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Abstract

Reconstructing causal dynamic networks from multivariate time series is a foundational problem in complex systems science. Yet, the key scientific issue is not simply causality detection, but causal interpretability. Interpretable causality is the foundation for testable mechanistic hypotheses, transferable forecasting, and principled decision-making for intervention and control. In real-world complex systems, causal inference is often compromised by noise, missing data, high dimensionality, nonlinearity, time delays, heterogeneity, and partial observability. Classic approaches to interpretable causality yield explicit, inspectable quantities such as causal graphs, coefficients, and governing equations. However, this methodological shift has heightened expectations: AI-extended approaches are increasingly required to recover explicit causal mechanisms rather than opaque predictive dependencies, thereby preserving interpretability. This review summarizes four classic methods and their AI-extended counterparts based on time series data, including Granger frameworks, information-theoretic measures, nonlinear state–space/manifold reconstruction, and mechanistic differential-equation learning. Next, we elucidate their motivations, core principles, the origins of interpretability, and the assumptions required for meaningful conclusions. Finally, we highlight representative applications across climate studies, neuroscience, epidemiology, finance, social science, ecology and molecular biology, followed by a discussion of comparative analysis, open challenges, and future research directions.