9 papers
Fast and stable global interpolation based on equidistant points
Xu-Qing Liu, Hao Liu, Jian-Ying Rong
This paper presents the symmetric wave interpolation method for stable global interpolation using readily available equidistant points. Its key achievement is the integration of th…
Finite Element Representation Network (FERN) for Operator Learning with a Localized Trainable Basis
Zecheng Zhang, Hao Liu, Guosheng Fu +2
We propose a finite-element local basis-based operator learning framework for solving partial differential equations (PDEs). Operator learning aims to approximate mappings from inp…
A PCA Based Model for Surface Reconstruction from Incomplete Point Clouds
Hao Liu
Point cloud data represents a crucial category of information for mathematical modeling, and surface reconstruction from such data is an important task across various disciplines.…
Fast Operator-Splitting Methods for Nonlinear Elliptic Equations
Jingyu Yang, Shingyu Leung, Jianliang Qian +1
Nonlinear elliptic problems arise in many fields, including plasma physics, astrophysics, and optimal transport. In this article, we propose a novel operator-splitting/finite eleme…
WG-IDENT: Weak Group Identification of PDEs with Varying Coefficients
Cheng Tang, Roy Y. He, Hao Liu
The identification of Partial Differential Equations (PDEs) has emerged as a prominent data-driven approach for mathematical modeling and has attracted considerable attention in re…
Image Decomposition with G-norm Weighted by Total Symmetric Variation
Roy Y. He, Martin Huska, Hao Liu
In this paper, we propose a novel variational model for decomposing images into their respective cartoon and texture parts. Our model characterizes certain non-local features of an…
SpaceSeg: A High-Precision Intelligent Perception Segmentation Method for Multi-Spacecraft On-Orbit Targets
Hao Liu, Pengyu Guo, Siyuan Yang +3
With the continuous advancement of human exploration into deep space, intelligent perception and high-precision segmentation technology for on-orbit multi-spacecraft targets have b…
Group Projected Subspace Pursuit for Block Sparse Signal Reconstruction: Convergence Analysis and Applications
Roy Y. He, Haixia Liu, Hao Liu
In this paper, we present a convergence analysis of the Group Projected Subspace Pursuit (GPSP) algorithm proposed by He et al. [HKL+23] (Group Projected subspace pursuit for IDENT…
Euler's Elastica Based Cartoon-Smooth-Texture Image Decomposition
Roy Y. He, Hao Liu
We propose a novel model for decomposing grayscale images into three distinct components: the structural part, representing sharp boundaries and regions with strong light-to-dark t…