30 mars 2022 à 1 avril 2022
Inria Bordeaux Sud Ouest
Fuseau horaire Europe/Paris

Field reconstruction using manifold learning and structure-preserving metrics

30 mars 2022, 14:30
50m
Ada Lovelace (Inria Bordeaux Sud Ouest)

Ada Lovelace

Inria Bordeaux Sud Ouest

200 avenue de la ville tour, 33405 TALENCE

Orateur

Dr Lionel Mathelin (LIMSI-CNRS)

Description

The problem of estimating the state of a physical system is ubiquitous in science. However observations are always limited so that the high-dimensional state cannot be observed and the associated mathematical problem is ill-posed. Popular workarounds include dimension reduction and regularization by imposing some structure to the class of elements in which the estimation is sought.
We here rely on a purely data-driven approach and learn the map between extended measurements and the nonlinear manifold the state vector lies on. Specifically, we use embedding to address the non-Markovianity of the raw measurements. Combined with multi-kernel learning, it results in high-dimensional measurement features. The state vector nonlinear manifold is approximated and the map from measurement features to the estimated state is the solution to a Sylvester equation.
The methodology is illustrated with the estimation of a fluid flow field from a few wall-mounted sensors.

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