Emiliano Díaz Salas-Porras

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 has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventions on the system under study. With the advent of big data and data-driven methods, the fields of causal and equation discovery have developed and accelerated progress in computer science, physics, statistics, philosophy, and many applied fields. 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 data-driven causal and equation discovery, point out connections, and showcase comprehensive 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 revolutionised with the efficient exploitation of observational data and simulations, modern machine learning algorithms and the combination with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems.

Land, atmosphere and climate interact constantly and at different spatial and temporal scales. In this paper we rely on causal discovery methods to infer spatial patterns of causal relations between several key variables of the carbon and water cycles: gross primary productivity, latent heat energy flux for evaporation, surface air temperature, precipitation, soil moisture and radiation. We introduce a methodology based on the convergent cross-mapping (CCM) technique. Despite its good performance in general, CCM is sensitive to (even moderate) noise levels and hyper-parameter selection. We present a robust CCM (RCCM) that relies on temporal bootstrapping decision scores and the derivation of more stringent cross-map skill scores. The RCCM method is combined with the information-geometric causal inference (IGCI) method to address the problem of strong and instantaneous variable coupling, another important and long-standing issue of CCM. The proposed methodology allows to derive spatially explicit global maps of causal relations between the involved variables and retrieve the underlying complexity of the interactions. Results are generally consistent with reported patterns and process understanding, and constitute a new way to quantify and understand carbon and water fluxes interactions

Causal discovery from observational data offers unique opportunities in many scientific disciplines: reconstructing causal drivers, testing causal hypotheses, and comparing and evaluating models for optimizing targeted interventions. Recent causal discovery methods focused on estimating the latent space of the data to get around a lack of causal sufficiency or additivity constraints. However, estimating the latent space significantly increases model complexity, compromising causal identifiability and making it hard to compare models that correspond to different causal hypotheses. We propose a kernel, non-parametric latent-space modelling approach and deal with the difficulty of comparing causal directions by measuring and controlling for the level of causal assumption fulfilment. We introduce a latent noise causal inference framework to estimate latent factors associated with the hypothesized causal direction by optimizing a loss function with kernel independence criteria. We extend the framework to work with time series using an additional time-dependent kernel regularizer. We discuss the additivity assumption and model complexity and give empirical evidence of performance in a wide range of synthetic and real causal discovery problems.