تقرير
A Review of Neural Network Solvers for Second-order Boundary Value Problems
| العنوان: | A Review of Neural Network Solvers for Second-order Boundary Value Problems |
|---|---|
| المؤلفون: | Sau, Ramesh Chandra, Yin, Luowei |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis |
| الوصف: | Deep learning-based partial differential equation(PDE) solvers have received much attention in the past few years. Methods of this category can solve a wide range of PDEs with high accuracy, typically by transforming the problems into highly nonlinear optimization problems of neural network parameters. This work reviews several deep learning solvers proposed a few years ago, including PINN, WAN, DRM, and VPINN. Numerical results are provided to make comparisons amongst them and address the importance of loss formulation and the optimization method. A rigorous error analysis for PINN is also presented. Finally, we discuss the current limitations and bottlenecks of these methods. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.00442 |
| رقم الأكسشن: | edsarx.2407.00442 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |