Causal inference in fluid mechanics: Introduction, progress, and outlook

Identifying causal relationships has long been a central yet challenging objective in scientific research, particularly in complex dynamical systems such as those encountered in fluid mechanics. Recent advances in data science have promoted the development of modern causal inference methods, offering powerful tools to extract causal mechanisms from large-scale flow data and facilitate causality-related research. This article aims at offering a comprehensive review of causal analysis techniques useful for fluid mechanics, covering intervention-based frameworks, causal graphical models, and a range of data-driven causal discovery approaches. For each category, we discuss the underlying theory, strengths and limitations, and applications in fluid mechanics. Through illustrative case studies, we compare the performance of three typical causal analysis algorithms (Granger causality, transfer entropy, and Liang–Kleeman information flow), demonstrating their potential for future research. Finally, we outline potential directions for advancing causal inference in fluid mechanics.