), 1834–1859, 2020.
- Hao Liu, Shingyu Leung. A Simple Semi-Implicit Scheme for Partial Differential Equations with Obstacle Constraints.
Numer. Math. Theor. Meth. Appl., 13, pp. 620-643, 2020.
- Yazhou Hu, Wenxue Wang, Hao Liu, Lianqing Liu.
Reinforcement Learning Tracking Control for Robotic Manipulator with Kernel-Based Dynamic Model.
IEEE Transactions on Neural Networks and Learning Systems, 31(9), 3570 - 3578, 2020.
- Yazhou Hu, Wenxue Wang, Hao Liu, Lianqing Liu.
Robotic Tracking Control with Kernel Trick-based Reinforcement Learning.
2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 997-1002, 2019.
- Hao Liu, Shingyu Leung.
An Alternating Direction Explicit Method for Time-Dependent Evolution Equations with Applications to Fractional Differential Equations.
Methods and Applications of Analysis, Special Issue in Honor of Roland Glowinski, 26(3), 249-268, 2019.
- Hao Liu, Roland Glowinski, Shingyu Leung and Jianliang Qian.
A Finite Element/Operator-Splitting Method for the Numerical Solution of the Three Dimensional Monge-Ampère Equation.
Journal of Scientific Computing, 81(3), 2271-2302, 2019.
- Roland Glowinski, Hao Liu, Shingyu Leung and Jianliang Qian.
A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge-Ampère Equation.
Journal of Scientific Computing, 79(1), 1-47, 2019.
- Hao Liu, Zhigang Yao, Shingyu Leung and Tony F. Chan.
A Level Set Based Variational Principal Flow Method for Nonparametric Dimension Reduction on Riemannian Manifolds.
SIAM J. Sci. Comput., 39(4), A1616-A1646, 2017.
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