Discovering Causal Relations and Equations from Data

TL;DR

This paper reviews methods and challenges in discovering causal relations and physical equations from observational data across various scientific domains, emphasizing the role of machine learning and domain knowledge.

Contribution

It provides a comprehensive taxonomy, discusses key concepts and methods, and showcases case studies in physics, Earth sciences, and neuroscience for causal and equation discovery.

Findings

Data-driven methods are revolutionizing causal and law discovery.

Machine learning enhances the extraction of physical laws from data.

Interdisciplinary approaches are crucial for understanding complex systems.

Abstract

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.