تقرير
Physics Informed Neural Networks for an Inverse Problem in Peridynamic Models
| العنوان: | Physics Informed Neural Networks for an Inverse Problem in Peridynamic Models |
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| المؤلفون: | Difonzo, Fabio Vito, Lopez, Luciano, Pellegrino, Sabrina Francesca |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis |
| الوصف: | Deep learning is a powerful tool for solving data driven differential problems and has come out to have successful applications in solving direct and inverse problems described by PDEs, even in presence of integral terms. In this paper, we propose to apply radial basis functions (RBFs) as activation functions in suitably designed Physics Informed Neural Networks (PINNs) to solve the inverse problem of computing the peridynamic kernel in the nonlocal formulation of classical wave equation, resulting in what we call RBF-iPINN. We show that the selection of an RBF is necessary to achieve meaningful solutions, that agree with the physical expectations carried by the data. We support our results with numerical examples and experiments, comparing the solution obtained with the proposed RBF-iPINN to the exact solutions. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2312.11316 |
| رقم الأكسشن: | edsarx.2312.11316 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |