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A numerical method to solve PDE through PINN based on ODENet
- 1 Macau University Of Science And Technology
* Author to whom correspondence should be addressed.
Abstract
With the rapid development of artificial intelligence, especially deep learning technology, scientific researchers have begun to explore its application in the field of traditional scientific computing. Traditional scientific computing relies on mathematical equations to describe and predict the scientific laws of nature, while deep learning provides a new perspective to solve complex mathematical problems by learning patterns in data. The introduction of the Physical Information Neural Network (PINN) and the Ordinary Differential Equation (ODENet) network layer enables deep learning technology to more accurately simulate and predict scientific phenomena. This study shows that by embedding an ODE-Net network layer in a physical information neural network (PINN), the fitting accuracy and generalization performance of the model can be significantly improved. Experimental results show that compared with traditional numerical methods and fully connected neural networks, this model combined with deep learning technology not only shows higher accuracy when solving partial differential equations, but also exhibits faster convergence speed and stronger adaptability. These findings not only promote the integration of scientific computing and deep learning, but also provide new research directions and practical strategies for using deep learning technology to solve complex scientific problems.
Keywords
AI for science, Pinn, ODE-Net, Deep learning, Numeral Calculations
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Cite this article
Wang,Z. (2024). A numerical method to solve PDE through PINN based on ODENet. Applied and Computational Engineering,68,249-257.
Data availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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Volume title: Proceedings of the 6th International Conference on Computing and Data Science
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