Toward Dynamic Stability Assessment of Power Grid Topologies using Graph Neural Networks

Referee: 'From topological information only' is ambiguous: in Schultz/Nitzbon/Hellmann ensembles M, D, P, K are usually fixed and only sign(P) varies. The manuscript should state which dynamical parameters vary, and add a controlled experiment with heterogeneous M, D, P on a fixed topology to disentangle topological learning from a memorized dynamical regime.

Authors: The referee is correct that this distinction is load-bearing and that the abstract phrasing is too compact. In our datasets M, D, and |P| as well as the global coupling K are indeed held to the canonical homogeneous values used in the Schultz/Nitzbon/Hellmann line of work; only the consumer/producer sign of P and the topology vary across samples. The accurate reading of our result is therefore 'topology given a fixed, homogeneous second-order swing-equation regime,' and we will state this explicitly in the abstract, in the dataset section, and in the discussion of scope. To address the referee's substantive point, we will add a controlled ablation in which M and D are drawn from heterogeneous distributions (and, separately, |P| is drawn from a non-uniform distribution) on a held-fixed topology ensemble, and we will report how predictive performance and the troublemaker ranking degrade as a function of the heterogeneity level. This separates the inductive contribution of topology from that of the dynamical regime and bounds the generality of the trained model. We thank the referee for forcing this clarification; it sharpens rather than weakens the paper's claims. revision: yes

Referee: The small-to-large transfer to the synthetic Texas grid is between two objects produced under the same modeling convention. The manuscript should document M, D, P, K assignment for the Texas model and report transfer under at least one mismatch (e.g., heterogeneous generator-fleet inertia/damping on the same topology). Otherwise 'real-world applicability' is not supported.

Authors: We accept this criticism. As currently described, the synthetic Texas test case inherits the same homogeneous parameter convention as the training ensembles, so shared synthetic-data structure is indeed a sufficient alternative explanation for the transfer. We will (a) add an explicit table specifying how M, D, P and K are assigned in the Texas model, making clear that they match the training convention, and (b) add a mismatch experiment on the Texas topology in which M and D are sampled from a generator-fleet-inspired heterogeneous distribution (and a second variant in which P magnitudes follow a load/generation-realistic distribution). We will report troublemaker recall and regression error under each mismatch, and we will explicitly soften 'illustrates the potential for real-world applications' to a claim about transfer across topologies within a shared dynamical regime, with the mismatch experiments delineating where that transfer breaks down. We agree this is the load-bearing experiment for the framing. revision: yes

Referee: Basin-stability targets are regime-dependent and class-imbalanced; troublemakers are rare. Report class-conditional precision/recall at operating thresholds and compare to simple topological baselines (degree, betweenness, dead-end / dead-tree indicators, spectral centralities). Quantify the GNN's marginal value over interpretable baselines.

Authors: We agree and will expand the evaluation accordingly. In the revision we will (i) report class-conditional metrics for the troublemaker class — precision, recall, F1 and PR-AUC at operating thresholds, alongside the aggregate regression metrics already shown — and (ii) include a baseline panel comprising degree, betweenness, current-flow betweenness, a spectral centrality, and the dead-end / dead-tree indicators of Nitzbon et al., as well as a logistic-regression and a small MLP fed these hand-crafted features. This makes the marginal value of the GNN over interpretable structural proxies explicit. We note, anticipating the result, that dead-end/dead-tree indicators are known to capture a substantial fraction of troublemakers in these ensembles, so the relevant question is exactly the one the referee poses: how much beyond such baselines does the GNN buy, and where. We will state this comparison quantitatively rather than rhetorically. revision: yes

Referee: 'Suitable for practical use cases' is a strong operational claim not tied to a defined use-case specification (false-negative tolerance, calibration, runtime vs. Monte-Carlo basin-stability at matched accuracy). Either define the use case quantitatively and demonstrate it, or soften the language.

Authors: The referee is right that the phrase as written is not falsifiable. We will take both remedies in combination. First, we will soften the abstract and conclusions, removing unqualified 'suitable for practical use' language. Second, we will define one concrete screening use case — flagging candidate troublemaker nodes for follow-up Monte-Carlo basin-stability simulation — and specify it operationally: a target recall on troublemakers (we will commit to a value, e.g. 95%), the resulting precision and the implied simulation budget reduction relative to exhaustive MC sampling at matched per-node uncertainty, and wall-clock runtime on the Texas-scale grid. We will additionally report calibration of the predicted probabilities (reliability diagrams, Brier score, and, if needed, post-hoc temperature scaling). Where the model meets the specification we will say so; where it does not, we will say that too. This converts the claim into something the reader can check. revision: yes