pith. sign in

arxiv: 2406.08917 · v1 · submitted 2024-06-13 · 📡 eess.SY · cs.LG· cs.SY

Predicting Fault-Ride-Through Probability of Inverter-Dominated Power Grids using Machine Learning

Pith reviewed 2026-05-24 00:25 UTC · model grok-4.3

classification 📡 eess.SY cs.LGcs.SY
keywords machine learningfault-ride-through probabilityinverter-dominated gridssynthetic power gridsdynamic stabilitygeneralizationIEEE-96 test systemprobabilistic analysis
0
0 comments X

The pith

Machine learning models accurately predict fault-ride-through probability in synthetic inverter-dominated power grids and generalize to the IEEE-96 test system.

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

The paper generates a dataset of synthetic power grid models with large inverter shares and runs dynamic simulations to calculate fault-ride-through probability, defined as the chance that a grid stays within its ride-through curve after a fault is cleared at a bus. Machine learning models are trained on grid features to predict this probability, sidestepping the computational limits of simulating every possible fault scenario. The models achieve accurate predictions on the synthetic grids. The same models also perform well when applied to the IEEE-96 Test System. This matters because rising inverter penetration makes exhaustive stability checks for many faults increasingly expensive, so an efficient predictor could support broader risk assessments.

Core claim

By constructing synthetic power grid models, performing dynamical simulations, and defining fault-ride-through probability as the probability of remaining inside a ride-through curve after fault clearance, the authors train machine learning models that accurately predict this quantity on the synthetic data and show that the models generalize when tested on an IEEE-96 Test System.

What carries the argument

Machine learning regression models that learn a mapping from synthetic power grid configurations to the fault-ride-through probability computed from dynamic simulations.

If this is right

  • Machine learning can replace exhaustive dynamic simulations when many fault scenarios must be evaluated for stability risk.
  • The same trained models can be applied directly to standardized test systems without retraining.
  • Probabilistic stability analysis becomes feasible at scale for grids that contain high shares of inverter-based resources.
  • Risk assessments can examine far more configurations than direct simulation budgets allow.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If synthetic data prove representative, operators could train similar models on historical or measured grid data for day-ahead stability forecasting.
  • The approach could be tested on other stability metrics such as frequency nadir or voltage recovery times using the same synthetic-grid pipeline.
  • Extending the input features to include time-varying renewable output patterns would reveal whether the current models remain reliable under realistic operating conditions not present in the training set.

Load-bearing premise

The synthetic power grid models and chosen fault scenarios capture the essential dynamical features of real inverter-dominated grids well enough that the learned mapping stays useful on other systems such as the IEEE-96 test case.

What would settle it

Full dynamic simulations on the IEEE-96 system for a held-out set of faults that produce large, systematic mismatches between the machine-learning predictions and the simulated outcomes would falsify the generalization result.

Figures

Figures reproduced from arXiv: 2406.08917 by Anna B\"uttner, Christian Nauck, Frank Hellmann, Michael Lindner, Sebastian Liemann.

Figure 1
Figure 1. Figure 1: The structure of the power system generation algorithm shows the [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Training setup: The GNN gets the full power grid as input (bus [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Example transients of the dynamical simulations, visualized by the [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The active and reactive power deviations [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The histograms of the pfrt for the IEEE test case are on the left and for the 1 000 synthetic grids on the right. The rows depict the four different bus types. NF1-3 denotes the different normal form parameterizations. For the loads, a different scaling of the vertical axis is used. grids, we see that different virtual inertia constants lead to different fault-ride-through behaviors. As expected, the buses… view at source ↗
Figure 6
Figure 6. Figure 6: Visualization of the performance of TAG. A perfect model would be [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
read the original abstract

Due to the increasing share of renewables, the analysis of the dynamical behavior of power grids gains importance. Effective risk assessments necessitate the analysis of large number of fault scenarios. The computational costs inherent in dynamic simulations impose constraints on the number of configurations that can be analyzed. Machine Learning (ML) has proven to efficiently predict complex power grid properties. Hence, we analyze the potential of ML for predicting dynamic stability of future power grids with large shares of inverters. For this purpose, we generate a new dataset consisting of synthetic power grid models and perform dynamical simulations. As targets for the ML training, we calculate the fault-ride-through probability, which we define as the probability of staying within a ride-through curve after a fault at a bus has been cleared. Importantly, we demonstrate that ML models accurately predict the fault-ride-through probability of synthetic power grids. Finally, we also show that the ML models generalize to an IEEE-96 Test System, which emphasizes the potential of deploying ML methods to study probabilistic stability of power grids.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript generates a dataset of synthetic power grid models with high inverter shares, performs dynamic simulations to compute fault-ride-through (FRT) probabilities, and trains ML models to predict these probabilities from grid features. It claims that the models accurately predict FRT probabilities on synthetic grids and generalize to the IEEE-96 test system.

Significance. If the generalization holds, the approach could enable efficient probabilistic stability assessments for large inverter-dominated grids, reducing the need for exhaustive dynamic simulations across many fault scenarios. The creation of a new synthetic dataset adds value for future benchmarking in the field.

major comments (2)
  1. [Generalization experiments (results on IEEE-96)] The central claim of generalization to the IEEE-96 Test System requires evidence that the synthetic ensemble and IEEE-96 represent meaningfully different regimes. The manuscript provides no statistical comparison (e.g., distributions or summary statistics) of parameters such as short-circuit ratios, line impedances, or inverter penetration levels between the synthetic training data and the IEEE-96 case. This leaves open whether reported performance reflects robust transfer or in-distribution interpolation.
  2. [Abstract and results section] The abstract asserts that the ML models 'accurately predict' FRT probability and 'generalize' but supplies no quantitative metrics (MAE, R², etc.), error bars, baseline comparisons, or details on architecture/training. The results section must report these explicitly with validation procedures to substantiate the accuracy claim.
minor comments (2)
  1. [Methods (FRT probability definition)] Add explicit statements of the ride-through curve parameters and any assumptions used when computing the FRT probability target from simulation outputs.
  2. [Figures] Figure captions should state the exact performance metric plotted and whether results are averaged over multiple random seeds or data splits.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive comments. We address each major point below and will revise the manuscript accordingly to strengthen the presentation of results and the generalization claim.

read point-by-point responses
  1. Referee: [Generalization experiments (results on IEEE-96)] The central claim of generalization to the IEEE-96 Test System requires evidence that the synthetic ensemble and IEEE-96 represent meaningfully different regimes. The manuscript provides no statistical comparison (e.g., distributions or summary statistics) of parameters such as short-circuit ratios, line impedances, or inverter penetration levels between the synthetic training data and the IEEE-96 case. This leaves open whether reported performance reflects robust transfer or in-distribution interpolation.

    Authors: We agree that a statistical comparison is necessary to support the generalization claim. In the revised manuscript we will add summary statistics and distribution plots comparing key parameters (short-circuit ratios, line impedances, inverter penetration levels, and related quantities) between the synthetic ensemble and the IEEE-96 system. These additions will clarify the degree of distributional shift and allow readers to assess whether the reported performance constitutes out-of-distribution transfer. revision: yes

  2. Referee: [Abstract and results section] The abstract asserts that the ML models 'accurately predict' FRT probability and 'generalize' but supplies no quantitative metrics (MAE, R², etc.), error bars, baseline comparisons, or details on architecture/training. The results section must report these explicitly with validation procedures to substantiate the accuracy claim.

    Authors: We accept that the abstract and results section should contain explicit quantitative metrics. In the revision we will update the abstract to report concrete performance figures (e.g., MAE, R²) together with error bars where appropriate. The results section will be expanded to include baseline comparisons, model architecture and training details, and a clear description of the validation procedure (train/validation/test splits, cross-validation, etc.). revision: yes

Circularity Check

0 steps flagged

No circularity: empirical ML trained on independent simulations

full rationale

The paper generates synthetic power grids, performs dynamical simulations to obtain fault-ride-through probabilities as targets, trains ML models on the resulting feature-target pairs, and evaluates generalization on held-out synthetic cases plus the external IEEE-96 system. No equations, definitions, or self-citations reduce any reported prediction to a fitted input by construction, nor invoke uniqueness theorems or ansatzes from prior author work. The derivation chain is a standard supervised learning pipeline whose outputs are falsifiable against new simulations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim depends on the representativeness of the generated synthetic grids and on the assumption that the chosen ride-through curves and fault-clearing model are adequate proxies for real inverter behavior. No new physical entities are postulated; the work is data-driven.

axioms (1)
  • domain assumption Synthetic power grid models with prescribed inverter shares reproduce the relevant dynamical stability properties of real grids for the purpose of ML training.
    The entire training pipeline rests on this modeling choice; the abstract does not provide independent validation against measured grid data.

pith-pipeline@v0.9.0 · 5727 in / 1433 out tokens · 28149 ms · 2026-05-24T00:25:38.017040+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

55 extracted references · 55 canonical work pages · 3 internal anchors

  1. [1]

    ENTSO-E, High penetration of power electronic inter- faced power sources and the potential contribution of grid forming converters , 2020

  2. [2]

    Conditions for stability of droop-controlled inverter-based microgrids,

    J. Schiffer, R. Ortega, A. Astolfi, J. Raisch, and T. Sezi, “Conditions for stability of droop-controlled inverter-based microgrids,” Automatica, vol. 50, no. 10, pp. 2457–2469, Oct. 1, 2014

  3. [3]

    Global phase and voltage synchronization for power inverters: A decentralized consensus-inspired approach,

    M. Colombino, D. Groß, and F. D ¨orfler, “Global phase and voltage synchronization for power inverters: A decentralized consensus-inspired approach,” in 2017 IEEE 56th Annual Conference on Decision and Control (CDC), Dec. 2017, pp. 5690–5695

  4. [4]

    A Review of Machine Learning Applications in Power System Re- silience,

    J. Xie, I. Alvarez-Fernandez, and W. Sun, “A Review of Machine Learning Applications in Power System Re- silience,” 2020 IEEE Power & Energy Society General Meeting (PESGM), Aug. 2, 2020

  5. [5]

    A comprehensive review: Machine learning and its application in integrated power system,

    A. Kumbhar, P. G. Dhawale, S. Kumbhar, U. Patil, and P. Magdum, “A comprehensive review: Machine learning and its application in integrated power system,” Energy Reports, vol. 7, pp. 5467–5474, Nov. 1, 2021

  6. [6]

    A Review of Graph Neural Networks and Their Applications in Power Systems,

    W. Liao, B. Bak-Jensen, J. R. Pillai, Y . Wang, and Y . Wang, “A Review of Graph Neural Networks and Their Applications in Power Systems,” Journal of Mod- ern Power Systems and Clean Energy , vol. 10, no. 2, pp. 345–360, 2022

  7. [7]

    Power flow forecasts at transmission grid nodes us- ing Graph Neural Networks,

    D. Beinert, C. Holzh ¨uter, J. M. Thomas, and S. V ogt, “Power flow forecasts at transmission grid nodes us- ing Graph Neural Networks,” Energy and AI , vol. 14, p. 100 262, Oct. 1, 2023

  8. [8]

    A Physics-Guided Graph Convolution Neural Network for Optimal Power Flow,

    M. Gao, J. Yu, Z. Yang, and J. Zhao, “A Physics-Guided Graph Convolution Neural Network for Optimal Power Flow,” IEEE Transactions on Power Systems, pp. 1–11, 2023

  9. [9]

    Leveraging Power Grid Topology in Machine Learning Assisted Optimal Power Flow,

    T. Falconer and L. Mones, “Leveraging Power Grid Topology in Machine Learning Assisted Optimal Power Flow,” IEEE Transactions on Power Systems , vol. 38, no. 3, pp. 2234–2246, May 2023

  10. [10]

    Topology-Aware Graph Neural Networks for Learning Feasible and Adaptive AC-OPF Solutions,

    S. Liu, C. Wu, and H. Zhu, “Topology-Aware Graph Neural Networks for Learning Feasible and Adaptive AC-OPF Solutions,” IEEE Transactions on Power Sys- tems, vol. 38, no. 6, pp. 5660–5670, Nov. 2023

  11. [11]

    Graph Neural Network and Koopman Models for Learning Networked Dynamics: A Comparative Study on Power Grid Transients Prediction,

    S. P. Nandanoori, S. Guan, S. Kundu, et al. , “Graph Neural Network and Koopman Models for Learning Networked Dynamics: A Comparative Study on Power Grid Transients Prediction,” IEEE Access , vol. 10, pp. 32 337–32 349, 2022

  12. [12]

    Fast Transient Stability Prediction Using Grid-informed Temporal and Topological Embedding Deep Neural Network

    P. Sun, L. Huo, S. Liang, and X. Chen. “Fast Transient Stability Prediction Using Grid-informed Temporal and Topological Embedding Deep Neural Network.” arXiv: 2201.09245 [cs, eess] . (Jan. 23, 2022), [Online]. Available: http://arxiv.org/abs/2201.09245 (visited on 03/01/2023), preprint

  13. [13]

    Structure-Informed Graph Learning of Networked Dependencies for On- line Prediction of Power System Transient Dynamics,

    T. Zhao, M. Yue, and J. Wang, “Structure-Informed Graph Learning of Networked Dependencies for On- line Prediction of Power System Transient Dynamics,” IEEE Transactions on Power Systems , vol. 37, no. 6, pp. 4885–4895, Nov. 2022

  14. [14]

    Neural Network Applications in Hybrid Data-Model Driven Dynamic Frequency Trajectory Prediction for Weak- Damping Power Systems,

    G. Wang, C. Wang, and M. Shahidehpour, “Neural Network Applications in Hybrid Data-Model Driven Dynamic Frequency Trajectory Prediction for Weak- Damping Power Systems,”IEEE Transactions on Power Systems, pp. 1–13, 2023

  15. [15]

    Predict- ing basin stability of power grids using graph neural networks,

    C. Nauck, M. Lindner, K. Sch ¨urholt, et al. , “Predict- ing basin stability of power grids using graph neural networks,” New Journal of Physics , vol. 24, no. 4, p. 043 041, Apr. 2022

  16. [16]

    Towards dynamic stability analysis of sustain- able power grids using graph neural networks,

    C. Nauck, M. Lindner, K. Sch ¨urholt, and F. Hell- mann, “Towards dynamic stability analysis of sustain- able power grids using graph neural networks,” NeurIPS 2022 Workshop on Tackling Climate Change with Ma- chine Learning, Dec. 21, 2022. arXiv: 2212 . 11130 [cs, eess]

  17. [17]

    Toward dynamic stability assessment of power grid topologies using graph neural networks,

    C. Nauck, M. Lindner, K. Sch ¨urholt, and F. Hellmann, “Toward dynamic stability assessment of power grid topologies using graph neural networks,” Chaos: An Interdisciplinary Journal of Nonlinear Science , vol. 33, no. 10, p. 103 103, Oct. 2, 2023

  18. [18]

    Predicting Instability in Complex Oscillator Networks: Limita- tions and Potentials of Network Measures and Machine Learning

    C. Nauck, M. Lindner, N. Molkenthin, et al. “Predicting Instability in Complex Oscillator Networks: Limita- tions and Potentials of Network Measures and Machine Learning.” arXiv: 2402.17500. (Feb. 27, 2024), [On- line]. Available: http : / / arxiv . org / abs / 2402 . 17500, preprint

  19. [19]

    Billinton and W

    R. Billinton and W. Li, Reliability Assessment of Electric Power Systems Using Monte Carlo Methods . Boston, MA: Springer US, 1994

  20. [20]

    Probabilistic Load Flow,

    B. Borkowska, “Probabilistic Load Flow,” IEEE Trans- actions on Power Apparatus and Systems , vol. PAS-93, no. 3, pp. 752–759, May 1974

  21. [21]

    ENTSO-E, All Continental Europe and Nordic TSOs’ proposal for assumptions and a Cost Benefit Analysis methodology in accordance with Article 156(11) of the Commission Regulation (EU) 2017/1485 of 2 August 2017 establishing a guideline on electricity transmission system operation, 2018

  22. [22]

    Probabilistic Stability Assessment for Active Distribution Grids,

    S. Liemann, L. Strenge, P. Schultz, et al., “Probabilistic Stability Assessment for Active Distribution Grids,” in 2021 IEEE Madrid PowerTech, Jun. 2021, pp. 1–6

  23. [23]

    Collective nonlinear dynamics and self-organization in decentralized power grids,

    D. Witthaut, F. Hellmann, J. Kurths, S. Kettemann, H. Meyer-Ortmanns, and M. Timme, “Collective nonlinear dynamics and self-organization in decentralized power grids,” Reviews of Modern Physics , vol. 94, no. 1, p. 015 005, Feb. 28, 2022

  24. [24]

    Deciphering the imprint of topology on nonlinear dynamical network stability,

    J. Nitzbon, P. Schultz, J. Heitzig, J. Kurths, and F. Hellmann, “Deciphering the imprint of topology on nonlinear dynamical network stability,” New Journal of Physics, vol. 19, no. 3, p. 033 029, Mar. 2017

  25. [25]

    Semi-Supervised Classi- fication with Graph Convolutional Networks,

    T. N. Kipf and M. Welling, “Semi-Supervised Classi- fication with Graph Convolutional Networks,” Feb. 22,

  26. [26]

    arXiv: 1609.02907 [cs, stat] . 10

  27. [27]

    Topology Adaptive Graph Convolutional Networks,

    J. Du, S. Zhang, G. Wu, J. M. F. Moura, and S. Kar, “Topology Adaptive Graph Convolutional Networks,” arxiv, Oct. 2017

  28. [28]

    BW, Need to develop grid-forming statcom systems - Position Paper of the German Transmission System Operators , 2020

    50Hertz, Amprion, Tennet, and T. BW, Need to develop grid-forming statcom systems - Position Paper of the German Transmission System Operators , 2020

  29. [29]

    MIGRATE - New Options in System Op- erations - Deliverable 3.4,

    MIGRATE, “MIGRATE - New Options in System Op- erations - Deliverable 3.4,” 2019

  30. [30]

    Necessary development of inverter-based generation with grid forming capabilities in Germany,

    H. Popella, T. Hennig, M. Kaiser, J. Massmann, L. M¨uller, and R. Pfeiffer, “Necessary development of inverter-based generation with grid forming capabilities in Germany,” in 20th International Workshop on Large- Scale Integration of Wind Power into Power Systems as Well as on Transmission Networks for Offshore Wind Power Plants (WIW 2021) , vol. 2021, Se...

  31. [31]

    Normal Form for Grid-Forming Power Grid Actors,

    R. Kogler, A. Plietzsch, P. Schultz, and F. Hellmann, “Normal Form for Grid-Forming Power Grid Actors,” PRX Energy, vol. 1, no. 1, p. 013 008, Jun. 30, 2022

  32. [32]

    Dispatchable Virtual Oscillator Control for Decentralized Inverter-dominated Power Systems: Analysis and Experiments,

    G.-S. Seo, M. Colombino, I. Subotic, B. Johnson, D. Groß, and F. D ¨orfler, “Dispatchable Virtual Oscillator Control for Decentralized Inverter-dominated Power Systems: Analysis and Experiments,” in 2019 IEEE Applied Power Electronics Conference and Exposition (APEC), Mar. 2019, pp. 561–566

  33. [33]

    WP3 - Control and Operation of a Grid with 100% Converter-Based Devices,

    T. Qoria, Q. Cossart, C. Li, X. Guillaud, F. Gruson, and X. Kestelyn, “WP3 - Control and Operation of a Grid with 100% Converter-Based Devices,” 2018

  34. [34]

    VDE, FNN guideline: Grid forming behaviour of HVDC systems and DC-connected PPMs , 2020

  35. [35]

    VDE, Technical connection rules for HVDC systems and via HVDC systems connected generation plants , 2019

  36. [36]

    Survivability of Deterministic Dynamical Systems,

    F. Hellmann, P. Schultz, C. Grabow, J. Heitzig, and J. Kurths, “Survivability of Deterministic Dynamical Systems,” Scientific Reports , vol. 6, no. 1, p. 29 654, 1 Jul. 13, 2016

  37. [37]

    On the distribution of points in a cube and the approximate evaluation of integrals,

    I. M. Sobol’, “On the distribution of points in a cube and the approximate evaluation of integrals,” USSR Computational Mathematics and Mathematical Physics, vol. 7, no. 4, pp. 86–112, Jan. 1, 1967

  38. [38]

    Ambient forcing: Sampling local perturbations in constrained phase spaces,

    A. B ¨uttner, J. Kurths, and F. Hellmann, “Ambient forcing: Sampling local perturbations in constrained phase spaces,” New Journal of Physics , vol. 24, no. 5, p. 053 019, May 2022

  39. [39]

    A framework for synthetic power system dynamics,

    A. B ¨uttner, A. Plietzsch, M. Anvari, and F. Hellmann, “A framework for synthetic power system dynamics,” Chaos: An Interdisciplinary Journal of Nonlinear Sci- ence, vol. 33, no. 8, p. 083 120, Aug. 7, 2023

  40. [40]

    A random growth model for power grids and other spatially embedded in- frastructure networks,

    P. Schultz, J. Heitzig, and J. Kurths, “A random growth model for power grids and other spatially embedded in- frastructure networks,” The European Physical Journal Special Topics, vol. 223, no. 12, pp. 2593–2610, Oct. 1, 2014

  41. [41]

    dena-Verteilnetzstudie: Ausbau- und Innova- tionsbedarf der Stromverteilnetze in Deutschland bis 2030

    dena. “dena-Verteilnetzstudie: Ausbau- und Innova- tionsbedarf der Stromverteilnetze in Deutschland bis 2030.” (Nov. 12, 2012), [Online]. Available: https : / / www.dena.de/newsroom/publikationsdetailansicht/pub/ dena- verteilnetzstudie- ausbau- und- innovationsbedarf- der-stromverteilnetze-in-deutschland-bis-2030/

  42. [42]

    DIW Berlin: Open Source Electricity Model for Germany (ELMOD-DE)

    J. Egerer. “DIW Berlin: Open Source Electricity Model for Germany (ELMOD-DE).” (2016), [Online]. Avail- able: https : / / www . diw . de / de / diw 01 . c . 528929 . de / publikationen / data documentation / 2016 0083 / open source electricity model for germany elmod - de.html

  43. [43]

    Enhancing power grid synchronization and stability through time-delayed feedback control,

    H. Taher, S. Olmi, and E. Sch ¨oll, “Enhancing power grid synchronization and stability through time-delayed feedback control,” Physical Review E , vol. 100, no. 6, p. 062 306, Dec. 11, 2019

  44. [44]

    Review of Reactive Power Planning: Objectives, Constraints, and Algo- rithms,

    W. Zhang, F. Li, and L. M. Tolbert, “Review of Reactive Power Planning: Objectives, Constraints, and Algo- rithms,” IEEE Transactions on Power Systems , vol. 22, no. 4, pp. 2177–2186, Nov. 2007

  45. [45]

    Milano, Power System Modelling and Scripting (Power Systems)

    F. Milano, Power System Modelling and Scripting (Power Systems). London: Springer, 2010, 556 pp

  46. [46]

    G ¨onen, Electrical Power Transmission System En- gineering: Analysis and Design , Third edition

    T. G ¨onen, Electrical Power Transmission System En- gineering: Analysis and Design , Third edition. Boca Raton: CRC Press, and imprint of Taylor & Francis, 2014, 1066 pp

  47. [47]

    The IEEE Reliability Test System-1996. A report prepared by the Reliability Test System Task Force of the Application of Probability Methods Subcommittee,

    C. Grigg, P. Wong, P. Albrecht, et al. , “The IEEE Reliability Test System-1996. A report prepared by the Reliability Test System Task Force of the Application of Probability Methods Subcommittee,” IEEE Transac- tions on Power Systems , vol. 14, no. 3, pp. 1010–1020, Aug. 1999

  48. [48]

    PowerDynam- ics.jl—An experimentally validated open-source pack- age for the dynamical analysis of power grids,

    A. Plietzsch, R. Kogler, S. Auer, et al., “PowerDynam- ics.jl—An experimentally validated open-source pack- age for the dynamical analysis of power grids,” Soft- wareX, vol. 17, Jan. 1, 2022

  49. [49]

    Net- workDynamics.jl—Composing and simulating complex networks in Julia,

    M. Lindner, L. Lincoln, F. Drauschke, et al. , “Net- workDynamics.jl—Composing and simulating complex networks in Julia,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 31, no. 6, p. 063 133, Jun. 1, 2021

  50. [50]

    DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia,

    C. Rackauckas and Q. Nie, “DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia,” Journal of Open Re- search Software, vol. 5, no. 1, p. 15, 1 May 25, 2017

  51. [51]

    PyTorch: An Imperative Style, High-Performance Deep Learning Li- brary,

    A. Paszke, S. Gross, F. Massa, et al. , “PyTorch: An Imperative Style, High-Performance Deep Learning Li- brary,” in Advances in Neural Information Processing Systems 32, H. Wallach, H. Larochelle, A. Beygelzimer, F. Alch ´e-Buc, E. Fox, and R. Garnett, Eds., Curran Associates, Inc., 2019, pp. 8024–8035

  52. [52]

    Fast Graph Representation Learning with PyTorch Geometric,

    M. Fey and J. E. Lenssen, “Fast Graph Representation Learning with PyTorch Geometric,” version 3, vol. arxiv preprint, 2019

  53. [53]

    Ray: A Distributed Framework for Emerging AI Applications

    P. Moritz, R. Nishihara, S. Wang, et al. , “Ray: A Distributed Framework for Emerging AI Applications,” Sep. 29, 2018. arXiv: 1712.05889 [cs, stat]

  54. [54]

    Tune: A Research Platform for Distributed Model Selection and Training

    R. Liaw, E. Liang, R. Nishihara, P. Moritz, J. E. Gonzalez, and I. Stoica. “Tune: A Research Platform for Distributed Model Selection and Training.” arXiv: 1807.05118 [cs, stat] . (Jul. 13, 2018), preprint. 11

  55. [55]

    Improving neural networks by preventing co-adaptation of feature detectors,

    G. E. Hinton, N. Srivastava, A. Krizhevsky, I. Sutskever, and R. R. Salakhutdinov, “Improving neural networks by preventing co-adaptation of feature detectors,” Jul. 2012