Non-linear reduced modelling for parametric PDEs

Abstract:

Reduced (or surrogate) modelling replaces a high-resolution PDE model with some simple model that only loses some small and known accuracy. Reduced models are designed to allow for fast or closed-form computation, opening the door for uncertainty quantification, inverse problems, or data assimilation and more.

I will present recent work in reduced models, including a discussion about worst-case versus average-case error optimisation, some results in optimal linear reduced models, and experiments in non-linear models.