Error Estimation for Physics-informed Neural Networks Approximating Semilinear Wave Equations
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915893610545152 |
|---|---|
| author | Lorenz, Beatrice Bacho, Aras Kutyniok, Gitta |
| author_facet | Lorenz, Beatrice Bacho, Aras Kutyniok, Gitta |
| contents | This paper provides rigorous error bounds for physics-informed neural networks approximating the semilinear wave equation. We provide bounds for the generalization and training error in terms of the width of the network's layers and the number of training points for a tanh neural network with two hidden layers. Our main result is a bound of the total error in the $H^1([0,T];L^2(Ω))$-norm in terms of the training error and the number of training points, which can be made arbitrarily small under some assumptions. We illustrate our theoretical bounds with numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07153 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Error Estimation for Physics-informed Neural Networks Approximating Semilinear Wave Equations Lorenz, Beatrice Bacho, Aras Kutyniok, Gitta Numerical Analysis Artificial Intelligence 35L05, 68T07, 65M15, 35G50, 35A35 This paper provides rigorous error bounds for physics-informed neural networks approximating the semilinear wave equation. We provide bounds for the generalization and training error in terms of the width of the network's layers and the number of training points for a tanh neural network with two hidden layers. Our main result is a bound of the total error in the $H^1([0,T];L^2(Ω))$-norm in terms of the training error and the number of training points, which can be made arbitrarily small under some assumptions. We illustrate our theoretical bounds with numerical experiments. |
| title | Error Estimation for Physics-informed Neural Networks Approximating Semilinear Wave Equations |
| topic | Numerical Analysis Artificial Intelligence 35L05, 68T07, 65M15, 35G50, 35A35 |
| url | https://arxiv.org/abs/2402.07153 |