A Level Set Based Variational Principal Flow Method for Nonparametric Dimension Reduction on Riemannian Manifolds. - Hao Liu 028; Zhigang Yao; Shingyu Leung; Tony F. Chan (SIAM J. Sci. Comput., 2017)

Robotic Tracking Control with Kernel Trick-based Reinforcement Learning. - Yazhou Hu; Wenxue Wang; Hao Liu 028; Lianqing Liu (IROS, 2019)

Fast Algorithms for Surface Reconstruction from Point Cloud. - Yuchen He 001; Martin Huska; Sung Ha Kang; Hao Liu 028 (CoRR, 2019)

A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge-Ampère Equation. - Roland Glowinski; Hao Liu 028; Shingyu Leung; Jianliang Qian (J. Sci. Comput., 2019)

Correction to: A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge-Ampère Equation. - Roland Glowinski; Hao Liu 028; Shingyu Leung; Jianliang Qian (J. Sci. Comput., 2019)

A Finite Element/Operator-Splitting Method for the Numerical Solution of the Three Dimensional Monge-Ampère Equation. - Hao Liu 028; Roland Glowinski; Shingyu Leung; Jianliang Qian (J. Sci. Comput., 2019)

Curvature Regularized Surface Reconstruction from Point Cloud. - Yuchen He 001; Sung Ha Kang; Hao Liu 028 (CoRR, 2020)

An Alternating Direction Explicit Method for Time Evolution Equations with Applications to Fractional Differential Equations. - Hao Liu 028; Shingyu Leung (CoRR, 2020)

Robust PDE Identification from Noisy Data. - Yuchen He 001; Sung Ha Kang; Wenjing Liao; Hao Liu 028; Yingjie Liu (CoRR, 2020)

On the Numerical Solution of Nonlinear Eigenvalue Problems for the Monge-Ampère Operator. - Roland Glowinski; Shingyu Leung; Hao Liu 028; Jianliang Qian (CoRR, 2020)

Doubly Robust Off-Policy Learning on Low-Dimensional Manifolds by Deep Neural Networks. - Minshuo Chen; Hao Liu 028; Wenjing Liao; Tuo Zhao (CoRR, 2020)

Curvature Regularized Surface Reconstruction from Point Clouds. - Yuchen He 001; Sung Ha Kang; Hao Liu 028 (SIAM J. Imaging Sci., 2020)

Reinforcement Learning Tracking Control for Robotic Manipulator With Kernel-Based Dynamic Model. - Yazhou Hu; Wenxue Wang; Hao Liu 028; Lianqing Liu (IEEE Trans. Neural Networks Learn. Syst., 2020)

Besov Function Approximation and Binary Classification on Low-Dimensional Manifolds Using Convolutional Residual Networks. - Hao Liu 028; Minshuo Chen; Tuo Zhao; Wenjing Liao (ICML, 2021)

An Operator-Splitting Method for the Gaussian Curvature Regularization Model with Applications in Surface Smoothing and Imaging. - Hao Liu 028; Xue-Cheng Tai; Roland Glowinski (CoRR, 2021)

A Color Elastica Model for Vector-Valued Image Regularization. - Hao Liu 028; Xue-Cheng Tai; Ron Kimmel; Roland Glowinski (SIAM J. Imaging Sci., 2021)

Benefits of Overparameterized Convolutional Residual Networks: Function Approximation under Smoothness Constraint. - Hao Liu 028; Minshuo Chen; Siawpeng Er; Wenjing Liao; Tong Zhang 001; Tuo Zhao (ICML, 2022)

An Efficient Operator-Splitting Method for the Eigenvalue Problem of the Monge-Ampère Equation. - Hao Liu 028; Shingyu Leung; Jianliang Qian (CoRR, 2022)

Numerical Identification of Nonlocal Potential in Aggregation. - Yuchen He 001; Sung Ha Kang; Wenjing Liao; Hao Liu 028; Yingjie Liu (CoRR, 2022)

High Dimensional Binary Classification under Label Shift: Phase Transition and Regularization. - Jiahui Cheng; Minshuo Chen; Hao Liu 028; Tuo Zhao; Wenjing Liao (CoRR, 2022)

Robust Identification of Differential Equations by Numerical Techniques from a Single Set of Noisy Observation. - Yuchen He 001; Sung Ha Kang; Wenjing Liao; Hao Liu 028; Yingjie Liu (SIAM J. Sci. Comput., 2022)

An Operator-Splitting Method for the Gaussian Curvature Regularization Model with Applications to Surface Smoothing and Imaging. - Hao Liu 028; Xue-Cheng Tai; Roland Glowinski (SIAM J. Sci. Comput., 2022)

Deep Nonparametric Estimation of Intrinsic Data Structures by Chart Autoencoders: Generalization Error and Robustness. - Hao Liu 028; Alexander Havrilla; Rongjie Lai; Wenjing Liao (CoRR, 2023)

Connections between Operator-splitting Methods and Deep Neural Networks with Applications in Image Segmentation. - Hao Liu 028; Xue-Cheng Tai; Raymond H. Chan (CoRR, 2023)

Fourier Features for Identifying Differential Equations (FourierIdent). - Mengyi Tang; Hao Liu 028; Wenjing Liao; Sung Ha Kang (CoRR, 2023)

Elastica Models for Color Image Regularization. - Hao Liu 028; Xue-Cheng Tai; Ron Kimmel; Roland Glowinski (SIAM J. Imaging Sci., 2023)

Group Projected subspace pursuit for IDENTification of variable coefficient differential equations (GP-IDENT). - Yuchen He 001; Sung Ha Kang; Wenjing Liao; Hao Liu 028; Yingjie Liu (J. Comput. Phys., 2023)

Generalization Error Guaranteed Auto-Encoder-Based Nonlinear Model Reduction for Operator Learning. - Hao Liu 028; Biraj Dahal; Rongjie Lai; Wenjing Liao (CoRR, 2024)

Deep Neural Networks are Adaptive to Function Regularity and Data Distribution in Approximation and Estimation. - Hao Liu 028; Jiahui Cheng; Wenjing Liao (CoRR, 2024)

Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces. - Hao Liu 028; Haizhao Yang; Minshuo Chen; Tuo Zhao; Wenjing Liao (J. Mach. Learn. Res., 2024)

Double-Well Net for Image Segmentation. - Hao Liu 028; Jun Liu 029; Raymond H. Chan; Xue-Cheng Tai (Multiscale Model. Simul., 2024)

Operator-Splitting/Finite Element Methods for the Minkowski Problem. - Hao Liu 028; Shingyu Leung; Jianliang Qian (SIAM J. Sci. Comput., 2024)

Learning Functions Varying along a Central Subspace. - Hao Liu 028; Wenjing Liao (SIAM J. Math. Data Sci., 2024)

PottsMGNet: A Mathematical Explanation of Encoder-Decoder Based Neural Networks. - Xue-Cheng Tai; Hao Liu 028; Raymond Chan 001 (SIAM J. Imaging Sci., 2024)

New Ways to Design Deep Neural Networks. - Xue-Cheng Tai; Hao Liu 028; Chan H. Raymond; Lingfeng Li (NAIS, 2025)

Image Decomposition with G-Norm Weighted by Total Symmetric Variation. - Roy Y. He; Martin Huska; Hao Liu 028 (SSVM (2), 2025)

Deep convolutional neural networks meet variational shape compactness priors for image segmentation. - Kehui Zhang; Lingfeng Li; Hao Liu 028; Jing Yuan 001; Xue-Cheng Tai (Neurocomputing, 2025)

A mathematical explanation of UNet. - Xue-Cheng Tai; Hao Liu 028; Raymond H. Chan; Lingfeng Li (Math. Found. Comput., 2025)