Applications of Partial Differential Equations

DOI

10.2991/978-94-6239-648-7_70How to use a DOI?

Keywords

Partial Differential Equation; Image Denoising; Image Restoration; Numerical Analysis

Abstract

Partial differential equations (PDEs) are descriptions of continuous changes. Using methods/algorithms, PDE-based models are applied in physical calculations, image processing, machine learning, etc. This paper discusses the applications of PDEs, especially in image denoising and inpainting. When denoising, the PDE diffusion model relies on local smoothing to balance noise suppression and edge protection. When inpainting, the PDE inpainting model relies on propagating structural information to make the visual reconstruction of the defective area more consistent. In computational physics (comp scenarios), the partial differential equation (PDE) model makes the features of the deep model more stable and easier to understand. However, there are challenges in the current application of PDE, such as high computational cost, insufficient numerical stability, difficult parameter selection, and limited model generation ability. Future research on partial differential equations (PDEs) will focus more on integrating data models, efficient algorithms, and interdisciplinary applications. This paper aims to demonstrate the diversity and importance of partial differential equations (PDEs) and provide references for subsequent research on partial differential equations (PDEs).

Copyright

© 2026 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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TY  - CONF
AU  - Ziran Zhang
PY  - 2026
DA  - 2026/04/24
TI  - Applications of Partial Differential Equations
BT  - Proceedings of the International Workshop on Advances in Deep Learning for Image Analysis and Computer Vision (IWADIC 2025)
PB  - Atlantis Press
SP  - 644
EP  - 651
SN  - 2352-538X
UR  - https://doi.org/10.2991/978-94-6239-648-7_70
DO  - 10.2991/978-94-6239-648-7_70
ID  - Zhang2026
ER  -