Assimilation de données
Objectives
This course provides theoretical and practical background on stochastic filtering and modelling and explore the connections between Bayesian approaches and Machine Learning
Description
The course reminds basics on data assimilation for dynamical system of finite dimension, based on the Bayesian formalism in order to introduce the non-linear filtering and its particle implementation. The Kalman filter is presented as a particular solution, and it is compared with the particle filter by considering the geometrical interpretation of the curse of the dimensionality. The connection between Bayesian DA and recurrent network will be presented
Targeted skills
Being able to model a practical forecasting problem into a mathematical framework
Apply the expressions for the estimation using dual or primal approaches
Perform a uncertainty quantification using the reresentation of DA as propagation of probability density function
Develop a software for variaitonnal and ensemble Data Assimilation
Develop a software to perform prediction with recurrent networks
Bibliography
G. Pavliotis and A. Stuart, Multiscale Methods: Averaging and Homogenization. Springer, 2008.
D. J. Higham, “An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations,” SIAM REVIEW, vol. 43, pp. 525–546, 2001.
Oksendal, Stochastic differential equations. Springer, 2003.
A. Jazwinski, Stochastic Processes and Filtering Theory. Dover Publications, 2007, p. 400.
Pre-requisites
Applied mathematics ; Linear algebra ; Optimization; Statistics