2505.20515
Semi-Explicit Neural DAEs: Learning Long-Horizon Dynamical Systems with Algebraic Constraints
Avik Pal, Alan Edelman, Chris Rackauckas
correctmedium confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper explicitly formulates the projection step as a constrained Euclidean projection with Lagrange-multiplier equations and a fixed-Jacobian Newton variant, and derives SNODE by substituting a one-step predictor and replacing 1/h with γ; it also states that the predictor-to-manifold distance is of order O(h^{p+1}) for an order-p method. These match the candidate solution’s three claims. The model’s write-up adds standard regularity/uniqueness details (LICQ, IFT on the KKT map) that the paper leaves implicit, but there is no substantive disagreement in the mathematics or derivations. See the projection/KKT and fixed-Jacobian Newton setup and the SNODE derivation in Section 3 and the surrounding equations, as well as the O(h^{p+1}) distance remark .
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The theoretical core—projection by solving a small nonlinear KKT system and a fixed-Jacobian Newton variant that connects to stabilized NODEs—is correct and consistent. The derivations agree with standard DAE projection analyses, and the empirical evaluation is thorough. To improve rigor and reproducibility, the manuscript should explicitly state LICQ/full-row-rank and smoothness assumptions near the manifold and label the 1/h→γ substitution as a modeling choice rather than a limit argument. These are clarifications rather than corrections, hence minor revisions. Key claims (projection/KKT, fixed-Jacobian Newton, SNODE derivation, and O(h\^{p+1}) predictor-to-manifold distance) are all present in the text .