Learning Deep Dissipative Dynamics

Yuji Okamoto, Ryosuke Kojima

incompletemedium confidence

Category: math.DS
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The candidate solution correctly proves idempotence and that the j≡0 projection P_{ℓ,V} yields V̇ ≤ w(u,y), matching the formulae and logic of Theorem 6, but it does not establish the union-of-images property required by the paper’s Definition of “dissipative projection.” The paper provides that property (via the general KYP/QME solution) and an idempotence check, but it omits the ∥∇V∥=0 case (division by ∥∇V∥2), and its Appendix A contains a sign error in the displayed relation between V̇ and w(u,y). Overall: model’s core derivation (for mapping into Sd and idempotence) is sound; the paper’s main construction and claims are sound but presented with missing regularity assumptions and a sign mistake in an auxiliary proof.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The paper presents an explicit, differentiable projection onto dissipative dynamics for neural ODEs and ties it to a general QME solution of the nonlinear KYP lemma. The contribution is practical and theoretically well-motivated. To reach publishable clarity, the authors should correct a sign error in the KYP display, add a regularity assumption or rule for ∥∇V∥=0, and streamline the appendix proof for the j≡0 case to avoid unnecessary use of Q\^{-1}.