Inferring time-delayed dynamic networks with nonlinearity and nonuniform lags

Reconstructing time-delayed interactions among nodes of nonlinear networked systems based on time-series data is important and challenging, especially for the cases with only limited noisy data but no knowledge of node dynamics. In this paper, by fusing multiple source datasets together, we propose a data-driven modeling method based on noisy time series, referred to as nonuniform embedding nonlinear conditional Granger causality (NENCGC), specially focusing on the nonlinearity and nonuniform time-delayed characteristics of real networked systems. Specifically, we first use a nonuniform embedding scheme to select causal lagged components and then group these selected lagged components into different clusters of different nodes. In nonlinear causal analysis, the lagged components in the same cluster are treated as a whole through radial basis functions to fit the nonlinear relationships among nodes. Compared with other popular methods, our proposed NENCGC is proved effective and accurate in discovering time-delayed interactions from noisy data in terms of standard metrics. Meanwhile, both superiority and robustness of NENCGC against the variations of samples, time delays, noise intensities, as well as coupling strengths, are demonstrated.