Deep Learning for predicting rate-induced tipping

The paper demonstrates empirically that DL-based R-tipping probabilities for groups A (tipping) and B (non-tipping) are distinguishable by two-sample KS tests up to long lead times—about 290, 130, and 1000 steps for the Saddle–node, Bautin, and Compost-bomb systems, respectively (main text and SI Fig. S2) . It also shows that classical CSD indicators (variance and lag-1 autocorrelation) fail to discriminate the groups: composite means and 99% envelopes largely overlap (main text Fig. 3), and KS decisions for CSD are reported alongside (SI Fig. S2) . Data preprocessing and CSD computations (alignment; detrending window 100; sliding window 120) match the model’s assumptions . Building on these empirical findings, the model’s measure-theoretic construction (a fixed Borel isomorphism on the past-window space) correctly yields an ℓ-independent univariate map whose pushforward distributions differ for A vs B at all tested lead times; consistency of KS then implies rejection at α = 0.01 for sufficiently large samples. Its structural argument for the CSD limitation is plausible and consistent with the reported results. Minor issues: the model conflates diagnostic windows in SI Fig. S1 (100/200/100 steps) with the DL input length, and it implicitly treats sample-level KS rejections as population truths; neither undermines the core conclusions .