Data-driven identification of a 2D wave equation model with port-Hamiltonian structure

The paper and the model outline the same four-step scheme (shift → Loewner → stability projection → shift-back) and the spectral-zero-based left/right selection that yields L ≻ 0 and M = −M^T, with the port-Hamiltonian realization recovered from S via skew/symmetric splitting. These steps and identities are stated in the paper (spectral zeros leading to L Hermitian positive definite and M skew-symmetric; Cholesky-based normalization and S-splitting; plus the shift/projection/shift-back modifications) but are presented as a methodological adjustment without a full proof that strict dissipativity is preserved after the stability projection P_∞, see §3.2–3.3 and comments . The candidate solution is largely aligned, but it overclaims that any Loewner interpolant of shifted data is strictly positive-real on iℝ and that choosing D_s > ∥Ĥ_s − P_∞(Ĥ_s)∥_{H∞} ensures the projected model remains strictly positive-real; this tacitly assumes uniform positive-realness of the initial interpolant along iℝ, which is not guaranteed by data shifting alone. Hence both are incomplete: the paper lacks full guarantees, and the model asserts a stronger property that requires missing assumptions.