{"id":"66e11daf-f005-48e8-90e6-d41d195a022b","arxiv_id":"2502.06412","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A new open-source toolbox trains physics-informed neural networks for power system components and demonstrates a 9th-order synchronous machine with AVR and governor, reaching 2.26e-3 mean absolute error with fast inference.","lead":"The authors present PowerPINN, an open-source Python toolbox that automates training of physics-informed neural networks for power system components, and they demonstrate it on a 9th-order synchronous machine with voltage regulator and governor. If the toolbox generalizes as intended, it could make PINN-based component models easier to build, share, and embed in power system simulators.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 9th-order demonstration is trained and tested only on a 3-dimensional slice of the state space; the central claim is not established for the full 9-dimensional component.","rationale":"The paper is a software/engineering contribution with a concrete, open-source implementation and a self-contained case study; I take its strongest claim to be that PowerPINN can produce a surrogate for a 9th-order component with the reported accuracy and speed. The ODE/reference-solver adequacy concern raised by the reader is real but secondary for a simulator-replacement use case: matching the ODE trajectories is exactly what a solver surrogate needs to do, and the authors are transparent that RK45 is the benchmark. The more load-bearing gap is that the case study never exercises the full state space: six state initial conditions are fixed to single values, so the network only ever sees a 3D affine slice of the 9D input domain. The accuracy numbers in Table I and Fig. 2 are therefore not evidence for a general 9th-order component model, and a user who instantiates the model near AVR/governor limits could see much larger errors. I found no internal inconsistency in the PINN formulation or the loss construction, and the inference-time comparison, while apples-to-oranges in hardware/vectorization, does not threaten the central claim. The clean test is to retrain/evaluate on a genuinely 9D initial-condition distribution; depending on the outcome, the paper should either claim a 9D surrogate or explicitly scope the model to the narrow operating slice. Since the reader already recommended conditional acceptance and this concern strengthens that recommendation without overturning it, I leave the verdict unchanged.","tokens_in":964,"tokens_out":954,"duration_ms":128363,"concrete_test":"Retrain the same architecture and loss weights with LHS initial conditions that vary all nine states in a physically meaningful box, e.g. δ∈[-2,2], ω∈[-1,1], E'q∈[0.9,1.1], E'd∈[-0.1,0.1], RF∈[0.8,1.2], Vr∈[0.9,1.3], Efd∈[0.9,1.3], PSV∈[0.6,0.9], PM∈[0.6,0.9]. Keep the same 80/10/10 trajectory split and report MAE/MaxAE on the held-out 10%. If the errors stay near the current values, the 9D claim is supported; if MAE grows by an order of magnitude or training fails to converge, the published numbers are specific to the 3D slice and the stated claim should be narrowed accordingly.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section IV-A1 fixes six of the nine dynamic states in the initial-condition sampling: E'd=0, RF=1, Vr=1.105, Efd=1.08, Psv=0.7048, Pm=0.7048. Only δ, ω, and E'q are sampled via LHS, so both training data and the 50 test trajectories in Section IV-C lie in a 3D slice of the 9D state space. The reported MAE 2.26e-3 and MaxAE 44.85e-3 therefore measure interpolation within that slice, not the ability to capture the dynamics of a 9th-order component from arbitrary initial states. This matters because the paper's central value proposition is a model library for power-system components: a library model must be valid over a stated 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. Without an out-of-slice evaluation, the '9th-order system' claim is a demonstration of a 3D-parameterized flow map of a 9-state ODE, not of a 9D surrogate. This is a correctness/generality risk, not an internal contradiction; the toolbox itself may be sound.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":9727,"tokens_out":5666,"duration_ms":52189,"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":[{"comment":"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.","section":"Section IV-A1 and Section IV-C"},{"comment":"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.","section":"Table II and Section IV-C"},{"comment":"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.","section":"Table I and Section IV-B"},{"comment":"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.","section":"Abstract and Section I"}],"minor_comments":[{"comment":"There are typos in this section: 'theoritically' should be 'theoretically' and 'appoximating' should be 'approximating'.","section":"Section II-B"},{"comment":"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.","section":"Section III-G and Table II"},{"comment":"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.","section":"Fig. 2 and Fig. 3"},{"comment":"The label 'Lic col' is an awkward typographical hybrid; it would be clearer to write 'L_ic' consistently with Eq. (7).","section":"Eq. (5)"},{"comment":"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.","section":"Section IV-A1"}],"recommendation":"major_revision","confidential_remarks":"The core toolbox contribution is plausible and the manuscript is within the journal's scope, but the strongest claims ('9th-order system', 'most complex to date', and the dramatic speedups) are not yet backed by the evidence. The main fixes are to add an out-of-slice evaluation or narrow the claims, to make the timing comparison fair, and to report repeated-run statistics. If the authors can do that, the paper would be a solid software/methods contribution; as it stands, the over-claims are too large to ignore."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe PowerPINN toolbox is a genuine contribution: an open-source, modular pipeline for training PINNs on power-system component ODEs, with a demonstration on a 9th-order synchronous machine with AVR and governor. That is the most useful thing here. The code is on GitHub, the training setup is described in enough detail to reproduce, and the accuracy numbers (MAE 2.26e-3 on held-out trajectories) are plausible. I agree with the reader's conditional verdict.\n\nThe stress-test note lands. The input domain fixes six of nine states (E'd=0, Rf=1, Vr=1.105, Efd=1.08, Psv=0.7048, Pm=0.7048), so the 50 test trajectories all start in a 3D slice. The PINN does learn the 9-state dynamics along trajectories from that slice, but it is not evaluated from arbitrary 9D initial conditions. The abstract's \"capture the dynamic characteristics of a 9th-order system\" is therefore overstated as written; the evidence supports a 3D-parameterized flow map. That does not sink the toolbox, but the claim needs to be scoped, or the evaluation needs to include initial conditions where the AVR and governor limits in (11) are active.\n\nOther soft spots, in order: no error bars or repeated runs, so the reported metrics could be a lucky seed; the timing comparison puts batched GPU inference against a serial CPU RK45 solver, so the 500-trajectory speedup is partly a hardware/parallelism comparison, not an algorithm comparison; and the \"probably most complex ... to date\" claim is unsupported by any literature sweep. These are addressable revision items, not fatal flaws.\n\nWhat the paper does well: the pipeline is genuinely modular, the data and collocation sampling are clearly specified, and the authors identify the static-weight choice and the accuracy/complexity tradeoff honestly. The example is nontrivial and the trained surrogate seems accurate within its tested domain.\n\nWho is this for? Power-systems researchers who want to build PINN component libraries without writing everything from scratch. If you work on PINN methodology per se, there is little new here. But as a software/demonstration paper, it deserves a serious referee. I would send it to review with a request to scope the claims, add repeated-run statistics, and make the timing comparison fairer. It is not ready as-is, but it is a solid basis for a useful paper.","headline":"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.","tokens_in":10275,"tokens_out":2727,"would_cite":true,"duration_ms":23287,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["physics-informed neural networks","power system dynamics","synchronous machine","automatic voltage regulator","governor","surrogate models","open-source toolbox","transient stability"],"falsifier":"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.","tokens_in":9301,"feed_emoji":"⚡","tokens_out":11476,"duration_ms":76091,"temperature":0.7,"pith_summary":"The paper's central claim is that a standardized, open-source training pipeline can make physics-informed neural networks (PINNs) practical as drop-in surrogate models for power system components. To support this, the authors build PowerPINN, a modular Python toolbox, and use it to train a PINN for a 9th-order system: a synchronous machine with an automatic voltage regulator and a governor. On a test set of 50 trajectories, the trained network approximates the solver's trajectories with mean absolute error of $2.26\\times10^{-3}$, while inferring 500 trajectories in 8.59 ms versus 5406.13 ms for the RK45 solver. The authors argue this demonstrates that the toolbox lowers the barrier to creating a library of PINN-based component models for fast power system simulation.","feed_headline":"An open-source PINN toolbox simulates a 9th-order power machine","feed_subtitle":"PowerPINN trains a neural surrogate with MAE 0.0023; 500 trajectories run in 8.6 ms, ~630x faster than RK45.","key_machinery":"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 $\\hat{x}(t)$.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the 9th-order ODE model of the synchronous machine with AVR and governor that the PINN is trained to approximate.","marker":"[3]"},{"why":"Establishes the standard PINN loss formulation that the paper's hybrid physics-plus-data loss builds on.","marker":"[6]"},{"why":"Shows how PINN component models can be integrated into power system dynamic simulations, motivating the toolbox's design.","marker":"[10]"},{"why":"Describes PINNSim, the PINN-based simulation engine that the proposed model library is meant to plug into.","marker":"[11]"},{"why":"Provides the Latin Hypercube sampling method used to generate diverse initial conditions for training and collocation data.","marker":"[13]"},{"why":"Documents the L-BFGS optimizer used to train the PINN in the demonstration.","marker":"[17]"}],"fun_headline_variants":["Open-source PINN toolbox simulates 9th-order power machine","PINN toolbox hits 630x speedup on 9th-order power system","Physics-informed neural net library for power grids goes open-source","PowerPINN trains 9th-order machine model 630x faster than solver"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Open-source PINN toolbox simulates 9th-order power machine","PINN toolbox hits 630x speedup on 9th-order power system","Physics-informed neural net library for power grids goes open-source","PowerPINN trains 9th-order machine model 630x faster than solver"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000477,"raw_usage":{"total_tokens":2365,"prompt_tokens":950,"completion_tokens":1415,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":566,"completion_tokens_details":{"reasoning_tokens":1336}},"tokens_in":566,"tokens_out":1415,"duration_ms":10784,"temperature":1.0,"reasoning_tokens":1336,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T15:31:40.164265+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the 9th-order ODE model of the synchronous machine with AVR and governor that the PINN is trained to approximate."},{"cited_title":"Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,","cited_arxiv_id":null,"evidence_quote":"Establishes the standard PINN loss formulation that the paper's hybrid physics-plus-data loss builds on."},{"cited_title":"Integrating physics- informed neural networks into power system dynamic simulations,","cited_arxiv_id":null,"evidence_quote":"Shows how PINN component models can be integrated into power system dynamic simulations, motivating the toolbox's design."},{"cited_title":"Pinnsim: A simulator for power system dynamics based on physics-informed neural networks,","cited_arxiv_id":null,"evidence_quote":"Describes PINNSim, the PINN-based simulation engine that the proposed model library is meant to plug into."},{"cited_title":"A comparison of three methods for selecting values of input variables in the analysis of output from a computer code,","cited_arxiv_id":null,"evidence_quote":"Provides the Latin Hypercube sampling method used to generate diverse initial conditions for training and collocation data."}],"review_version":1}