Data-driven identification of latent port-Hamiltonian systems

The paper rigorously establishes that, under the projection property Ψ_e∘Ψ_d = Id_Z and its Jacobian identity, a latent port-Hamiltonian (pH) system pushes forward through the decoder into a pH system on the physical manifold X̃, with J|_{x̃} = DΨ_d J DΨ_d^⊤, R|_{x̃} = DΨ_d R DΨ_d^⊤ (skew and positive semidefinite, respectively), and the same port power, yielding dissipation, passivity, Lyapunov stability, and a Lipschitz-based boundedness transfer bound (Theorem 3 and the subsequent arguments) . The candidate reproduces the structural pushforward and the property-transfer program, but asserts R|_{x̃} is symmetric negative semidefinite and uses that sign in the dissipation step, which reverses the inequality and is incorrect for pH systems; the paper explicitly uses R ⪰ 0 and the standard dissipation inequality d/dt H ≤ y^⊤u , and then transfers passivity and Lyapunov stability to X̃ correctly . The paper’s boundedness transfer bound ∥x̃(t)−x̃_0∥ ≤ L_{Ψ_d,U} C_Z is also stated with appropriate regularity assumptions on Ψ_d over the (bounded) neighborhood U . The model’s argument would become correct after flipping the definiteness/sign of R throughout; as written, it contains a sign error in a key inequality.