Causal inference for complex systems and applications to turbulent flows

Abstract

Causality lies at the heart of scientific inquiry, serving as the fundamental basis for understanding interactions among variables in physical systems. Despite its central role, current methods for causal inference face significant challenges due to nonlinear dependencies, stochastic interactions, self-causation, collider effects, and influences from exogenous factors, among others. While existing methods can effectively address some of these challenges, no single approach has successfully integrated all these aspects. Here, we address these challenges with SURD: Synergistic-Unique-Redundant Decomposition of causality (Nat. Commun., vol. 15, 2024, p. 9296). SURD quantifies causality as the increments of redundant, unique, and synergistic information gained about future events from past observations. The formulation is non-intrusive and applicable to both computational and experimental investigations, even when samples are scarce. We benchmark SURD in scenarios that pose significant challenges for causal inference and demonstrate that it offers a more reliable quantification of causality compared to previous methods. We further illustrate the applicability of our approach in two turbulent-flow scenarios: the energy transfer across scales in the turbulent energy cascade and the interaction between motions across scales in a turbulent boundary layer. Our results show that, without accounting for redundant and synergistic effects, traditional approaches to causal inference may lead to incomplete or misleading conclusions.