Reservoir cross mapping as a nonlinear framework for detecting dynamical causality

Identifying causal relations from observational time series is essential for understanding complex systems but remains a challenging problem. Mutual cross mapping (MCM), a widely used causality detection method, has addressed the nonseparability problem in nonlinear systems via state space reconstruction and approximates cross mapping between reconstructed manifolds. However, MCM relies on accurately estimated parameters and a locally linear estimation of the cross mapping, limiting its general applicability. This work presents reservoir cross mapping (RCM), a causality detection framework that integrates reservoir computing (RC) with MCM to accurately detect dynamical causality. RCM provides a nonlinear approach based on RC's embedding capability by reconstructing the dynamics of different variables and identifies causal relations and their strengths by evaluating the smoothness of the cross mapping between reservoirs. Evaluations of various simulated and real-world datasets demonstrate the effectiveness and robustness of RCM in detecting causality.