2506.12819
Nonlinear Model Order Reduction of Dynamical Systems in Process Engineering: Review and Comparison
Jan C. Schulze, Alexander Mitsos
correctmedium confidence
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s Section 3.1.5 defines h(x̂,ẑ,û)=x̂−ψ†(ẑ,û), invokes strict causality to set Dx h^{-1} D_u h≡0 (hence Duψ†≡0 for this h), and projects f onto the manifold to obtain Dzψ†(z,u) ż = f(ψ†(z,u),u), which after left-multiplying by the pseudoinverse yields the ROM ż = Dzψ†(z,u)+ f(ψ†(z,u),u) (Eqs. (20)–(23)). This matches the candidate’s derivation, which additionally makes explicit the normal-equation/minimum-norm characterization and the orthonormal-tangent special case, and recovers the standard manifold–Galerkin formulas (Eqs. (17)–(19)) when ψ† is u-independent. Aside from a minor slip in the candidate’s statement of the dimension of M (it is n_z+n_u, not n_z), both arguments agree technically and substantively with the same proof structure .
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper’s input-aware manifold–Galerkin extension is correctly derived from the general invariance condition under strict causality and is consistent with standard manifold–Galerkin when the decoder is u-independent. The exposition is clear, practical, and situated within a useful survey. Minor additions clarifying assumptions (rank persistence, the modeling nature of Duψ†≡0, and manifold dimensions) would improve rigor and reproducibility.