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Partial differential equations (PDEs) on surfaces arise in a wide range of applications. The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is a recent embedding method that has been used to solve a…

数值分析 · 数学 2019-11-04 A. Petras , S. J. Ruuth

Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that lead to fulfilling a PDE can be challenging and…

机器学习 · 计算机科学 2023-04-12 Aleksandr Dekhovich , Marcel H. F. Sluiter , David M. J. Tax , Miguel A. Bessa

Time-dependent Partial Differential Equations with given initial conditions are considered in this paper. New differentiation techniques of the unknown solution with respect to time variable are proposed. It is shown that the proposed…

数值分析 · 数学 2022-10-24 Marat S. Mukhametzhanov

The goal of this work is to apply a denoising image transformer to remove the distortion from underwater images and compare it with other similar approaches. Automatic restoration of underwater images plays an important role since it allows…

图像与视频处理 · 电气工程与系统科学 2022-04-11 Abderrahmene Boudiaf , Yuhang Guo , Adarsh Ghimire , Naoufel Werghi , Giulia De Masi , Sajid Javed , Jorge Dias

The Closest Point Method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys. 2008] and successfully applied to a variety of surface PDEs. In this paper we study…

数值分析 · 数学 2013-07-30 Thomas März , Colin B. Macdonald

Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…

机器学习 · 计算机科学 2025-03-25 Edgar Torres , Jonathan Schiefer , Mathias Niepert

Due to complex and volatile lighting environment, underwater imaging can be readily impaired by light scattering, warping, and noises. To improve the visual quality, Underwater Image Enhancement (UIE) techniques have been widely studied.…

计算机视觉与模式识别 · 计算机科学 2025-08-01 Yannan Zheng , Weiling Chen , Rongfu Lin , Tiesong Zhao

With the development of image recovery models,especially those based on adversarial and perceptual losses,the detailed texture portions of images are being recovered more naturally.However,these restored images are similar but not identical…

图像与视频处理 · 电气工程与系统科学 2022-11-29 Zhiyu Wang , Jiayan Zhuang , Ningyuan Xu , Sichao Ye , Jiangjian Xiao , Chengbin Peng

In general, underwater images suffer from color distortion and low contrast, because light is attenuated and backscattered as it propagates through water (differently depending on wavelength and on the properties of the water body). An…

计算机视觉与模式识别 · 计算机科学 2024-02-09 Tanmoy Mondal , Ricardo Mendoza , Lucas Drumetz

I provide an introduction to the application of deep learning and neural networks for solving partial differential equations (PDEs). The approach, known as physics-informed neural networks (PINNs), involves minimizing the residual of the…

计算物理 · 物理学 2024-03-04 Hubert Baty

Solving inverse partial differential equation (PDE) problems is a fundamental topic in scientific research due to its broad significance across a wide range of real-world applications. Inverse PDE problems arise across medical imaging,…

人工智能 · 计算机科学 2026-05-19 Zhentao Tan , Yuze Hao , Boyi Zou , Mingsheng Long , Yi Yang , Gang Bao

Repair and maintenance of underwater structures as well as marine science rely heavily on the results of underwater object detection, which is a crucial part of the image processing workflow. Although many computer vision-based approaches…

计算机视觉与模式识别 · 计算机科学 2022-09-22 Radhwan Adnan Dakhil , Ali Retha Hasoon Khayeat

Physics-informed deep operator networks (DeepONets) have emerged as a promising approach toward numerically approximating the solution of partial differential equations (PDEs). In this work, we aim to develop further understanding of what…

机器学习 · 计算机科学 2024-11-28 Emily Williams , Amanda Howard , Brek Meuris , Panos Stinis

Images captured underwater are often characterized by low contrast, color distortion, and noise. To address these visual degradations, we propose a novel scheme by constructing an adaptive color and contrast enhancement, and denoising…

计算机视觉与模式识别 · 计算机科学 2021-08-03 Xinjie Li , Guojia Hou , Kunqian Li , Zhenkuan Pan

Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current state-of-the-art machine learning libraries, e.g.,…

机器学习 · 计算机科学 2024-10-22 Hamid El Bahja , Jan Christian Hauffen , Peter Jung , Bubacarr Bah , Issa Karambal

Many computer vision and image processing problems can be posed as solving partial differential equations (PDEs). However, designing PDE system usually requires high mathematical skills and good insight into the problems. In this paper, we…

计算机视觉与模式识别 · 计算机科学 2011-09-07 Risheng Liu , Zhouchen Lin , Wei Zhang , Kewei Tang , Zhixun Su

Physics-informed neural networks (PINNs) are a versatile tool in the burgeoning field of scientific machine learning for solving partial differential equations (PDEs). However, determining suitable training strategies for them is not…

数值分析 · 数学 2026-03-09 Saad Qadeer , Panos Stinis

Enhancing underwater images is crucial for exploration. These images face visibility and color issues due to light changes, water turbidity, and bubbles. Traditional prior-based methods and pixel-based methods often fail, while deep…

计算机视觉与模式识别 · 计算机科学 2025-07-04 Fanghai Yi , Zehong Zheng , Zexiao Liang , Yihang Dong , Xiyang Fang , Wangyu Wu , Xuhang Chen

Underwater images suffer from extremely unfavourable conditions. Light is heavily attenuated and scattered. Attenuation creates change in hue, scattering causes so called veiling light. General state of the art methods for enhancing image…

计算机视觉与模式识别 · 计算机科学 2018-07-12 Tomasz Łuczyński , Andreas Birk

In low-light environments, the performance of computer vision algorithms often deteriorates significantly, adversely affecting key vision tasks such as segmentation, detection, and classification. With the rapid advancement of deep…

计算机视觉与模式识别 · 计算机科学 2026-01-22 Fangxue Liu , Lei Fan
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