Gabriel Turinici
Université Paris Dauphine - PSL, Paris, France

We investigate the efficient representation of sets of objects such as parametric solutions of PDEs or controlled PDEs, images or other high dimensional objects. When the set is close to some lower dimensional linear manifold, the "reduced bases" techniques have been employed successfully. But sometimes the manifold is not linear and techniques closed to "vector quantization" methods can be employed. We will describe in this talk some recent works, including existence results, related to the theoretical foundations of quantization of measures with a finite set of Dirac masses in the context Huber-energy kernels. We will next show how this can be used in applications in transport equations, physics, machine learning measure dependent PDEs, and numerical statistics.