{"id":"0ba7098d-8fef-410d-b23d-cf70178a3932","arxiv_id":"2508.19083","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"Sampling the total active power load instead of individual loads produces more diverse AC-OPF datasets, and a slack-variable formulation lets the generator scale to 4,661-bus grids.","lead":"This paper proposes HEDGeOPF, a faster method for generating AC optimal power flow (AC-OPF) training datasets, and three metrics for judging how good such datasets are. The authors show the method runs on test grids with more than 4,000 buses, where earlier high-quality sampling approaches did not scale.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"No slack-validity check: if load slacks in (7) activate materially, HEDGeOPF's stored (input, solution) pairs are not AC-OPF solutions for the nominal sampled setpoints, undermining the claimed quality benchmark.","rationale":"I focused on the slack-augmented formulation rather than the metric-definition issue because it is a correctness condition for the dataset itself. The reader's weakest_assumption already identified this gap, and the open-source release makes the test direct. If the test passes (slacks essentially never activate), the concern is retired and the remaining debate is about whether Q1–Q3 measure ML-relevant quality. If it fails, the central 'best balance' claim is unsupported regardless of metric choices. The paper's own convergence discussion (Section III.B) makes slack activation likely in the unclassified polytope, so the missing statistic is not a minor omission. The verdict should stay conditional rather than reject because the outcome depends on an empirical check that the code makes easy.","tokens_in":17083,"tokens_out":7613,"duration_ms":84203,"concrete_test":"Using the released HEDGeOPF.jl code, generate 10,000-instance datasets for IEEE 118-bus and GOC 2000-bus systems with default parameters. For each stored instance, compare the sampled load vector ŝd with the load vector sd used in KCL of the solved model; report the fraction of instances with max_d(|sup_d| + |sdw_d|) > 1e-4 MW/MVAr and the distribution of slack magnitudes. Then take 100 instances with nonzero slack, fix slacks to zero, and re-solve the standard AC-OPF at ŝd; record feasibility status and objective gap. If more than ~1% of instances show nonzero slack or the re-solved problems are infeasible, HEDGeOPF's stored pairs are not solutions to the nominal inputs, and the quality comparison must be recomputed on zero-slack instances only.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that HEDGeOPF offers the best quality/scalability balance presupposes that each stored sample is a valid AC-OPF training pair for the reported load input. In the generation formulation (7), KCL (7b) is enforced with sd = ŝd + sdw_d − sup_d (7d): the fixed sampled load ŝd is augmented by nonnegative slack variables before the power-flow equations are solved. Algorithm 1 stores every converged solve as a dataset instance and never reports how often sup_d/sdw_d are nonzero, their magnitudes, or any post-filtering. The text says only that a VOLL-sized penalty makes slacks a last resort, not that they are zero. Since Section III.B motivates the slack mechanism precisely because the unclassified load polytope (6) contains infeasible setpoints, a material fraction of large-system instances are likely solved with modified loads. If those instances record ŝd as the input, the pair is not a solution for ŝd; if they record sd, the claimed uniform-in-total-load distribution is silently distorted by wherever slacks are needed. Either way, Q1–Q3 metrics and the headline comparison are computed over objects whose validity as AC-OPF/ML training data is not established. This is more fundamental than the lack of NN validation: a benchmark over potentially mislabeled instances cannot support the central claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes HEDGeOPF, a heuristic for generating AC-OPF datasets by sampling load setpoints from slices of a convex polytope with explicit control of total active power, then solving an AC-OPF with load slack variables to improve convergence. It introduces three quality metrics (Q1: mean normalized Shannon entropy of primal variables; Q2: average normalized Hamming distance of ternary constraint-activation patterns; Q3: normalized bound-activation frequency) and compares HEDGeOPF (MX) with OPFData (M0/20), independent uniform sampling (M0), OPFLearn (M1), and RAMBO (M2) on nine PGLib test cases up to 4661 buses. The central claim is that MX offers the best balance between dataset quality and scalability, consistently beating uniform random sampling while approaching RAMBO's quality at much lower computational cost.","tokens_in":17430,"tokens_out":6322,"duration_ms":63733,"significance":"The contribution is timely and practically oriented. If the framework is accepted, it provides a standardizable way to compare AC-OPF dataset generators and a scalable baseline for large power systems. Strengths include the open-source Julia implementation, the use of large PGLib cases, the explicit discussion of the concentration-of-measure effect, and the interpretability of the three proposed metrics. The paper also makes a useful empirical observation that the widely used OPFData-style sampling leads to very low constraint-activation diversity. However, the validity of the generated training pairs is not established, the metrics are introduced and operationalized by the same paper that claims its method scores best, and the comparative claims are stronger than the single-run tables support.","major_comments":[{"comment":"The slack-augmented formulation keeps the AC-OPF feasible by allowing the actual load sd in KCL (7b) to differ from the sampled setpoint ŝd via sd = ŝd + sdw_d − sup_d (7d). Algorithm 1 stores every converged solve as a dataset instance and never reports how often sup_d/sdw_d are nonzero or their magnitudes. If the slacks activate materially, the stored (input, solution) pairs are either not AC-OPF solutions for the sampled inputs, or the intended distribution over load setpoints is silently distorted. The manuscript itself motivates the slacks precisely because the unclassified load polytope (6) contains infeasible setpoints, so this is not a remote edge case. Please report slack-activation statistics (share of instances with nonzero slacks, maximum magnitudes) and either post-filter instances with nonzero slacks or record the effective load sd as the input feature.","section":"§III-B, Eq. (7d) and Alg. 1"},{"comment":"The headline claim that MX 'consistently outperforms' random sampling is not supported by the tables as stated. For Q1 on generator reactive power (Table III-b), M0 has higher values than MX on grids 39 (43.7 vs 41.8), 500 (40.1 vs 37.2), and 1354 (37.1 vs 34.1), while M1 beats MX on grids 30, 39, and 57. Yet the Conclusion states 'MX consistently outperforms M0 and M1 on all test cases.' The claim should be restricted to the variable classes and metrics where it holds, or supported by a pre-specified aggregate ranking with confidence intervals. As written, the abstract's central claim is overstated.","section":"§V-B, Tables III–V; Conclusion"},{"comment":"The paper defines Q1–Q3 as 'dataset quality for ML applications' but never validates these metrics against any downstream ML outcome. No NN is trained; no evidence is given that datasets scoring higher on Q1–Q3 improve generalization, constraint satisfaction, or sample efficiency. Since the same paper proposes the metrics and then uses them to evaluate its own method, the benchmark is at risk of being circular. The authors justify avoiding NN benchmarks on reproducibility grounds, but then the abstract's 'dataset quality' claim should either be softened to 'quality as measured by Q1–Q3' or supported by at least one NN experiment on a small and a large test case.","section":"§IV-B, §V"},{"comment":"The computational comparison rests on a single run per method and grid, with no confidence intervals or repeated-seed variability. Table VI covers only four grids for M2 versus MX, and the sentence 'MX's solve time only exceeds that of M2 on the 118-bus system when scaling up to the 4661-bus grid' is difficult to parse. Since scalability is a central contribution, please report multiple independent repetitions or at least give per-instance timing distributions, and clarify the comparison on large grids where M2 could not be run.","section":"§V-C, Table VI"}],"minor_comments":[{"comment":"Typos: 'seperately' (Sec. V-A), 'al least once' (Sec. III-A), 'fis feasible' (Alg. 1).","section":"Throughout"},{"comment":"The sentence about MX's solve time on the 4661-bus system is ambiguous and should be rewritten for clarity.","section":"§V-C"},{"comment":"The bin count B is fixed to 100 without sensitivity analysis. Since Q1 values depend on the discretization, please report robustness to B or give a principled criterion for choosing it.","section":"§IV-B, Eq. (8)"},{"comment":"The comparison is not on identical input spaces: M0/M0/20 have no qd/pd ratio constraint while M1 and MX do, and M1 has a wider reactive variation. This should be stated more prominently in the fairness discussion, as it weakens the direct comparability of M1 against the others.","section":"§V-A, Table II"}],"recommendation":"major_revision","confidential_remarks":"The practical contribution is real, and the open-source release plus large-scale tests are strengths. However, the slack-validity issue is load-bearing for the validity of every generated instance, and the absence of any external validation of the proposed metrics makes the central 'best quality' claim premature. I would be willing to reconsider after a revision that reports slack statistics, adds at least one downstream ML check, and qualifies the comparative claims."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First thing to know: this is a genuinely useful engineering paper, not a paradigm shift. HEDGeOPF samples load setpoints uniformly in total active power and solves an AC-OPF with load slack variables, achieving convergence up to 4661-bus systems where prior methods (OPFLearn, RAMBO) don't run. The authors are honest that the total-load sampling idea comes from [1] and [8]; their contribution is the slack-variable formulation for convergence and the Q1-Q3 metric framework. They release code, compare four open-source methods, and openly admit RAMBO beats them on Q2/Q3. That's good practice.\n\nThe soft spots are real but not fatal. The load-bearing one is the slacks. In (7), the solved load sd differs from the sampled ŝd by sdw_d − sup_d. The paper says slacks are penalized with VOLL to make them a last resort, but it never reports how often they activate or how large they are. Algorithm 1 stores every converged solve as a dataset instance. If slacks are nonzero, the stored pair is not an AC-OPF solution for the nominal input ŝd. That would make the Q1-Q3 comparison partly a comparison over mislabeled pairs. This is more important than the lack of NN validation: the dataset's validity as training data is not established without checking slack magnitude.\n\nTwo lesser issues. The metrics are defined and operationalized by the same paper that claims its method scores best; there's no external anchor (e.g., NN generalization to OOD instances) to show they track what matters. And the headline 'consistently outperforms' overstates Table III: MX loses to M0 on pg for the 57-bus, and there are single runs without error bars. The scalability comparison also stops at 118 buses for RAMBO, so 'best balance' is an extrapolation.\n\nThis is for researchers working on AC-OPF ML, dataset generation, or benchmark design. If I were refereeing it, I would ask for three things: (1) report slack activation statistics and re-run the comparison after filtering instances with slack above a small threshold; (2) train a simple NN on MX, M0, and RAMBO datasets and compare OOD feasibility/optimality, to anchor the metrics; (3) add error bars or multiple seeds for the solve-time comparisons. None of these require changing the core method. The paper deserves a serious referee; with those additions it should be accepted.","headline":"Valuable, reproducible AC-OPF dataset generator; the load-slack validity check is the key missing evidence for the 'best balance' claim.","tokens_in":17960,"tokens_out":3851,"would_cite":true,"duration_ms":38708,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that sampling power-grid load setpoints by their system-wide total, rather than independently, produces AC-OPF datasets with more diverse optima and constraint activation, and that this heuristic scales to grids with over 4","keywords":["AC optimal power flow","machine learning datasets","synthetic data generation","constraint activation","load sampling","dataset quality metrics","power grid scalability"],"falsifier":"Train the same neural-network architecture on a HEDGeOPF dataset and on a uniform-sampling dataset that scores lower on the three metrics, evaluate both on a fixed held-out set of feasible AC-OPF instances, and compare out-of-sample constraint violation and optimality gap; if the lower-scored dataset is not worse, the metrics do not carry the paper's claim. Independently, record the fraction of converged HEDGeOPF instances in which any load slack variable is nonzero; a large fraction would show the dataset labels correspond to modified loads, not the sampled setpoints.","tokens_in":16970,"feed_emoji":"⚡","tokens_out":7268,"duration_ms":62252,"temperature":0.7,"pith_summary":"Machine learning models that directly approximate AC-OPF solutions are only as good as the datasets they train on, but the standard way of building those datasets—sampling each load uniformly around its nominal value—quietly destroys diversity on large systems. The paper shows why: the total active load across independently sampled setpoints concentrates in a narrow band as the number of loads grows, so most AC-OPF instances look alike and many generators sit pinned at their limits. Its proposed generator samples the load polytope in thin slices at controlled total-load values and solves an AC-OPF with load slack variables to keep convergence high. To make comparisons fair, it proposes three interpretable metrics—marginal entropy, activation-pattern Hamming distance, and bound activation frequency—and uses them to benchmark its method against uniform sampling, a polytope-coverage method, and a bi-level exploration method. Across nine test systems up to 4,661 buses, the heuristic ranked best among the scalable methods and consistently beat uniform sampling, which is what the paper is trying to establish.","feed_headline":"Sampling by total load beats uniform draws for AC-OPF data","feed_subtitle":"Three new metrics show the heuristic wins on quality yet still runs on 4,600-bus grids.","key_machinery":"The load-slicing sampler: draw total active-load values uniformly, add a constraint slicing the load polytope into a thin band around each value, and sample each slice with a coordinate-directions hit-and-run walk. The AC-OPF is augmented with load slack variables, penalized by a value-of-lost-load cost, so convergence no longer requires preemptive polytope reduction. The three quality metrics—Q1, mean normalized Shannon entropy of primal-variable marginals; Q2, mean normalized Hamming distance between ternary constraint-activation patterns; and Q3, mean normalized activation frequency of non-redundant bounds—carry the comparative evaluation.","core_discovery":"The central claim is that a simple change in how load setpoints are sampled—forcing the system-wide total active load to vary uniformly instead of letting it concentrate—fixes the diversity deficit of AC-OPF datasets. The paper argues that under independent or polytope-uniform sampling, the total active load concentrates near its mean by the central limit theorem and the concentration of measure effect, so large systems produce nearly identical optima. Its solver samples a thin slice of the load polytope for each drawn total-load value, then solves an AC-OPF with load slack variables and a large penalty so that even infeasible setpoints become feasible with minimal load adjustments. The pape","pith_inferences":["The paper never trains a neural network; the next test would be whether datasets ranked higher by Q1–Q3 actually improve the generalization of a fixed architecture on an unseen feasible test set.","The slack-augmented formulation means some dataset instances are solutions for slightly adjusted loads rather than the nominal setpoints; the paper does not report how often slacks activate, so the effective input distribution may deviate from the intended one.","Total-load slicing could apply to security-constrained or stochastic OPF datasets, where aggregate loading similarly drives which constraints bind and which generators are marginal.","A hybrid strategy is suggested by the comparison: use the scalable heuristic for large grids, and reserve the more expensive bi-level exploration for small systems where its higher activation diversity can pay off."],"forward_implications":["A dataset generated by uniform total-load slicing has higher Q1, Q2, and Q3 scores than independent uniform sampling on every tested grid, so machine-learning models will see more varied generator setpoints and constraint behavior.","Because the degeneracy argument scales with load count, any uniform-sampling-based dataset for large grids is likely to be degenerate regardless of the variation range, making explicit total-load control essential.","Removing polytope reduction makes AC-OPF dataset generation practical for grids above 4,000 buses, with per-instance solve time remaining modest.","Across all compared methods, bus-voltage and branch-flow bounds activate rarely, so networks trained on these datasets may not learn those constraints; feasibility claims on such datasets should be treated cautiously."],"supporting_citations":[{"why":"Supplies the polytope-coverage baseline and the convex load-space formulation the paper builds on.","marker":"[26]"},{"why":"Supplies the bi-level exploration baseline whose higher quality on small grids the paper must match while showing it does not scale.","marker":"[27]"},{"why":"Supplies the infeasibility-certificate polytope-reduction procedure the paper removes for scalability.","marker":"[30]"},{"why":"Supplies the central-limit and concentration-of-measure results that predict total-load degeneracy.","marker":"[36]"},{"why":"Supplies the coordinate-directions hit-and-run sampler used to draw load setpoints inside polytope slices.","marker":"[37]"},{"why":"Supplies the base AC-OPF formulation that the paper augments with load slack variables.","marker":"[39]"},{"why":"Supplies the reference uniform-sampling datasets used as the literature baseline.","marker":"[44]"},{"why":"Supplies the nine test cases used for the benchmark comparison.","marker":"[45]"},{"why":"Supplies the non-linear solver used to compute every AC-OPF instance and all timings.","marker":"[48]"}],"fun_headline_variants":["Total-load sampling outperforms uniform AC-OPF data draws","Uniform total-load sampling diversifies AC-OPF data better","New metrics: total-load sampling boosts AC-OPF dataset quality","Total-load uniform sampling beats polytope methods for AC-OPF data","Scalable AC-OPF data generation: total-load sampling wins on quality"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The ranking of datasets depends on the premise that the three proposed metrics predict how well a machine-learning model generalizes and respects constraints on AC-OPF, and that the slack-augmented solutions used as training labels still represent the sampled load setpoints; the paper provides no neural-network validation and no slack-activation statistics.","fun_headline_variants_meta":{"raw":{"variants":["Total-load sampling outperforms uniform AC-OPF data draws","Uniform total-load sampling diversifies AC-OPF data better","New metrics: total-load sampling boosts AC-OPF dataset quality","Total-load uniform sampling beats polytope methods for AC-OPF data","Scalable AC-OPF data generation: total-load sampling wins on quality"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000503,"raw_usage":{"total_tokens":2283,"prompt_tokens":722,"completion_tokens":1561,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":466,"completion_tokens_details":{"reasoning_tokens":1482}},"tokens_in":466,"tokens_out":1561,"duration_ms":11186,"temperature":1.0,"reasoning_tokens":1482,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T15:57:15.578706+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Train the same neural-network architecture on a HEDGeOPF dataset and on a uniform-sampling dataset that scores lower on the three metrics, evaluate both on a fixed held-out set of feasible AC-OPF instances, and compare out-of-sample constraint violation and optimality gap; if the lower-scored dataset is not worse, the metrics do not carry the paper's claim. Independently, record the fraction of converged HEDGeOPF instances in which any load slack variable is nonzero; a large fraction would show the dataset labels correspond to modified loads, not the sampled setpoints.","supporting_citations":[{"cited_title":"OPF-Learn: An Open- Source Framework for Creating Representative AC Optimal Power Flow Datasets,","cited_arxiv_id":null,"evidence_quote":"Supplies the polytope-coverage baseline and the convex load-space formulation the paper builds on."},{"cited_title":"Scalable Bilevel Optimization for Gen- erating Maximally Representative OPF Datasets,","cited_arxiv_id":null,"evidence_quote":"Supplies the bi-level exploration baseline whose higher quality on small grids the paper must match while showing it does not scale."},{"cited_title":"Efficient creation of datasets for data-driven power system applications,","cited_arxiv_id":null,"evidence_quote":"Supplies the infeasibility-certificate polytope-reduction procedure the paper removes for scalability."},{"cited_title":"Vershynin, High-dimensional probability: An introduction with ap- plications in data science","cited_arxiv_id":null,"evidence_quote":"Supplies the central-limit and concentration-of-measure results that predict total-load degeneracy."},{"cited_title":"volesti: V olume Approximation and Sampling for Convex Polytopes in R,","cited_arxiv_id":null,"evidence_quote":"Supplies the coordinate-directions hit-and-run sampler used to draw load setpoints inside polytope slices."},{"cited_title":"Powermodels.jl: An open-source framework for exploring power flow formulations,","cited_arxiv_id":null,"evidence_quote":"Supplies the base AC-OPF formulation that the paper augments with load slack variables."},{"cited_title":"OPFData: Large-scale datasets for AC optimal power flow with topological perturbations,","cited_arxiv_id":null,"evidence_quote":"Supplies the reference uniform-sampling datasets used as the literature baseline."},{"cited_title":"OPFLearn.jl,","cited_arxiv_id":null,"evidence_quote":"Supplies the non-linear solver used to compute every AC-OPF instance and all timings."}],"review_version":1}