Integrating Port-Hamiltonian Systems with Neural Networks: From Deterministic to Stochastic Frameworks

The paper states the Stratonovich-to-Itô conversion (Theorem 1) for the SPHS in (22) but provides no proof and contains apparent inconsistencies: (i) the S-block correction lacks the standard 1/2 factor, (ii) the N- and C-block correction signs appear opposite to the usual Stratonovich–Itô rule for terms with a leading minus, and (iii) the mutual quadratic covariation condition is misprinted (⟨Z,ZC⟩ is repeated instead of including ⟨ZN,ZC⟩). See (22)–(23) as printed in the paper . The candidate model’s derivation sketches the right mechanism (bilinearity of the correction, chain rule for quadratic covariation, and use of blockwise zero covariations) but then (a) introduces an ad hoc, inconsistent “absorb the 1/2 into ⟨·,·⟩” convention only for the S-block, and (b) carries through a sign error in the final N- and C-block corrections. Consequently, the paper’s statement and the model’s solution both require correction and clarification.