Data-Driven Modeling and Prediction of Non-Linearizable Dynamics via Spectral Submanifolds

Mattia Cenedese, Joar Axås, Bastian Bäuerlein, Kerstin Avila, George Haller

correctmedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper derives the same planar, autonomous extended normal form on the forced 2D SSM (eq. (7)) and states that 1:1 periodic responses correspond to fixed points with amplitude–phase relations given in eq. (8) (matching the candidate’s formulas). The candidate solution reproduces those relations directly from the fixed-point conditions and adds a correct, explicit Jacobian/trace/determinant for linear stability. The paper mentions stability via linearization but does not spell out the Jacobian; the candidate’s derivation is consistent with the paper’s framework. See the paper’s eqs. (7)–(8) and surrounding text for the formal statements and context .

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

Both the paper and the model correctly identify that 1:1 periodic responses correspond to fixed points of the planar forced-SSM dynamics and provide the same closed-form amplitude–phase relations. The model augments the paper by writing out the Jacobian and stability criteria explicitly. Minor clarifications would improve the presentation: state existence conditions next to the formulas, note the domain restriction ρ>0, and avoid ambiguous bifurcation terminology.