تقرير
Accuracy Analysis of Physics-Informed Neural Networks for Approximating the Critical SQG Equation
| العنوان: | Accuracy Analysis of Physics-Informed Neural Networks for Approximating the Critical SQG Equation |
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| المؤلفون: | Abdo, Elie, Hu, Ruimeng, Lin, Quyuan |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, Mathematics - Analysis of PDEs |
| الوصف: | We systematically analyze the accuracy of Physics-Informed Neural Networks (PINNs) in approximating solutions to the critical Surface Quasi-Geostrophic (SQG) equation on two-dimensional periodic boxes. The critical SQG equation involves advection and diffusion described by nonlocal periodic operators, posing challenges for neural network-based methods that do not commonly exhibit periodic boundary conditions. In this paper, we present a novel approximation of these operators using their nonperiodic analogs based on singular integral representation formulas and use it to perform error estimates. This idea can be generalized to a larger class of nonlocal partial differential equations whose solutions satisfy prescribed boundary conditions, thereby initiating a new PINNs theory for equations with nonlocalities. Comment: 21 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2401.10879 |
| رقم الأكسشن: | edsarx.2401.10879 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |