Solving Differential Equations with Physics-Informed Neural Networks

Chenghao Dong

doi:10.54254/2753-8818/2025.20346

Research Article

Open access

Published on 15 January 2025

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Dong,C. (2025). Solving Differential Equations with Physics-Informed Neural Networks. Theoretical and Natural Science,87,137-146.

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Solving Differential Equations with Physics-Informed Neural Networks

Chenghao Dong *^,1,

¹ Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK

* Author to whom correspondence should be addressed.

https://doi.org/10.54254/2753-8818/2025.20346

Abstract

Solving differential equations is an extensive topic in various fields, such as fluid mechanics and mathematical finance. The recent resurgence in deep neural networks has opened up a brand new track for numerically solving these equations, with the potential to better deal with nonlinear problems and overcome the curse of dimensionality. The Physics-Informed Neural Network (PINN) is one of the fundamental attempts to solve differential equations using deep learning techniques. This paper aims to briefly review the application of PINNs and their variants in solving differential equations through a few simple examples, and to provide practitioners interested in this direction with a quick introduction to the relevant topic

Keywords

neural networks, PINNs, differential equations, Fourier features

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Cite this article

Dong,C. (2025). Solving Differential Equations with Physics-Informed Neural Networks. Theoretical and Natural Science,87,137-146.

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The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.

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About volume

Volume title: Proceedings of the 4th International Conference on Computing Innovation and Applied Physics

Conference website: https://2025.confciap.org/

ISBN：978-1-83558-927-4(Print) / 978-1-83558-928-1(Online)

Conference date: 17 January 2025

Editor：Ömer Burak İSTANBULLU, Marwan Omar, Anil Fernando

Series: Theoretical and Natural Science

Volume number: Vol.87

ISSN：2753-8818(Print) / 2753-8826(Online)

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