Designing Chaotic Attractors: A Semi-supervised Approach

The paper empirically demonstrates semi-supervised points ρ*—where the closed-loop LESN has MLE>0 while the output remains visually close to a periodic “skeleton”—and outlines a heuristic procedure to find them, but it does not provide a theorem or a rigorous proof of existence beyond case studies and bifurcation plots (see definitions and figures around ρ(P), ρ(E), and ρ* and the stated search protocol) . The model’s solution sketches a plausible rigorous route via center-manifold reduction and rank-one theory, but it relies on substantial, unverified hypotheses (e.g., uniform transverse contraction inherited from negative driven CLE, one-dimensional center, unimodality/nonflat criticality, and applicability of Wang–Young theory to the trained LESN family) that are neither established in the paper nor verified for the LESN setting. Consequently, the paper is incomplete as a proof, and the model is incomplete because key assumptions are not justified.