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.

介绍了学习方法在地球科学中应用的主要挑战，提出了几种融合了物理学和机器学习的方法，包括从数据中提取微分方程、加入物理先验和依赖性约束的数据驱动模型、改进参数化、模拟物理模型以及融合数据驱动和基于过程的模型，从而发现地球系统中的知识。