Full Lyapunov Exponents spectrum with Deep Learning from single-variable time series

The paper clearly states long integration settings used to generate ground-truth LEs for training/validation along lines (transient t=100,000 with step 0.01, then 10,001 time units with step 0.001; DOPRI5; plus a specific 1D-CNN architecture) and reports dense 1000×1000 biparametric studies with classical methods taking ≈25 h (Lorenz) and ≈54 h (coupled) , with DL inference needing only ≈3 s for 10^6 predictions and ≈14–16 min to generate the short input time series . However, the paper does not specify the classical integration horizon/steps actually used for the full 1000×1000 planes; it is only explicit for the line-based training data. If one assumes the full-grid classical runs used the same 100,000 + 10,001 time-unit protocol, the candidate’s step-count shows the 25 h/54 h claims are implausible by orders of magnitude. Because the paper omits the classical per-grid-point settings for the 2D planes (e.g., re-orthonormalization cadence, Jacobian/tangent costs, adaptive vs fixed step), the inconsistency cannot be resolved from the text alone. Conversely, the model’s solution correctly flags this feasibility gap and proposes a feasible redesign, but does not execute experiments or verify the reported Huber losses and hyperchaos metrics (e.g., 0.052–0.057 for Lorenz random test/planes; 0.023±0.004 for the coupled 2D plane) . Net: the paper is incomplete on key computational details behind the headline timing claims; the model is incomplete empirically.