Mechanism Informed Early Warning of Simulated Dynamical Transitions

Abstract

Background  early warning of a dynamical transition is an operational decision problem: a score is useful only when it yields an alarm with actionable lead time and a controlled false-alarm burden. Classical indicators based on critical slowing down are interpretable but can be weak, mechanism dependent and sensitive to observation design. Methods  this simulation study evaluates a mechanism-informed feature strategy on a Rosenzweig–MacArthur predator–prey system approaching Hopf onset and a one-state harvesting model approaching a fold. Rolling mean, variance and lag-one autocorrelation are combined with local estimates of equilibrium and vector-field geometry. Logistic Regression (LR), random forest and multilayer-perceptron baselines produce window-level risk scores, while a validation-calibrated cumulative-sum rule converts those scores into trajectory-level alarms. Thirty realizations are reported per model and noise level, with complete trajectories separated into sub-training, validation and test sets. Results  At 5% observation noise on the Hopf task, the augmented logistic detector has a reported mean trajectory ROC AUC of 0.901 ± 0.103, compared with 0.690 ± 0.280 for the univariate classical logistic baseline. Seven of 12 test trajectories alarm within the predefined 80-step imminence window, and no far-region alarm is observed in that test sample. However, a matched-channel classical ablation using both prey and predator statistics reaches 0.897 ± 0.115 AUC; the paired comparison between augmented and baseline logistic AUCs is not significant after the stated procedure (p=0.064). On the fold task, augmentation adds little (0.997 versus 0.996 AUC at 5% noise). Conclusion  the reported experiments support a restrained conclusion: Local geometry can help when a one-channel warning is weak, but most of the Hopf gain is attributable to observing the second state, and the fold task is nearly saturated. The study clarifies how mechanism-informed features, matched-channel ablations and validation-only sequential calibration can be combined, while also identifying the experiments required for transfer beyond fixed, regularly sampled simulations.