Report
Error Estimation for Physics-informed Neural Networks Approximating Semilinear Wave Equations
| العنوان: | Error Estimation for Physics-informed Neural Networks Approximating Semilinear Wave Equations |
|---|---|
| المؤلفون: | Lorenz, Beatrice, Bacho, Aras, Kutyniok, Gitta |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, Computer Science - Artificial Intelligence, 35L05, 68T07, 65M15, 35G50, 35A35 |
| الوصف: | 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 $H^1([0,T];L^2(\Omega))$-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. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.07153 |
| رقم الانضمام: | edsarx.2402.07153 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |