REVIEW 4 major objections 5 minor 20 references
Toolbox for Developing Physics Informed Neural Networks for Power Systems Components
T0 review · 4 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash
Pith's one-line read This paper claims its open-source PINN toolbox can simulate a 9th-order synchronous machine with MAE 2.26e-3 and about 630x batched speedup over the RK45 solver.
desk verdict Useful open-source PINN toolbox for power systems; the 9th-order demo is narrower than advertised because it only varies 3 of 9 initial states. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The central object is the hybrid loss $L = \lambda_d L_{\text{data}} + \lambda_{dp} L_{\text{data physics}} + \lambda_{cp} L_{\text{col physics}} + \lambda_{ic} L_{\text{ic}}$ of Eq. (7), which combines labeled trajectory data with the ODE residuals evaluated at both data points and collocation points, plus an initial-condition penalty. The toolbox automates data generation through Latin Hypercube sampling of initial conditions, RK45 solution of the model equations, and point-skipping that keeps many trajectories while thinning each one; the trained network maps $(x_0, t)$ to $\hat{x}(t)$.
What would settle it
Gather high-fidelity measurements of the same synchronous machine with AVR and governor under the same disturbance (for example, from a validated electromagnetic-transient simulator or a physical machine) and compare the PINN's predictions to them; if the error against those measurements is orders of magnitude larger than its error against the RK45 training data, the claim that the toolbox captures the component's dynamics is falsified.
Extended reading notes
Core claim
The discovery the paper reports is that a hybrid physics-plus-data loss formulation, implemented in a modular pipeline, is enough to train a feed-forward PINN to track the nine state variables of a synchronous machine with AVR and governor over a 1 s transient horizon. With four hidden layers of 64 tanh units, L-BFGS optimization over 750 epochs, and static loss weights, the network reaches MAE $2.26\times10^{-3}$ and Max AE $44.85\times10^{-3}$ relative to RK45-generated ground truth, with the largest errors occurring in the first moments of the transient. The same network computes one trajectory in 1.95 ms and 500 trajectories in 8.59 ms, against 10.81 ms and 5406.13 ms for the solver. The authors state this is probably the most complex power system component trained with a PINN to date.
Load-bearing premise
The load-bearing premise is that the paper's 9th-order ODE model and its RK45 numerical solutions accurately represent the real synchronous machine's dynamic behavior; the PINN is trained and tested only against these simulated trajectories.
Editorial extensions
If this is right
- If the reported accuracy generalizes, PINN surrogates trained with this toolbox can replace numerical ODE solvers for individual power system components inside larger simulations.
- Because inference cost is nearly flat as batch size grows (1.95 ms for one trajectory vs 8.59 ms for 500), the method is especially attractive for studies that scan many initial conditions, such as transient stability assessment.
- The point-skipping observation that many trajectories matter more than dense points along each one can guide dataset design for other PINN training tasks.
- The toolbox's modular structure is intended to make it straightforward to add new components, such as inverter-based resources, to a shared model library.
Reading between the lines
- The speed comparison is likely sensitive to hardware: the PINN inferences run on a V100 GPU while the RK45 solver runs on CPU, so the speedup partly reflects parallelization rather than algorithmic superiority; a fairer benchmark would time both on the same device.
- Because the PINN is trained only on simulated RK45 trajectories, its physical fidelity cannot exceed that of the ODE model used to generate the data; if that model misses dynamics present in real machines, the reported accuracy will not transfer to field data.
- The authors' 'most complex to date' claim is inherently fragile, since it depends on an informal literature scan; a more testable claim would be a benchmark against specific published PINN power-system models.
- A natural extension would be to train on a mixture of simulated and real measurement data, which the toolbox already partially supports by allowing simulated trajectories to be disregarded; this could make the surrogate more faithful to actual components than the simulator alone.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper introduces PowerPINN, a Python toolbox for training physics-informed neural networks (PINNs) as surrogates for power system component ODE models. The toolbox automates dataset generation with Latin Hypercube sampling, collocation-point construction, and a hybrid loss combining labeled data, physics residuals, and initial-condition penalties. The demonstration is a ninth-order synchronous machine with an AVR and governor modeled by the Sauer-Pai equations. A feed-forward network with four hidden layers of 64 tanh units is trained on 500,000 data points and 500,000 collocation points. On 50 held-out trajectories the reported accuracy is MAE 2.26e-3, MSE 10.04e-6, and Max AE 44.85e-3, and the reported inference times are substantially lower than an RK45 baseline for single and batched trajectories. The central claim is that this is the most complex power system component trained with a PINN to date and that the toolbox provides a standardized pathway toward a library of such models.
Significance. If the claims are substantiated, the toolbox would be a useful and timely contribution because it addresses reproducibility and standardization in an area where bespoke implementations dominate. The open-source code, the explicit pipeline for data generation and loss assembly, and the use of held-out trajectories from the same solver as a surrogate-model test protocol are genuine strengths; the latter is a standard practice and not circular. However, the evidence as presented is not yet sufficient for the strongest claims. The accuracy experiment varies only three of the nine state variables in the initial conditions, the timing comparison may conflate algorithmic speedup with hardware differences, and the quoted metrics come from a single training run without variance or sensitivity analysis. These gaps are fixable either by additional experiments or by narrowing the claims, so the manuscript has a sound core but needs revision.
major comments (4)
- [Section IV-A1 and Section IV-C] The input domain fixes six of the nine dynamic states: E'd = 0, RF = 1, Vr = 1.105, Efd = 1.08, Psv = 0.7048, and Pm = 0.7048, while only theta, omega, and E'q are sampled. Consequently, the training data, the collocation points, and the 50 test trajectories all lie in a three-dimensional affine slice of the nine-dimensional state space. The accuracy metrics in Table I and the visualizations in Fig. 3 therefore demonstrate interpolation within that slice, not the ability to capture the dynamics of the full 9th-order component from arbitrary initial states. This matters because the paper's value proposition is a reusable component model valid over an operating domain, including states where the AVR/governor limits in Eq. (11) are active and where Efd, VR, PSV, PM, and RF depart from their nominal values. The authors should either add out-of-slice test trajectories (for example, sampling all nine states or at least the states that affect the limit behavior) or explicitly restrict the '9th-order system' claim to a flow map on the sampled slice.
- [Table II and Section IV-C] The timing comparison does not state which hardware executed the RK45 solver and which executed the PINN. The experimental setup in Section IV-B lists a 16-core Intel Xeon 6226R CPU and an NVIDIA V100 GPU, but the text does not say whether the ODE solver ran on the CPU while the PINN ran on the GPU. If so, the speedup in Table II conflates algorithmic advantage with hardware advantage. The 500-trajectory RK45 time of 5406.13 ms versus the 50-trajectory time of 54.06 ms also indicates that the solver was run sequentially per trajectory, whereas the PINN batches all trajectories; this is not an apples-to-apples comparison. The paper should report the hardware and software configuration for each method, include a CPU-only PINN baseline if relevant, and describe the measurement procedure (repeated runs, warm-up, batching) for the inference times.
- [Table I and Section IV-B] The accuracy numbers come from a single training run with a fixed set of hyperparameters; no random seed, number of repeated runs, or confidence intervals are reported. PINN training is sensitive to initialization, the static loss weights lambda in Eq. (7), and the network architecture, so it is unclear whether MAE 2.26e-3 and Max AE 44.85e-3 are representative or the result of a favorable run. The authors should either report statistics over multiple training runs or provide a sensitivity analysis over the main hyperparameters, at least over the loss weights that the text identifies as important.
- [Abstract and Section I] The claim that the 9th-order system is 'probably the most complex power system component trained with a PINN to date' is not supported by any comparison with prior work. No literature baseline is given, and the hedge 'probably' does not substitute for evidence. The authors should either provide a concrete comparison with the highest-order power system component trained with a PINN in prior publications or remove the claim and replace it with a factual statement about the order of their demonstration.
minor comments (5)
- [Section II-B] There are typos in this section: 'theoritically' should be 'theoretically' and 'appoximating' should be 'approximating'.
- [Section III-G and Table II] The text says the computation-time benchmark examines 'a single set and 100 sets of initial conditions,' but Table II reports 50 and 500 trajectories. The text and table should be aligned.
- [Fig. 2 and Fig. 3] The per-state metrics and example trajectories omit the AVR and governor states (Efd, Rf, Vr, PM, PSV). Since these states are part of the 9th-order claim, showing their errors or sample trajectories would make the demonstration more convincing.
- [Eq. (5)] The label 'Lic col' is an awkward typographical hybrid; it would be clearer to write 'L_ic' consistently with Eq. (7).
- [Section IV-A1] The notation is inconsistent: the input domain uses 'theta' and 'Vr', while Eq. (8) uses 'delta' and 'VR', and 'Ef d' appears with and without a space. Please standardize the symbol names.
Circularity Check
No significant circularity: the PINN accuracy claims are held-out empirical results against RK45 trajectories, with same-author citations only as background.
full rationale
The paper is a toolbox demonstration, not a derivation chain: the central claim is that a PINN surrogate trained with a hybrid data/physics loss approximates RK45-generated trajectories of a 9th-order Sauer-Pai model. The accuracy metrics in Section IV-C are computed on 50 held-out trajectories from the same data-generation protocol, which is a standard surrogate-model evaluation and not a fitted parameter renamed as a prediction. The physical loss (6) and data loss (3) are distinct objectives, and neither is defined in terms of the final test metric. The same-author references ([10], [11], [14]) are background material on simulator integration and trustworthiness; none supplies a uniqueness theorem or a load-bearing premise required for the numerical results. The Picard-Lindelof discussion is a textbook external theorem, not imported from the authors. The limitation that initial conditions span only a 3D slice of the 9D state space (Section IV-A1 fixes six states) is a correctness/generality concern, not circularity, because the 50 test trajectories are held out from training and the reported error does not equal the training loss by construction. No circular step is present.
Assumptions & free parameters
free parameters (3)
- Static loss weights =
λd=1, λdp=0.01, λcp=0.001, λic=0.01
- Network architecture and optimizer settings =
4 hidden layers x 64 nodes, tanh, LBFGS, lr=0.001, 750 epochs
- Sampling intervals and domain bounds =
23-step interval for data, 19-step for collocation; input domain as in Section IV-A.1; 500 initial conditions per set
assumptions (3)
- domain assumption The Sauer and Pai [3] model equations (8)-(11) accurately describe the synchronous machine with AVR and governor dynamics.
- standard math Feedforward networks with tanh have sufficient expressive capacity to approximate the 9th-order flow map on the chosen domain.
- domain assumption Latin Hypercube sampling with 500 initial conditions gives sufficient coverage of the input domain for the reported generalization.
Cite this review
Pith. "Pith review of Toolbox for Developing Physics Informed Neural Networks for Power Systems Components." pith.science (2026). https://pith.science/paper/M4OF6FJS
@misc{pith2026250206412,
author = {Pith},
title = {Pith review of: Toolbox for Developing Physics Informed Neural Networks for Power Systems Components},
year = {2026},
howpublished = {\url{https://pith.science/paper/M4OF6FJS}},
note = {Machine review of arXiv:2502.06412}
}
read the original abstract
This paper puts forward the vision of creating a library of neural-network-based models for power system simulations. Traditional numerical solvers struggle with the growing complexity of modern power systems, necessitating faster and more scalable alternatives. Physics-Informed Neural Networks (PINNs) offer promise to solve fast the ordinary differential equations (ODEs) governing power system dynamics. This is vital for the reliability, cost optimization, and real-time decision-making in the electricity grid. Despite their potential, standardized frameworks to train PINNs remain scarce. This poses a barrier for the broader adoption and reproducibility of PINNs; it also does not allow the streamlined creation of a PINN-based model library. This paper addresses these gaps. It introduces a Python-based toolbox for developing PINNs tailored to power system components, available on GitHub https://github. com/radiakos/PowerPINN. Using this framework, we capture the dynamic characteristics of a 9th-order system, which is probably the most complex power system component trained with a PINN to date, demonstrating the toolbox capabilities, limitations, and potential improvements. The toolbox is open and free to use by anyone interested in creating PINN-based models for power system components.
Figures
Reference graph
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Reviewed August 8, 2026 · model on record in the stance chip above.
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