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Research Interests

My research focuses on deep learning theory, PDE learning, numerical PDEs and image processing.

Publication

  1. Hao Liu, Xue-Cheng Tai, Ron Kimmel, Roland Glowinski. Elastica Models for Color Image Regularization. Submitted, 2022.
  2. Hao Liu, Dong Wang. Fast operator splitting methods for obstacle problems. Submitted, 2022.
  3. Minshuo Chen, Hao Liu, Wenjing Liao, Tuo Zhao. Doubly Robust Off-Policy Learning on Low-Dimensional Manifolds by Deep Neural Networks. Submitted, 2022.
  4. Yuchen He, Sung Ha Kang, Wenjing Liao, Hao Liu, Yingjie Liu. Robust Identification of Differential Equations by Numerical Techniques from a Single Set of Noisy Observation. SIAM J. Sci. Comput., 44(3), A1145-A1175, 2022.
  5. Hao Liu, Xue-Cheng Tai, Roland Glowinski. An Operator-Splitting Method for the Gaussian Curvature Regularization Model with Applications to Surface Smoothing and Imaging. SIAM J. Sci. Comput., 44(2), A935-A963, 2022.
  6. 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.
  7. 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.
  8. 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.
  9. Yuchen He, Sung Ha Kang, Hao Liu. Curvature Regularized Surface Reconstruction from Point Cloud. SIAM Journal on Imaging Sciences, 13(4), 1834–1859, 2020.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. Yuchen He, Martin Huska, Sung Ha Kang, Hao Liu. Fast Algorithms for Surface Reconstruction from Point Cloud. Proceeding of International Workshop On Image Processing and Inverse Problems, 2021.
  17. 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.

Academic Talk

  1. Elastica Models for Color Image Regularization. Workshop on Recent Advances in Image Processing, CUHK(Shenzhen), April 2022
  2. Off-policy learning and classification on low-dimensional manifold by deep neural networks. Mathematical Data Science Seminar, Purdue University, Feb. 2022
  3. Besov Function Approximation and Binary Classification on Low-Dimensional Manifolds Using Convolutional Residual Networks. ICML, July 2021
  4. Data with Low-Dimensional Structures: Deep Neural Networks and PDE Learning. CUHK(Shenzhen), Jan. 2021
  5. High-Dimensional Data Analysis: Off-Policy Learning by Deep Neural Networks and PDE Learning. Southern University of Science and Technology, Jan. 2021
  6. High-Dimensional Data Analysis: Off-Policy Learning by Deep Neural Networks and PDE Learning. Peking University, Dec. 2020
  7. Learning functions varying along an active subspace. SIAM Student Seminar, Georgia Institute of Technology, Feb. 2020
  8. Approximate functions varying along an active subspace. Workshop on New Trends in Machine Learning and Numerical PDEs, Hong Kong Baptist University, Dec. 2019
  9. A level set based variational principal flow method for nonparametric dimension reduction on Riemannian manifolds. Scientific Computing Seminars, University of Houston, Nov. 2018

Poster Presentation

  1. Learning functions varying along an active subspace. 2020 Georgia Scientific Computing Symposium, Emory University, Feb. 2020.
  2. Approximate functions varying along an active subspace. Workshop on Recent Developments on Mathematical/Statistical approaches in DAta Science (MSDAS), The University of Texas at Dallas, May. 2019.
  3. A level set based variational principal flow method for nonparametric dimension reduction on Riemannian manifolds. 2019 Georgia Scientific Computing Symposium, Georgia Institute of Technology, Feb. 2019.
  4. A level set based variational principal flow method for nonparametric dimension reduction on Riemannian manifolds. Meeting the Statistical Challenges in High Dimensional Data and Complex Networks, National University of Singapore, Feb. 2018.