Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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ERROR ESTIMATES OF PHYSICS-INFORMED NEURAL NETWORKS FOR INITIAL VALUE PROBLEMS

  • JIHAHM YOO (KOREA SCIENCE ACADEMY OF KAIST) ;
  • JAYWON KIM (KOREA SCIENCE ACADEMY OF KAIST) ;
  • MINJUNG GIM (NATIONAL INSTITUTE FOR MATHEMATICAL SCIENCES) ;
  • HAESUNG LEE (DEPARTMENT OF MATHEMATICS AND BIG DATA SCIENCE, KUMOH NATIONAL INSTITUTE OF TECHNOLOGY)
  • Received : 2024.03.03
  • Accepted : 2024.03.25
  • Published : 2024.03.25
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Abstract

This paper reviews basic concepts for Physics-Informed Neural Networks (PINN) applied to the initial value problems for ordinary differential equations. In particular, using only basic calculus, we derive the error estimates where the error functions (the differences between the true solution and the approximations expressed by neural networks) are dominated by training loss functions. Numerical experiments are conducted to validate our error estimates, visualizing the relationship between the error and the training loss for various first-order differential equations and a second-order linear equation.

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Acknowledgement

This research was supported by Kumoh National Institute of Technology(2023 ~ 2024)

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