Revisiting Deep AC-OPF

Neil D. Lawrence; Oluwatomisin I. Dada

REVIEW 4 major objections 5 minor 31 references

Revisiting Deep AC-OPF

T0 review · 4 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper claims that simple linear baselines match or beat deep-learning surrogates for AC optimal power flow, making the reported gains of ML approaches marginal once these baselines are included.

desk verdict A fair empirical shot across the bow of ML-for-AC-OPF: linear baselines are strong in the near-linear regime tested, but the scope is narrower than the title implies. read the letter →

arxiv 2509.00655 v1 pith:5SMILAWV submitted 2025-08-31 eess.SY cs.LGcs.SY

Oluwatomisin I. Dada , Neil D. Lawrence This is my paper · ORCID

classification eess.SYcs.LGcs.SY

keywords ACoptimalpowerflowmachinelearningsurrogateslinearbaselinesvoltagepredictiontransformerDeepOPF-VOPF-Learndatasethot-start

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks whether the speed and accuracy claims made for machine-learning surrogates for AC optimal power flow survive comparison with simple, carefully chosen baselines. It introduces OPFormer-V, a transformer that predicts bus voltages and outperforms the earlier DeepOPF-V network on every dataset tested. The main result, however, is that simple linear baselines are strong: ordinary least squares regression achieves a lower fractional variance unexplained than DeepOPF-V on the self-generated IEEE case30 and case118 datasets and is the best method on the OPF-Learn case30 dataset. The authors conclude that current ML solvers offer only marginal improvements over linear methods, and that strong linear baselines should be a standard part of future evaluations. If true, this changes how the community should benchmark learned AC-OPF solvers.

What carries the argument

The comparison is carried by a set of deliberately simple predictors: gridwise averaging (a data-driven flat start), nodewise averaging (the per-bus mean voltage), and ordinary least squares regression with the load vector as input. Against these sit two linearized power-flow solvers—DC-OPF, with its flat-start Taylor assumptions, and a hot-start linear power flow built from a first-order Taylor expansion about the nodal voltage average, whose truncation-error bound selects that reference point—plus the FCNN DeepOPF-V and the new transformer OPFormer-V, which encodes each bus as a token and jointly predicts voltage magnitude and angle. The load-to-voltage linearity revealed by the baselines

What would settle it

A reader could settle this by downloading the OPF-Learn case30 data already used here, adding a second dataset generated with loads drawn from a wider or skewed distribution (for example, ±80% or scenarios that push voltages against their limits), and comparing linear regression's FVU with OPFormer-V's; if the linear advantage reverses or disappears under wider voltage excursions, the paper's central claim is conditional rather than general.

Watch

Extended reading notes

Core claim

The central claim is that the load-to-voltage map in the evaluated AC-OPF problems is close enough to linear that ordinary least squares regression—one linear model per voltage target—matches or beats the leading learned surrogate. On the self-generated IEEE case30 and case118 grids, linear regression's FVU is lower than DeepOPF-V's for both voltage magnitude and angle, and only the newly proposed OPFormer-V transformer does better. On the OPF-Learn case30 dataset, linear regression is the best method overall. The paper also derives a warm-start linear power flow model from a first-order Taylor expansion around the nodal voltage average, with an explicit error bound that justifies the refere

Load-bearing premise

The load-bearing assumption is that the benchmark datasets are representative, yet they are generated by sampling loads uniformly within ±50% of a nominal case, keeping voltages in a narrow range where the load-to-voltage relation is nearly linear and where linear baselines can win.

Editorial extensions

If this is right

Published ML surrogate accuracy claims for AC-OPF should be reported together with at least a linear regression baseline before gains are attributed to model complexity.
OPFormer-V's transformer architecture is a viable alternative to the FCNN: it improves on DeepOPF-V in both regression and power metrics on the self-generated grids.
The value of ML surrogates depends on the operating regime: on the OPF-Learn dataset, designed to include many distinct active constraint sets, linear regression wins, so gains do not transfer across dataset-generation strategies.
A hot-start linear power flow based on a first-order Taylor expansion around the nodal average outperforms DC-OPF in voltage-angle error and optimality gap, showing DC-OPF is not the right linear benchmark for voltage prediction.
Improvements in voltage prediction do not automatically lower generation-limit violation rates, so feasibility constraints need explicit treatment.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper's conclusion likely depends on the operating envelope: because loads are sampled within ±50% of nominal, voltages stay in a narrow band where linearization error is small. A testable extension is to repeat the comparison on datasets with heavier loading, contingency cases, or voltage-bound violations and check whether linear regression's edge persists.
The results imply that published 'speedup vs solver' claims for AC-OPF surrogates should be paired with training-inclusive cost comparisons: linear regression requires no training run and can be fit in closed form, so a fair comparison must include the ML training cost, not just inference time.
The weak coupling between voltage-prediction accuracy and generation-limit violation rate suggests that improving MSE/FVU alone is not the binding constraint for ML-AC-OPF; attention should shift to architectures or losses that enforce feasibility, which the paper did not develop.
OPFormer-V's token-per-bus representation, with static per-node features, is a natural route to topology generalization; the paper only tests fixed topologies, so whether the representation helps under N-1 contingencies remains an open question.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The paper's real message is simple and worth hearing: on the datasets used, a linear regression baseline matches or beats DeepOPF-V, and even nodewise averaging is competitive. That is a useful, somewhat uncomfortable result for the ML-for-OPF community, and the authors deserve credit for running the comparison cleanly—multiple seeds, train/val/test splits, and both regression and power metrics. OPFormer-V is a genuine new architecture and it does beat DeepOPF-V on voltage prediction, though the power-metric tables show the gains do not translate into meaningfully lower constraint violations, which the authors honestly note.

The strongest part of the paper is the hot-start linear power flow with the error-bound analysis. That is a real technical contribution, and the bound's use to motivate the reference point is a nice touch. The simple baselines (gridwise/nodewise averaging, OLS) are well chosen and clearly explained.

Now the soft spots, in order of importance. First, the scope problem: the self-generated data use ±50% uniform load perturbations around a nominal case, which the paper itself concedes produces small voltage variances. In that near-linear regime, a linear map is expected to do well. The headline "linear baselines achieve comparable performance" is only established for that regime, and the OPF-Learn case30 set also has very small angle variance. This is not an internal inconsistency, but the title "Revisiting Deep AC-OPF" implies a broader verdict. Second, the appendix tables include a "GP" method with no definition anywhere in the text or tables. That is a concrete omission that must be fixed before the results are reproducible. Third, the dismissal of DeepOPF-V's post-processing step is based on the original paper's reported effect; the authors do not re-run with it, so the comparison excludes a piece of the published method. That is defensible, but it should be stated more carefully as a modeling choice, not a settled fact. Fourth, no code or data are shipped, which matters for a paper whose main claim is empirical.

The core finding is likely correct for the tested datasets. The paper is honest about its limitations in the conclusion, but the abstract and title push the interpretation further than the evidence supports. Still, this is exactly the kind of paper that should go to peer review: the question is important, the experiments are straightforward and mostly well done, and the missing pieces are fixable in revision. I would cite it if I worked on OPF surrogates, and I would want the GP baseline defined and the scope claim sharpened before recommending acceptance.

Referee Report

4 major / 5 minor

Summary. The paper revisits claims that ML surrogates achieve high accuracy for AC-OPF by introducing OPFormer-V, a transformer-based voltage predictor, and comparing it against DeepOPF-V as well as simple linear baselines. Experiments are run on two self-generated datasets (IEEE 30 and 118 bus, with loads sampled uniformly in ±50% around nominal) and on the OPF-Learn case30 dataset. The central empirical finding is that OPFormer-V consistently outperforms DeepOPF-V in regression and power metrics, but simple linear methods—especially ordinary least squares—achieve comparable or better voltage-prediction accuracy on the three test sets, including the best FVU on OPF-Learn case30. The paper also develops a hot-start linear power flow approximation with an error-bound-based reference point. The authors conclude that ML surrogates offer only marginal gains over strong linear baselines and that such baselines should be standard in future evaluations.

Significance. If the conclusions hold, the paper is a useful methodological correction to the AC-OPF ML literature: it provides a direct comparison of a state-of-the-art architecture against carefully chosen linear baselines, gives a detailed transformer architecture, includes an error-bound analysis for the hot-start linear model, and reports seed variability. The paper is honest about a key limitation in §7: the data-generation process yields small voltage variances. The main strength is that the empirical protocol is transparent enough to be replicated, and the linear-baseline point is worth making. However, the scope of the claim is broader than the evidence: the tested regime is nearly linear, so the general 'marginal gains' conclusion is not yet established outside that regime.

major comments (4)

[§4, §5.2.2, §7, Tables 1–3] The central claim that simple linear baselines match or beat DeepOPF-V is established only in a low-voltage-variance, near-linear regime. The self-generated data in §4 use load samples uniformly in ±50% of nominal, but the resulting voltage variance is tiny: e.g., grid-average MSE for Vm is 3.577e-4 pu² (case30, Table 1) and 1.564e-4 pu² (case118, Table 2), and the OPF-Learn Va variance is 3.111e-6 rad² (Table 3). The paper itself relies on this small variance in §5.2.2 and A.1.2 to justify linear approximations. In this regime OLS is expected to be near-optimal. Since §7 states the conclusion generally, the paper needs either experiments in regimes where voltage/reactive limits bind, loads vary more widely or are spatially correlated, or a substantially narrowed claim. This is load-bearing, not a mere caveat.
[§5.4, §6] DeepOPF-V is compared without its post-processing step. The text says the effect of that step is 'minimal from the reported results', but no citation or quantitative comparison is given, and §6 states that both DeepOPF-V and OPFormer-V are evaluated without it. Since DeepOPF-V is the state-of-the-art baseline and the paper's title is a revisiting of Deep AC-OPF, omitting a component of the published method could inflate the relative improvements of OPFormer-V and the linear baselines. Please either implement the post-processing, report its effect on the metrics used here, or explicitly justify with numbers from the original paper why omitting it is inconsequential.
[Appendix A.2, Tables 6–13] A method labeled 'GP' appears in the appendix regression tables without any definition or description. It is not introduced in §5.1–5.5, so the reader cannot interpret these results. The paper should either define the GP model (including its kernel, training, and hyperparameters) or remove it from the tables. This is a missing-support issue in the empirical record.
[Tables 14–15, A.4.5] The reported speedups compare a solver run on MATLAB Online with ML models trained or run on a local Apple M1 Pro. This is not a controlled comparison, and the 'Approx. Speedup' numbers should not be used as evidence of practical speed superiority without a common hardware/software environment. If speed is part of the contribution, please provide a fairer measurement or explicitly describe the numbers as rough, non-comparable estimates.

minor comments (5)

[§1, §5.2.2] Typos: 'datatsets' in §1; 'simplyfying' in §5.2.2. Also 'OPFormer-V , feats 8outperforms' in §6.1 needs spacing and a verb.
[§5.3] Subsection 5.3 'ML approaches' is empty and should be removed or filled.
[Tables 6–13] The tables in the appendix use inconsistent notation ('Grid Avg.', 'Node Avg.', 'Hot-Start', 'OLS', 'GP'), and some entries print '1.000 × 10−0' where '1.000' is clearer.
[§5.2.2] Equation (12) introduces Λ in the line above but uses 'E[|Λ|]ub' without explicitly defining the subscript 'ub'; please clarify the notation.
[§4] The self-generated datasets are stated to contain 100k samples each, but the split is 60/15/25; please confirm the exact training/validation/test sizes, since some appendix tables show near-zero GP training error that may indicate leakage or memorization if sample sizes are small.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central empirical comparisons are held-out evaluations against external baselines and datasets.

full rationale

The paper's main claims are empirical and are evaluated on held-out test splits against external benchmarks (DeepOPF-V from Huang et al. 2021 and the OPF-Learn dataset from Joswig-Jones et al. 2022). The linear baselines are defined independently of the ML models: gridwise averaging and nodewise averaging are simple statistical predictors, linear regression is ordinary least squares on the same training split, DC-OPF is a standard linear power-flow approximation, and the hot-start linear power-flow method selects its reference point by minimizing an analytic upper bound on the Taylor remainder (Eqs. 11-12) rather than by fitting to test targets. The observation that Grid Average has FVU = 1.000 is explicitly a consequence of predicting the training mean and is a sanity check, not a derived prediction. The conclusion's acknowledgement that the data-generation process yields small voltage variances is a scope limitation of the datasets, not a circular step. No equation in the paper reduces to its own inputs by construction, no fitted parameter is renamed as a prediction, and there are no load-bearing self-citations by the authors. The paper is self-contained against external benchmarks, so the appropriate finding is no significant circularity.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The central empirical claim does not rest on hidden fitted parameters. The hot-start reference point is a modeling choice, and the transformer hyperparameters are standard. The key assumptions are the small-variance dataset generation (acknowledged by the authors) and the approximation E[f(x)] ≈ f(E[x]).

free parameters (2)

Hot-start reference point = nodal voltage averages
The reference point for the 1st-order Taylor linearization is chosen as the average nodal voltages, which is a data-derived choice but not fitted to the test set. It affects the hot-start baseline, not the central ML-vs-linear claim.
OPFormer-V hyperparameters
Transformer depth, width, heads, and dropout are chosen by hand (Appendix A.4.1) and not tuned per dataset. They affect the model's reported performance but are not central to the linear baseline finding.

assumptions (3)

domain assumption E[f(x)] is well approximated by f(E[x]) for the voltage mapping
Section 5.2.2 and Appendix A.1.2 assume the mapping from load to voltage has bounded second derivative and small load variance, allowing the data-efficient hot-start reference point. This is a stated approximation, validated numerically on the self-generated datasets.
domain assumption Independence and symmetry of vi, vj, delta_ij for error bound minimization
In Appendix A.1.1, the expected truncation error bound is minimized at the mean under an independence/symmetry assumption; otherwise a Cauchy-Schwarz bound is used. This underpins the reference point choice for hot-start.
standard math MATPOWER AC-OPF solutions are treated as ground truth
All optimality gaps and regression targets are defined using MATPOWER solutions, which is standard practice in this literature but remains an external solver assumption.

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Cite this review

Pith. "Pith review of Revisiting Deep AC-OPF." pith.science (2026). https://pith.science/paper/5SMILAWV

@misc{pith2026250900655,
  author       = {Pith},
  title        = {Pith review of: Revisiting Deep AC-OPF},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5SMILAWV}},
  note         = {Machine review of arXiv:2509.00655}
}

read the original abstract

Recent work has proposed machine learning (ML) approaches as fast surrogates for solving AC optimal power flow (AC-OPF), with claims of significant speed-ups and high accuracy. In this paper, we revisit these claims through a systematic evaluation of ML models against a set of simple yet carefully designed linear baselines. We introduce OPFormer-V, a transformer-based model for predicting bus voltages, and compare it to both the state-of-the-art DeepOPF-V model and simple linear methods. Our findings reveal that, while OPFormer-V improves over DeepOPF-V, the relative gains of the ML approaches considered are less pronounced than expected. Simple linear baselines can achieve comparable performance. These results highlight the importance of including strong linear baselines in future evaluations.

Figures

Figures reproduced from arXiv: 2509.00655 by the authors.

**Figure 1.** Sum Absolute Error in in active power generation for all generators sorted by aggregate active power demand for the self-generated 30 node case dataset. This figure compares this error in DC-OPF and the hot-start linear power flow. This figure shows error in DC-OPF approximation is typically worse than for hot-start and that this error is dependent on aggregate demand and generally worsens as we increase aggregate … view at source ↗

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Reference graph

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