Assimilation de données

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  • Code : N9EN21A

Objectifs

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

Compétences visées

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

 

 

Bibliographie

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.

Conditions d'admission

Applied mathematics ; Linear algebra ; Optimization; Statistics

Session 1 ou session unique - Contrôle des connaissances

ModalitéNatureCoefficientRemarques
CT (contrôle terminal) Oral/Ecrit100%Examen Assimilation de données

Session 2 - Contrôle des connaissances

ModalitéNatureCoefficientRemarques
CT (contrôle terminal) Oral/Ecrit100%Examen Assimilation de données

Contact(s)

GRATTON SERGE

Lieu(x)

  • Toulouse

Contactez l’ENSEEIHT

L’École Nationale Supérieure d'Électrotechnique, d'Électronique, d'Informatique, d'Hydraulique et des Télécommunications

2, rue Charles Camichel - BP 7122
31071 Toulouse Cedex 7, France

+33 (0)5 34 32 20 00

Certifications

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