Following the 2012 breakthrough in deep learning for classification and visions problems, the last decade has seen tremendous raise of interest in machine learning in a wider mathematical research community from foundational research through field specific analysis to applications. 

As data is at the core of any inverse problem, it was a natural direction for the field to investigate how machine learning could aid various aspects of inversion yielding numerous approaches from somewhat ad-hoc but very effective like learned unrolled methods to provably convergent learned regularisers with everything in between. In this talk I will review some on these developments through a lens of the research of our group.   

We introduce a new methodology based on the multirevolution idea for constructing integrators for stochastic differential equations in the situation where the fast oscillations themselves are driven by a Stratonovich noise. Applications include in particular highly-oscillatory Kubo oscillators and spatial discretizations of the nonlinear Schrödinger equation with fast white noise dispersion. We construct a method of weak order two with computational cost and accuracy both independent of the stiffness of the oscillations. A geometric modification that conserves exactly quadratic invariants is also presented. If time allows, we will discuss ongoing work on uniformly accurate methods for such systems. This is a joint work with Gilles Vilmart.