16 papers
Physics Matters in PnP: Recovery Guarantees with the MMSE and NN Denoisers
Tobias Wolf, Jalal Fadili, Jin Guo +1
We investigate the forward-backward-splitting version of the Plug and Play (PnP) method for linear ill-posed problems with MMSE estimators as denoisers. In contrast to existing lit…
PDE Identification Using Noise Adaptive Differentiation in Strong Form (S-IDENT)
Roy Y. He, Sung Ha Kang
We explore identifying partial differential equations (PDEs) from noisy observations of single time-space trajectories. Recent developments show the benefits of identifying PDEs in…
Second-Order Path Kernel Interpolation Formulas in Machine Learning
Jin Guo, Roy Y. He, Jean-Michel Morel
Understanding how training data shape neural network predictions is a central problem in modern learning theory. In 2020, Pedro Domingos proposed an interpolation formula valid for…
On Interpolation Formulas Describing Neural Network Generalization
Jin Guo, Roy Y. He, Jean-Michel Morel
In 2020 Domingos introduced an interpolation formula valid for "every model trained by gradient descent". He concluded that such models behave approximately as kernel machines. In…
From Frequency Bias to Spectral Balance: Operator-Aware Preconditioners for PINNs
Roy Y. He, Ying Liang, Hongkai Zhao +1
When neural networks (NNs) are used as a type of nonlinear parametric representation to solve partial differential equations (PDEs), they often display frequency-dependent learning…
Phase-IDENT: Identification of Two-phase PDEs with Uncertainty Quantification
Edward L. Yang, Roy Y. He
We propose a novel method, Phase-IDENT, for identifying partial differential equations (PDEs) from noisy observations of dynamical systems that exhibit phase transitions. Such phen…
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…
A Formalization of Image Vectorization by Region Merging
Roy Y. He, Sung Ha Kang, Jean-Michel Morel
Image vectorization converts raster images into vector graphics composed of regions separated by curves. Typical vectorization methods first define the regions by grouping similar…
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…