Fast data-driven model reduction for nonlinear dynamical systems

The paper’s fastSSM derivation and formulas for the cubic 2D normal form, including T3 = G3/λ, T4 = G4/λ̄, T5 = G5/(2λ̄ − λ), and γ = 2 G3 T4 + G4 T̄4 + G4 T3 + 2 G5 T̄5 + G7, match the candidate solution exactly. The data-fitting steps (SVD-based tangent space, polynomial regression for manifold and reduced dynamics) and the recursive homological-equation approach to enforce conjugacy also align with the paper’s presentation. See the manifold/dynamics fitting and conjugacy setup (equations (11)–(15)) and the explicit cubic 2D normal form and coefficients (equations (16)–(19)) in the paper . Assumptions listed by the model (closeness to SSM, removal of transients, embedding/diffeomorphism, nonresonance, derivative estimation) are also articulated in the paper’s methodology and pre/post-processing sections, including SSM existence/uniqueness and data preprocessing (delay embedding, transient removal) . Minor wording differences (e.g., why quartic terms are absent in the cubic normal form remainder written as O(5)) do not change the outcome.