  Most problems in Earth sciences aim to do inferences about the system, where
accurate predictions are just a tiny part of the whole problem. Inferences mean
understanding variables relations, deriving models that are physically
interpretable, that are simple parsimonious, and mathematically tractable.
Machine learning models alone are excellent approximators, but very often do
not respect the most elementary laws of physics, like mass or energy
conservation, so consistency and confidence are compromised. In this paper, we
describe the main challenges ahead in the field, and introduce several ways to
live in the Physics and machine learning interplay: to encode differential
equations from data, constrain data-driven models with physics-priors and
dependence constraints, improve parameterizations, emulate physical models, and
blend data-driven and process-based models. This is a collective long-term AI
agenda towards developing and applying algorithms capable of discovering
knowledge in the Earth system.
