Physics is a field of science that has traditionally used the scientific method to answer questions about why natural phenomena occur and to make testable models that explain the phenomena. Discovering equations, laws and principles that are invariant, robust and causal explanations of the world has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventional studies in the system under study. With the advent of big data and the use of data-driven methods, causal and equation discovery fields have grown and made progress in computer science, physics, statistics, philosophy, and many applied fields. All these domains are intertwined and can be used to discover causal relations, physical laws, and equations from observational data. This paper reviews the concepts, methods, and relevant works on causal and equation discovery in the broad field of Physics and outlines the most important challenges and promising future lines of research. We also provide a taxonomy for observational causal and equation discovery, point out connections, and showcase a complete set of case studies in Earth and climate sciences, fluid dynamics and mechanics, and the neurosciences. This review demonstrates that discovering fundamental laws and causal relations by observing natural phenomena is being revolutionised with the efficient exploitation of observational data, modern machine learning algorithms and the interaction with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems.

翻译：物理学是一门传统上运用科学方法回答自然现象为何发生，并构建可检验模型以解释这些现象的学科。数世纪以来，发现具有不变性、鲁棒性且能对世界进行因果解释的方程、定律和原理，一直是物理科学的基础。这些发现源于对世界的观察，并在可能的情况下通过对所研究系统进行干预性研究得以实现。随着大数据时代的到来以及数据驱动方法的应用，因果关系与方程发现领域在计算机科学、物理学、统计学、哲学及众多应用学科中取得了长足进展。这些领域相互交织，可用于从观测数据中发现因果关系、物理定律和方程。本文综述了物理学广泛领域中关于因果关系与方程发现的概念、方法及相关工作，并指出了最重要的挑战和未来有前景的研究方向。我们还为观测性因果关系与方程发现提供了一套分类体系，阐明了各领域间的联系，并展示了地球与气候科学、流体动力学与力学以及神经科学中的完整案例研究。本综述表明，通过高效利用观测数据、现代机器学习算法以及与领域知识的交互，通过观察自然现象发现基本定律和因果关系的范式正在发生革命性变革。激动人心的时代即将到来，我们面临着诸多挑战和机遇，以深化对复杂系统的理解。