Related papers: Discontinuous Galerkin Neural Operator for Patholo…

Accurate prediction of machining deformation in structural components is essential for ensuring dimensional precision and reliability. Such deformation often originates from residual stress fields, whose distribution and influence vary…

For hyperbolic conservation laws, traditional methods and physics-informed neural networks (PINNs) often encounter difficulties in capturing sharp discontinuities and maintaining temporal consistency. To address these challenges, we…

Artificial Intelligence (AI)-powered pathology is a revolutionary step in the world of digital pathology and shows great promise to increase both diagnosis accuracy and efficiency. However, defocus and motion blur can obscure tissue or cell…

Microscopy is a powerful visualization tool in biology, enabling the study of cells, tissues, and the fundamental biological processes; yet, the observed images typically suffer from blur and background noise. In this work, we propose a…

Accurately forecasting the long-term evolution of turbulence represents a grand challenge in scientific computing and is crucial for applications ranging from climate modeling to aerospace engineering. Existing deep learning methods,…

We introduce Discontinuous Galerkin Finite Element Operator Network (DG--FEONet), a data-free operator learning framework that combines the strengths of the discontinuous Galerkin (DG) method with neural networks to solve parametric partial…

Diffusion models have achieved significant progress in image generation. The pre-trained Stable Diffusion (SD) models are helpful for image deblurring by providing clear image priors. However, directly using a blurry image or pre-deblurred…

A new scheme for communication between overset grids using subcells and Weighted Essentially Non Oscillatory (WENO) reconstruction for two-dimensional problems has been proposed. The effectiveness of this procedure is demonstrated using the…

In recent years, large convolutional neural networks have been widely used as tools for image deblurring, because of their ability in restoring images very precisely. It is well known that image deblurring is mathematically modeled as an…

Motion deblurring is one of the fundamental problems of computer vision and has received continuous attention. The variability in blur, both within and across images, imposes limitations on non-blind deblurring techniques that rely on…

Non-uniform blind deblurring for general dynamic scenes is a challenging computer vision problem as blurs arise not only from multiple object motions but also from camera shake, scene depth variation. To remove these complicated motion…

Computational imaging is crucial in many disciplines from autonomous driving to life sciences. However, traditional model-driven and iterative methods consume large computational power and lack scalability for imaging. Deep learning (DL) is…

Numerical solution of nonlocal constrained value problems with integrable kernels are considered. These nonlocal problems arise in nonlocal mechanics and nonlocal diffusion. The structure of the true solution to the problem is analyzed…

We propose a general framework for the Discontinuous Galerkin-induced Neural Network (DGNN), inspired by the Interior Penalty Discontinuous Galerkin Method (IPDGM). In this approach, the trial space consists of piecewise neural network…

Most existing deep-learning-based single image dynamic scene blind deblurring (SIDSBD) methods usually design deep networks to directly remove the spatially-variant motion blurs from one inputted motion blurred image, without blur kernels…

For single image defocus deblurring, acquiring well-aligned training pairs (or training triplets), i.e., a defocus blurry image, an all-in-focus sharp image (and a defocus blur map), is a challenging task for developing effective deblurring…

Spatially varying image deblurring remains a fundamentally ill-posed problem, especially when degradations arise from complex mixtures of motion and other forms of blur under significant noise. State-of-the-art learning-based approaches…

Spherical deep learning has been widely applied to a broad range of real-world problems. Existing approaches often face challenges in balancing strong spherical geometric inductive biases with the need to model real-world heterogeneity. To…

In this paper, we consider a class of discontinuous Galerkin (DG) methods for one-dimensional nonlocal diffusion (ND) problems. The nonlocal models, which are integral equations, are widely used in describing many physical phenomena with…

This paper introduces the Kernel Neural Operator (KNO), a provably convergent operator-learning architecture that utilizes compositions of deep kernel-based integral operators for function-space approximation of operators (maps from…