Statistical inverse problems and gradient flow structures in the space of probability measures

Speaker: Prof. Dr. Sebastian Reich
Affiliation: Universität Potsdam (Germany)
Organized by: FAU DCN-AvH, Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship at FAU Erlangen-Nürnberg (Germany)

Zoom link
Meeting ID: 923 1605 7419 | PIN code: 000474

Abstract. Statistical inverse problems lead to complex optimisation and/or Monte Carlo
sampling problems. Gradient descent and Langevin samplers are typically examples of widely used algorithms. In my talk, I will present recent results on optimisation and sampling algorithms, which can be viewed as interacting particle systems, and their mean-field limits.

I will highlight the geometric structure of these mean-field equations within the, so called, Otto
calculus, that is, a gradient flow structure in the space of probability measures. An important outcome
of recent work on the subject are affine invariant formulations, a property shared with Newton’s
method, but not with gradient descent and ordinary Langevin samplers.

Joint work with Luc Hillairet (Orléans) and Emmanuel Trélat (Paris).