2504.17268
Parameter estimation in ODE models with certified polynomial system solving ⋆
Alexander Demin, Alexey Ovchinnikov, Fabrice Rouillier
incompletemedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s toy example states the 4×4 quadratic system has only two solutions and reports (μ, x0) ≈ (0.49, 1.00) and (0.25, −2.00), explicitly noting this is a heuristic illustration without a rigorous analysis. The candidate solution gives a complete algebraic derivation using the system’s triangular structure, proving exactly two solutions and finding the exact pairs (μ, x0) = (0.50, 1.00) and (0.25, −2.00). The paper’s qualitative claim (two solutions) matches, but it neither supplies a proof nor the exact μ = 0.50 for x0 = 1.00; thus, the paper is incomplete while the model is correct .
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper compellingly demonstrates that certified RUR-based solvers can be competitive and sometimes superior to homotopy continuation for polynomial systems arising from ODE parameter estimation. The toy example is illustrative but would benefit from a brief rigorous derivation and exact numerics; otherwise, the narrative is clear and the empirical benchmarking useful. These edits are minor and do not affect the conclusions.