图 书 馆
微分方程模型不确定性量化的概率积分法Probabilistic Integration for Uncertainty Quantification in Differential Equation Models |
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| 课程网址: | http://videolectures.net/nipsworkshops2012_calderhead_equation_mo... |
| 主讲教师: | Ben Calderhead |
| 开课单位: | 伦敦大学学院 |
| 开课时间: | 2013-01-15 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | In this talk I discuss recent joint work with Oksana Chkrebtii, Prof. Dave Campbell and Prof. Mark Girolami, in which we develop a probabilistic formalism for solving systems of differential equations. This generalises classes of existing numerical solvers while making the modelling assumptions explicit. The approach discussed yields a probability distribution on a function space of possible solutions, instead of a single deterministic solution that approximately satisfies model dynamics to within a given error tolerance. Viewing solution estimation as an inference problem (O'Hagan, 1992; Skilling, 1991) allows us to quantify solver error using the tools of Bayesian function estimation. In particular, we make use of Gaussian process priors on an underlying function space, while incorporating regularity assumptions by modelling states and their derivatives by their kernel integral transforms. |
| 关 键 词: | 微分方程组; 概率; 函数空间 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2019-09-08：lxf |
| 阅读次数: | 69 |