A Causality-Based Learning Approach for Discovering the Underlying Dynamics of Complex Systems from Partial Observations with Stochastic Parameterization

Nan Chen, Yinling Zhang

incompletemedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper states the conditional-sampling SDE (3) and the filter/smoother ODEs (5a)–(5d) but does not provide a derivation, citing prior work. Moreover, (5a) contains a clear typographical error (A2 should be A1), and (5d) has a second-term factor that should be C^T = (b2 b2^T Rf^{-1})^T rather than (b2 b2^T) Rf as printed. These issues are visible in the text presenting Proposition 1 and equations (5a)–(5d) , alongside the model set-up (2a)–(2b) . By contrast, the candidate solution supplies a complete, standard linear–Gaussian derivation (Kalman–Bucy filtering, fixed-interval smoothing in information form, and the reverse-time SDE) and identifies the two typos precisely, yielding the correct formulas.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The conditional-sampling SDE and associated filter/smoother equations are central and, in intent, correct, but two typographical errors in (5a) and (5d) risk misleading readers. The exposition omits derivations, relying on a citation. Adding an erratum for the typos and either a brief proof sketch or precise canonical references would render the presentation rigorous without changing the substance.