Fig. 2.

DDC recovers ground-truth connectivity across multiple three-node networks. (A–C) DDC estimation results based on different network structures (chain and confounder) simulated using linear and nonlinear dynamics. Left: Ground-truth network structure. Black solid lines are directed physical connections and red dashed lines are false positive connections commonly inferred by covariance estimation. The edges labeled $(i,j)$, indicating a connection from j to i, stand for the matrix entry at the ith row and jth column. Right: Estimated ΔL and ΔReLU. (D) Left: Phase diagram of $x_1$ and $x_2$ of the Rössler system governed by system equations shown above. Right: estimated ΔL and ΔReLU. (E and F) Estimation error, quantified as normalized Euclidean distance between the ground truth and estimation, over 50 trials for both linear and nonlinear models benchmarked with state-of-the-art network inference algorithms. c-Granger, conditional Granger causality; Cov, sample covariance estimation; Δc, differential covariance matrix; Δp, partial differential covariance matrix; L1/L2-reg, L1/L2-regularized partial covariance matrix; P, partial covariance estimation; partial-MI, partial mutual information; std, SD (standard deviation).