We will discuss recent progress in our understanding of Gaussian process based inference methods for parameters or states of time evolution phenomena modelled by non-linear partial differential equations (PDEs) such as Navier Stokes, McKean Vlasov, and reaction diffusion systems. We will show that posteriors can deliver consistent solutions in the `informative’ large data/small noise limit, discuss probabilistic approximations to the fluctuations of such posterior measures in infinite dimensions, and how such results can be used to show that the non-convex problem of computation of the associated `filtering’ distributions are polynomial time problems.
Personal website of Richard Nickl