Report
Theoretical Guarantees for the Statistical Finite Element Method
| العنوان: | Theoretical Guarantees for the Statistical Finite Element Method |
|---|---|
| المؤلفون: | Papandreou, Yanni, Cockayne, Jon, Girolami, Mark, Duncan, Andrew B. |
| سنة النشر: | 2021 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, 65N75 (Primary) 35R60, 65C30 (Secondary) |
| الوصف: | The statistical finite element method (StatFEM) is an emerging probabilistic method that allows observations of a physical system to be synthesised with the numerical solution of a PDE intended to describe it in a coherent statistical framework, to compensate for model error. This work presents a new theoretical analysis of the statistical finite element method demonstrating that it has similar convergence properties to the finite element method on which it is based. Our results constitute a bound on the Wasserstein-2 distance between the ideal prior and posterior and the StatFEM approximation thereof, and show that this distance converges at the same mesh-dependent rate as finite element solutions converge to the true solution. Several numerical examples are presented to demonstrate our theory, including an example which test the robustness of StatFEM when extended to nonlinear quantities of interest. Comment: 27 pages for main article, 11 pages for supplement, 8 figures; typos corrected |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2111.07691 |
| رقم الانضمام: | edsarx.2111.07691 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |