7 papers · 1 filter
What Can One Expect When Solving PDEs Using Shallow Neural Networks?
Roy Y. He, Ying Liang, Hongkai Zhao +1
We use elliptic partial differential equations (PDEs) as examples to show various properties and behaviors when shallow neural networks (SNNs) are used to represent the solutions.…
Improving OCR using internal document redundancy
Diego Belzarena, Seginus Mowlavi, Aitor Artola +9
Current OCR systems are based on deep learning models trained on large amounts of data. Although they have shown some ability to generalize to unseen data, especially in detection…
Stoch-IDENT: New Method and Mathematical Analysis for Identifying SPDEs from Data
Jianbo Cui, Roy Y. He
In this paper, we propose Stoch-IDENT, a novel framework for identifying stochastic partial differential equations (SPDEs) from observational data. Our method can handle linear and…
IDENT Review: Recent Advances in Identification of Differential Equations from Noisy Data
Roy Y. He, Hao Liu, Wenjing Liao +1
Differential equations and numerical methods are extensively used to model various real-world phenomena in science and engineering. With modern developments, we aim to find the und…
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…
Dynamic PET Image Reconstruction via Non-negative INR Factorization
Chaozhi Zhang, Wenxiang Ding, Roy Y. He +2
The reconstruction of dynamic positron emission tomography (PET) images from noisy projection data is a significant but challenging problem. In this paper, we introduce an unsuperv…