.png){kind=icon}
返回
Statistical finite elements for misspecified models
.png){kind=icon}
OA
AI
DOI：10.1073/pnas.2015006118.png)
.png){kind=icon}
.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
We present a statistical finite element method for nonlinear, time-dependent phenomena, illustrated in the context of nonlinear internal waves (solitons). We take a Bayesian approach and leverage the finite element method to cast the statistical problem as a nonlinear Gaussian state-space model, updating the solution, in receipt of data, in a filtering framework. The method is applicable to problems across science and engineering for which finite element methods are appropriate. The Korteweg-de Vries equation for solitons is presented because it reflects the necessary complexity while being suitably familiar and succinct for pedagogical purposes. We present two algorithms to implement this method, based on the extended and ensemble Kalman filters, and demonstrate effectiveness with a simulation study and a case study with experimental data. The generality of our approach is demonstrated in SI Appendix, where we present examples from additional nonlinear, time-dependent partial differential equations (Burgers equation, Kuramoto-Sivashinsky equation).
Keyword:
Bayesian calibration
finite element methods
model discrepancy
AI总结
对已上传原文的论文进行重点信息的提取，主要内容包括：简要概述、研究摘要、背景介绍、关键亮点、图文解析、展望与总结。
期刊
P
IF:
9.1
论文数:
10.8W
被引数:
73.5W
机构
引用论文
.png){kind=icon}
Dedalus: A flexible framework for numerical simulations with spectral methodsDedalus: 用谱方法进行数值模拟的灵活框架OAAI
OAAI分享收藏
查看更多内容