8 papers
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…
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 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…
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…
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…