2202.08208
Front Transport Reduction for Complex Moving Fronts — Nonlinear Model Reduction for an Advection–Reaction–Diffusion Equation with a Kolmogorov–Petrovsky–Piskunov Reaction Term
Philipp Krah, Steffen Büchholz, Matthias Häringer, Julius Reiss
incompletemedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper correctly formulates the FTR objective and proposes practical solvers (iterative rank‑truncation and an autoencoder), but it does not provide a rigorous convergence or optimality analysis. Key steps—dropping f′ in the gradient and projecting by hard rank truncation—are only heuristically justified. By contrast, the model’s solution places the same objective on the fixed‑rank manifold with a standard Riemannian line‑search framework that guarantees monotone decrease and convergence to critical points under mild smoothness assumptions, and it correctly notes NP‑hardness barriers to global guarantees.
Referee report (LaTeX)
\textbf{Recommendation:} major revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The FTR formulation is well-motivated for front-dominated dynamics, and the experiments are persuasive. However, the optimization section is heuristic: the central algorithm lacks a convergence analysis, and key methodological statements (e.g., that line search or quasi-Newton steps would not help) are asserted without proof. Providing a minimal descent/convergence result—ideally via a Riemannian line-search treatment—or at least an acceptance test that guarantees nonincreasing objective would notably strengthen the work.