2411.00923
Resolvent-Type Data-Driven Learning of Generators for Unknown Continuous-Time Dynamical Systems
Yiming Meng, Ruikun Zhou, Melkior Ornik, Jun Liu
correctmedium confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper and the candidate solution establish the same resolvent identities, Yosida representation, strong convergence, and finite-horizon truncation bound. The paper proves the convergence rate by a shift-to-contraction argument, while the model uses a second-variation/variation-of-constants route yielding L_λ h − L h = R(λ)L^2 h under slightly stronger regularity. Results agree; proofs differ in technique.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
Technically sound development of resolvent/Yosida machinery for Koopman generators with explicit convergence rates and a practically useful truncation bound. The work is coherent and relevant to data-driven operator learning. Minor clarifications on domain and regularity assumptions would further improve accessibility.