2407.11684
α-SGHN: A Robust Model for Learning Particle Interactions in Lattice Systems
Yixian Gao, Ru Geng, Panayotis Kevrekidis, Hong-Kun Zhang, Jian Zu
incompletemedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper empirically demonstrates that α-SGHN can infer ring links from trajectories and approximately preserve the systems’ conservation laws, but it does not give formal identifiability guarantees or invariant-preservation proofs. The model’s candidate solution provides a concrete, correct construction: (a) an interaction score equal to time-averaged absolute cross-partials that exactly recovers the ring for FK/Rotator/Toda (for generic data) and (b) graph-only Hamiltonian predictors that provably conserve the stated invariants (energy; energy and momentum; and Toda trace invariants).
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The work is a useful and timely contribution toward structure discovery and conservation-aware prediction in lattice Hamiltonian systems. Its empirical performance is compelling and the scope (FK, Rotator, Toda; integrability sweep) is well-chosen. To elevate the contribution, the paper should clarify how |α| is defined/regularized, provide robustness analyses, and, if possible, sketch conditions under which the inferred graph provably matches the underlying ring.