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Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
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Open Access Research Article

Nonlinear PDE models for deep learning architecture stability analysis

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pp. 2131–2139Vol. 28Issue 6September 2025DOI: 10.47974/JIM-2354XML
Received:
10 Dec 2024
Published Online:
30 Sep 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-2354
Pages:
2131–2139

Abstract

Stability, robustness, and convergence are problems that deep learning systems often have to deal with when training dynamics aren’t linear and there are hostile changes. Nonlinear partial differential equation (PDE) models are used in this study to look at and improve the stability of deep learning.  Neural dynamics are connected to PDE models, and nonlinear diffusion processes show how weight changes over time and keep things from becoming unstable. Numerical discretization and large-scale computing methods make it possible to run models on systems that are very complicated. Compared to baseline models, the results show big improvements in stability, accuracy of convergence, and resistance to changes.

Keywords

Subject Classifications

35A0268T07

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