تقرير
Error estimates of physics-informed neural networks for approximating Boltzmann equation
| العنوان: | Error estimates of physics-informed neural networks for approximating Boltzmann equation |
|---|---|
| المؤلفون: | Abdo, Elie, Chai, Lihui, Hu, Ruimeng, Yang, Xu |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis |
| الوصف: | Motivated by the recent successful application of physics-informed neural networks (PINNs) to solve Boltzmann-type equations [S. Jin, Z. Ma, and K. Wu, J. Sci. Comput., 94 (2023), pp. 57], we provide a rigorous error analysis for PINNs in approximating the solution of the Boltzmann equation near a global Maxwellian. The challenge arises from the nonlocal quadratic interaction term defined in the unbounded domain of velocity space. Analyzing this term on an unbounded domain requires the inclusion of a truncation function, which demands delicate analysis techniques. As a generalization of this analysis, we also provide proof of the asymptotic preserving property when using micro-macro decomposition-based neural networks. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.08383 |
| رقم الأكسشن: | edsarx.2407.08383 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |