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Most problems in Earth sciences aim to do inferences about the system, whereaccurate predictions are just a tiny part of the whole problem. Inferences meanunderstanding variables relations, deriving models that are physicallyinterpretable, that are simple parsimonious, and mathematically tractable.Machine learning models alone are excellent approximators, but very often donot respect the most elementary laws of physics, like mass or energyconservation, so consistency and confidence are compromised. In this paper, wedescribe the main challenges ahead in the field, and introduce several ways tolive in the Physics and machine learning interplay: to encode differentialequations from data, constrain data-driven models with physics-priors anddependence constraints, improve parameterizations, emulate physical models, andblend data-driven and process-based models. This is a collective long-term AIagenda towards developing and applying algorithms capable of discoveringknowledge in the Earth system.

Living in the Physics and Machine Learning Interplay for Earth Observation