In this paper, we present results on improving out-of-domain weather prediction and uncertainty estimation as part of the \texttt{Shifts Challenge on Robustness and Uncertainty under Real-World Distributional Shift} challenge. We find that by leveraging a mixture of experts in conjunction with an advanced data augmentation technique borrowed from the computer vision domain, in conjunction with robust \textit{post-hoc} calibration of predictive uncertainties, we can potentially achieve more accurate and better-calibrated results with deep neural networks than with boosted tree models for tabular data. We quantify our predictions using several metrics and propose several future lines of inquiry and experimentation to boost performance.

Recent developments in Machine Learning approaches for modelling physical systems have begun to mirror the past development of numerical methods in the computational sciences. In this survey, we begin by providing an example of this with the parallels between the development trajectories of graph neural network acceleration for physical simulations and particle-based approaches. We then give an overview of simulation approaches, which have not yet found their way into state-of-the-art Machine Learning methods and hold the potential to make Machine Learning approaches more accurate and more efficient. We conclude by presenting an outlook on the potential of these approaches for making Machine Learning models for science more efficient.