A machine learning framework for correcting under-resolved simulations of turbulent systems using nudged datasets

Due to the rapidly changing climate, the frequency and severity of extreme weather, such as storms and heatwaves is expected to increase drastically over the coming decades. Accurately quantifying the risk of such events with high spatial resolution is a critical step in the implementation of strategies to prepare for and mitigate the damages. As fully resolved simulations remain computationally out of reach, policy makers must rely on coarse resolution climate models which either parameterize or completely ignore sub-grid scale dynamics. In this work we propose a machine learning framework to debias under-resolved simulations of complex and chaotic dynamical systems such as atmospheric dynamics. The proposed strategy uses ``nudged'' simulations of the coarse model to generate training data designed to minimize the effects of chaotic divergence. We illustrate through a prototype QG model that the proposed approach allows us to machine learn a map from the chaotic attractor of under-resolved dynamics to that of the fully resolved system. In this way we are able to recover extreme event statistics using a very small training dataset.