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Foundation models for partial differential equations (PDEs) have emerged as powerful surrogates pre-trained on diverse physical systems, but adapting them to new downstream tasks remains challenging due to limited task-specific data and…

机器学习 · 计算机科学 2026-03-17 Vlad Medvedev , Leon Armbruster , Christopher Straub , Georg Kruse , Andreas Rosskopf

Due to the selective absorption and scattering of light by diverse aquatic media, underwater images usually suffer from various visual degradations. Existing underwater image enhancement (UIE) approaches that combine underwater physical…

计算机视觉与模式识别 · 计算机科学 2025-08-04 Dazhao Du , Lingyu Si , Fanjiang Xu , Jianwei Niu , Fuchun Sun

In this paper we focus on learning optimized partial differential equation (PDE) models for image filtering. In this approach, the grey-scaled images are represented by a vector field of two real-valued functions and the image restoration…

数值分析 · 数学 2019-07-12 Sílvia Barbeiro , Diogo Lobo

Underwater object detection is a crucial and challenging problem in marine engineering and aquatic robot. The difficulty is partly because of the degradation of underwater images caused by light selective absorption and scattering.…

计算机视觉与模式识别 · 计算机科学 2023-12-01 Yudong Wang , Jichang Guo , Wanru He , Huan Gao , Huihui Yue , Zenan Zhang , Chongyi Li

It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). Recently, several deep learning-based approximation algorithms for attacking this problem…

数值分析 · 数学 2023-02-10 Christian Beck , Martin Hutzenthaler , Arnulf Jentzen , Benno Kuckuck

Motivated by important applications in image processing, we study a class of second-order geometric quasilinear hyperbolic partial differential equations (PDEs). This is inspired by the recent development of second-order damping systems…

偏微分方程分析 · 数学 2025-01-06 Guozhi Dong , Michael Hintermüller , Ye Zhang

Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks. We introduce a generalization for these methods that manifests as a…

数值分析 · 数学 2021-03-25 Remco van der Meer , Cornelis Oosterlee , Anastasia Borovykh

Underwater images play a key role in ocean exploration, but often suffer from severe quality degradation due to light absorption and scattering in water medium. Although major breakthroughs have been made recently in the general area of…

图像与视频处理 · 电气工程与系统科学 2019-07-09 Yan Wang , Wei Song , Giancarlo Fortino , Lizhe Qi , Wenqiang Zhang , Antonio Liotta

Activities in underwater environments are paramount in several scenarios, which drives the continuous development of underwater image enhancement techniques. A major challenge in this domain is the depth at which images are captured, with…

A main challenge faced in the deep learning-based Underwater Image Enhancement (UIE) is that the ground truth high-quality image is unavailable. Most of the existing methods first generate approximate reference maps and then train an…

计算机视觉与模式识别 · 计算机科学 2022-07-21 Zhenqi Fu , Wu Wang , Yue Huang , Xinghao Ding , Kai-Kuang Ma

In this survey we present some recent results concerning computer-assisted proofs in partial differential equations, focusing in those coming from problems in incompressible fluids. Particular emphasis is put on the techniques, as opposed…

偏微分方程分析 · 数学 2018-10-02 Javier Gómez-Serrano

Partial differential equations (PDEs) serve as the cornerstone of mathematical physics. In recent years, Physics-Informed Neural Networks (PINNs) have significantly reduced the dependence on large datasets by embedding physical laws…

机器学习 · 计算机科学 2025-06-09 Wenxuan Huo , Qiang He , Gang Zhu , Weifeng Huang

Multifarious image enhancement algorithms have been used in different applications. Still, some algorithms or modules are imperfect for practical use. When the image enhancement modules have been fixed or combined by a series of algorithms,…

计算机视觉与模式识别 · 计算机科学 2011-03-03 Lijun Wang , Ling Shao

This paper examines aspirational requirements for software addressing mixed-integer optimization problems constrained by the nonlinear Shallow Water partial differential equations (PDEs), motivated by applications such as river-flow…

最优化与控制 · 数学 2026-05-26 Fabio DiFonzo , Michael Holst , Morteza Kimiaei , Vyacheslav Kungurtsev , Songqiang Qiu

Underwater optical images inevitably suffer from various degradation factors such as blurring, low contrast, and color distortion, which hinder the accuracy of object detection tasks. Due to the lack of paired underwater/clean images, most…

计算机视觉与模式识别 · 计算机科学 2025-04-08 Bin Li , Li Li , Zhenwei Zhang , Yuping Duan

The discovery of partial differential equations (PDEs) is a challenging task that involves both theoretical and empirical methods. Machine learning approaches have been developed and used to solve this problem; however, it is important to…

机器学习 · 统计学 2023-06-09 Kalpesh More , Tapas Tripura , Rajdip Nayek , Souvik Chakraborty

Raw underwater images are degraded due to wavelength dependent light attenuation and scattering, limiting their applicability in vision systems. Another factor that makes enhancing underwater images particularly challenging is the diversity…

计算机视觉与模式识别 · 计算机科学 2019-06-03 Pritish Uplavikar , Zhenyu Wu , Zhangyang Wang

Images captured underwater often suffer from suboptimal illumination settings that can hide important visual features, reducing their quality. We present a novel single-image low-light underwater image enhancer, L^2UWE, that builds on our…

计算机视觉与模式识别 · 计算机科学 2020-11-09 Tunai Porto Marques , Alexandra Branzan Albu

Recently, researchers have utilized neural networks to accurately solve partial differential equations (PDEs), enabling the mesh-free method for scientific computation. Unfortunately, the network performance drops when encountering a high…

机器学习 · 计算机科学 2021-09-29 Pongpisit Thanasutives , Masayuki Numao , Ken-ichi Fukui

This paper presents machine learning techniques and deep reinforcement learningbased algorithms for the efficient resolution of nonlinear partial differential equations and dynamic optimization problems arising in investment decisions and…

最优化与控制 · 数学 2021-04-19 Maximilien Germain , Huyên Pham , Xavier Warin