(TA) Graduate students project supervision

Supervised by full professor Anthony Nouy.

Description

Matrix completion via optimization on low-rank matrix manifolds

The goal is to approximate an unknown matrix given a limited number of its entries. We investigate the low-rank approximation format, which results in optimizing a quadratic loss function defined fixed-rank matrix manifolds.

Inverse problem and dimension reduction

The goal is to approximate an unknown high-dimensional function (e.g. solution of a parameterized PDE) given linear measurements on it. We investigate the so-called PBDW method, which leverage prior linear model reduction (e.g. POD).

Linear features learning using gradient evaluations

The goal is to approximate a multivariate function given pointwise evaluation of the function and its gradient. We investigate the so-called Active-Subspace Method, which build a linear low-dimensional featuring of the input, certified thanks to Poincaré inequalities.