Fig. 7: Visualizing networked systems in 1-dimensional decision space.
From: Deep learning resilience inference for complex networked systems
We illustrate the probability distributions of k and βeff and α for networked systems with mutualistic (a, d, g), gene regulatory (b, e, h), and neuronal (c, f, i) dynamics, taking one experiments of Fig. 4 for each dynamics as examples. The critical thresholds inferred by ResInf, kc, are shown as the grey dashed lines in (a–c). The critical thresholds computed by GBB, \({\beta }_{{{\rm{eff}}}}^{c}\), are shown as grey dashed lines in (d–f). We also show the critical threshold from SDR, αc (g–i). We find resilient and non-resilient samples (resilient sp. and non-resilient sp.) are more linearly separable in k-space than β-space and α-space, which demonstrates the stronger resilience prediction capability of our proposed approach ResInf. j–l We illustrate the receiver operating characteristic (ROC) curve of GBB, SDR, and ResInf with the same experiment settings as Fig. 4 as well as the corresponding average AUC. Transparent lines represent experiments with different random seeds (n = 50), and solid lines represent the average ROC curve.
