ERROR ESTIMATES OF PHYSICS-INFORMED NEURAL NETWORKS FOR INITIAL VALUE PROBLEMSERROR ESTIMATES OF PHYSICS-INFORMED NEURAL NETWORKS FOR INITIAL VALUE PROBLEMS
- Other Titles
- ERROR ESTIMATES OF PHYSICS-INFORMED NEURAL NETWORKS FOR INITIAL VALUE PROBLEMS
- Authors
- JIHAHM YOO; JAYWON KIM; 김민중; 이해성
- Issue Date
- Mar-2024
- Publisher
- 한국산업응용수학회
- Keywords
- neural networks; PINN; error estimates; existence; uniqueness; stability; initial value problems; differential equations.
- Citation
- Journal of the Korean Society for Industrial and Applied Mathematics, v.28, no.1, pp 33 - 58
- Pages
- 26
- Journal Title
- Journal of the Korean Society for Industrial and Applied Mathematics
- Volume
- 28
- Number
- 1
- Start Page
- 33
- End Page
- 58
- URI
- https://scholarworks.bwise.kr/kumoh/handle/2020.sw.kumoh/28587
- DOI
- 10.12941/jksiam.2024.28.033
- ISSN
- 1226-9433
1229-0645
- 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 train- ing loss functions. Numerical experiments are conducted to validate our error estimates, visual- izing 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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