In this perspective paper, I offer an overview of the very exciting and timely subject of building data-driven deep learning models from the observations of a geoscience or climate system. I explain how data assimilation and machine learning can be combined to build data-driven deep learning models, from sparse and noisy observations. I present a few key perspectives and their inherent obstacles based on my experience and view on the subject, such as the hybrid paradigm where one combines a physical model with a neural network, and how to achieve uncertainty quantification when combining data assimilation and machine learning. Moreover, I provide 115 references, most of them very recent, that I found very useful when investigating the subject.

The paper is entitled Surrogate modeling for the climate sciences dynamics with machine learning and data assimilation, and is published (open access) in Frontiers in Applied Mathematics and Statistics, as a perspective paper, at the invitation of Axel Hutt, and reviewed by Geir Evensen and Peter Jan van Leeuwen.