Network Measure-Enriched GNNs: A New Framework for Power Grid Stability Prediction.

Frank Hellmann

Junyou Zhu Christian Nauck Michael Lindner Langzhou He Philip S. Yu Klaus-Robert Müller Jürgen Kurths Frank Hellmann Network Measure-Enriched GNNs: A New Framework for Power Grid Stability Prediction. 518-531 2026 January 38 IEEE Trans. Knowl. Data Eng. 1 https://doi.org/10.1109/TKDE.2025.3624222 db/journals/tkde/tkde38.html#ZhuNLHYMKH26 streams/journals/tkde

Martin Sadric Sebastian Pütz Christian Nauck Veit Hagenmeyer Frank Hellmann Benjamin Schäfer 0001 Assessing Explanations of Graph Neural Networks for Dynamic Stability Assessment of Power Grids. 183-199 2026 Sustainability Week https://doi.org/10.1145/3765611.3815508 conf/sustainability/2026 db/conf/sustainability/sustainability2026.html#SadricPNHHS26

Christian Nauck Junyou Zhu Michael Lindner Frank Hellmann Learning Dynamic Stability Landscapes in Synchronization Networks. 2026 May abs/2605.23708 CoRR https://doi.org/10.48550/arXiv.2605.23708 db/journals/corr/corr2605.html#abs-2605-23708 streams/journals/corr

Nubius Brandner Frank Hellmann Hans Würfel Jürgen Kurths Anton Plietzsch Anna Büttner Nodal Braess's Paradox and Inertia Destabilization with Dynamic Node and Line Failures in Power Grids. 2026 June abs/2606.20060 CoRR https://doi.org/10.48550/arXiv.2606.20060 db/journals/corr/corr2606.html#abs-2606-20060 streams/journals/corr

Anna Büttner Hans Würfel Sebastian Liemann Johannes Schiffer Frank Hellmann Complex-Phase, Data-Driven Identification of Grid-Forming Inverter Dynamics. 4854-4864 2025 November 16 IEEE Trans. Smart Grid 6 https://doi.org/10.1109/TSG.2025.3591891 db/journals/tsg/tsg16.html#ButtnerWLSH25 streams/journals/tsg

Junyou Zhu Langzhou He Chao Gao 0001 Dongpeng Hou Zhen Su 0002 Philip S. Yu Jürgen Kurths Frank Hellmann SDMG: Smoothing Your Diffusion Models for Powerful Graph Representation Learning. 2025 ICML https://proceedings.mlr.press/v267/zhu25g.html https://openreview.net/forum?id=lNyaQIJ5Z7 conf/icml/2025 db/conf/icml/icml2025.html#ZhuHGHSYKH25

Jakob Niehues Anna Büttner Anne Riegler Frank Hellmann Complex Phase Analysis of Power Grid Dynamics. 2025 June abs/2506.22054 CoRR https://doi.org/10.48550/arXiv.2506.22054 db/journals/corr/corr2506.html#abs-2506-22054 streams/journals/corr

Christian Nauck Rohan Gorantla Michael Lindner Konstantin Schürholt Antonia S. J. S. Mey Frank Hellmann Dirac–Bianconi Graph Neural Networks – Enabling Non-Diffusive Long-Range Graph Predictions. GRaM 2024 146-157 conf/gram/2024 https://proceedings.mlr.press/v251/nauck24a.html db/conf/gram/gram2024.html#NauckGLSMH24 streams/conf/gram

Christian Nauck Michael Lindner Nora Molkenthin Jürgen Kurths Eckehard Schöll Jörg Raisch Frank Hellmann Predicting Instability in Complex Oscillator Networks: Limitations and Potentials of Network Measures and Machine Learning. 2024 abs/2402.17500 CoRR https://doi.org/10.48550/arXiv.2402.17500 db/journals/corr/corr2402.html#abs-2402-17500

Christian Nauck Anna Büttner Sebastian Liemann Frank Hellmann Michael Lindner Predicting Fault-Ride-Through Probability of Inverter-Dominated Power Grids using Machine Learning. 2024 abs/2406.08917 CoRR https://doi.org/10.48550/arXiv.2406.08917 db/journals/corr/corr2406.html#abs-2406-08917

Christian Nauck Rohan Gorantla Michael Lindner Konstantin Schürholt Antonia S. J. S. Mey Frank Hellmann Dirac-Bianconi Graph Neural Networks - Enabling Non-Diffusive Long-Range Graph Predictions. 2024 abs/2407.12419 CoRR https://doi.org/10.48550/arXiv.2407.12419 db/journals/corr/corr2407.html#abs-2407-12419 streams/journals/corr

Anna Büttner Hans Würfel Sebastian Liemann Johannes Schiffer Frank Hellmann Complex-Phase, Data-Driven Identification of Grid-Forming Inverter Dynamics. 2024 abs/2409.17132 CoRR https://doi.org/10.48550/arXiv.2409.17132 db/journals/corr/corr2409.html#abs-2409-17132 streams/journals/corr

Alistair White Anna Büttner Maximilian Gelbrecht Valentin Duruisseaux Niki Kilbertus Frank Hellmann Niklas Boers Projected Neural Differential Equations for Learning Constrained Dynamics. 2024 abs/2410.23667 CoRR https://doi.org/10.48550/arXiv.2410.23667 db/journals/corr/corr2410.html#abs-2410-23667 streams/journals/corr

Jakob Niehues Robin Delabays Frank Hellmann Small-signal stability of power systems with voltage droop. 2024 abs/2411.10832 CoRR https://doi.org/10.48550/arXiv.2411.10832 db/journals/corr/corr2411.html#abs-2411-10832 streams/journals/corr

Anna Büttner Frank Hellmann Probabilistic Behavioral Aggregation: A Case Study on the Nordic Power Grid. 2024 abs/2412.11899 CoRR https://doi.org/10.48550/arXiv.2412.11899 db/journals/corr/corr2412.html#abs-2412-11899 streams/journals/corr

K. Hauke Kraemer Frank Hellmann Mehrnaz Anvari Jürgen Kurths Norbert Marwan Spike Spectra for Recurrences. 1689 2022 November 24 Entropy 11 https://doi.org/10.3390/e24111689 db/journals/entropy/entropy24.html#KraemerHAKM22

Anton Plietzsch Raphael Kogler Sabine Auer Julia Merino Asier Gil-de-Muro Jan Liße Christina Vogel Frank Hellmann PowerDynamics.jl - An experimentally validated open-source package for the dynamical analysis of power grids. 100861 2022 17 SoftwareX https://doi.org/10.1016/j.softx.2021.100861 https://www.wikidata.org/entity/Q115036753 db/journals/softx/softx17.html#PlietzschKAMGLV22

Anna Büttner Hans Würfel Anton Plietzsch Michael Lindner Frank Hellmann An Open Source Software Stack for Tuning the Dynamical Behavior of Complex Power Systems. 1-6 2022 OSMSES https://doi.org/10.1109/OSMSES54027.2022.9769114 conf/osmses/2022 db/conf/osmses/osmses2022.html#ButtnerWPLH22

Christian Nauck Michael Lindner Konstantin Schürholt Frank Hellmann Dynamic stability of power grids - new datasets for Graph Neural Networks. 2022 abs/2206.06369 CoRR https://doi.org/10.48550/arXiv.2206.06369 db/journals/corr/corr2206.html#abs-2206-06369

Christian Nauck Michael Lindner Konstantin Schürholt Frank Hellmann Towards dynamic stability analysis of sustainable power grids using graph neural networks. 2022 abs/2212.11130 CoRR https://doi.org/10.48550/arXiv.2212.11130 db/journals/corr/corr2212.html#abs-2212-11130

Anton Plietzsch Raphael Kogler Sabine Auer Julia Merino Asier Gil-de-Muro Jan Liße Christina Vogel Frank Hellmann PowerDynamics.jl - An experimentally validated open-source package for the dynamical analysis of power grids. 2021 abs/2101.02103 CoRR https://arxiv.org/abs/2101.02103 db/journals/corr/corr2101.html#abs-2101-02103

Raphael Kogler Anton Plietzsch Paul Schultz Frank Hellmann A normal form for grid forming power grid components. 2021 abs/2106.00644 CoRR https://arxiv.org/abs/2106.00644 db/journals/corr/corr2106.html#abs-2106-00644

Sebastian Liemann Lia Strenge Paul Schultz Holm Hinners Johannis Porst Marcel Sarstedt Frank Hellmann Probabilistic Stability Assessment for Active Distribution Grids. 2021 abs/2106.09624 CoRR https://arxiv.org/abs/2106.09624 db/journals/corr/corr2106.html#abs-2106-09624

Christian Nauck Michael Lindner Konstantin Schürholt Haoming Zhang Paul Schultz Jürgen Kurths Ingrid Isenhardt Frank Hellmann Predicting Dynamic Stability of Power Grids using Graph Neural Networks. 2021 abs/2108.08230 CoRR https://arxiv.org/abs/2108.08230 db/journals/corr/corr2108.html#abs-2108-08230

Frank Hellmann Ekaterina Zolotarevskaia Jürgen Kurths Jörg Raisch Probabilistic Behavioral Distance and Tuning - Reducing and aggregating complex systems. 2021 abs/2111.12521 CoRR https://arxiv.org/abs/2111.12521 db/journals/corr/corr2111.html#abs-2111-12521

Anna Büttner Hans Würfel Anton Plietzsch Michael Lindner Frank Hellmann An Open Source Software Stack for Tuning the Dynamical Behavior of Complex Power Systems. 2021 abs/2112.00347 CoRR https://arxiv.org/abs/2112.00347 db/journals/corr/corr2112.html#abs-2112-00347

Lia Strenge Xiaohan Jing Ruth Boersma Paul Schultz Frank Hellmann Jürgen Kurths Jörg Raisch Thomas Seel Iterative learning control in prosumer-based microgrids with hierarchical control. 2020 abs/2003.11806 CoRR https://arxiv.org/abs/2003.11806 db/journals/corr/corr2003.html#abs-2003-11806

Lia Strenge Paul Schultz Jürgen Kurths Jörg Raisch Frank Hellmann A multilayer, multi-timescale model approach for economic and frequency control in power grids. 2020 abs/2003.11807 CoRR https://arxiv.org/abs/2003.11807 db/journals/corr/corr2003.html#abs-2003-11807

Michael Lindner Lucas Lincoln Fenja Drauschke Julia Monika Koulen Hans Würfel Anton Plietzsch Frank Hellmann NetworkDynamics.jl - Composing and simulating complex networks in Julia. 2020 abs/2012.12696 CoRR https://arxiv.org/abs/2012.12696 db/journals/corr/corr2012.html#abs-2012-12696

Mehrnaz Anvari Sabine Auer Niklas Boers Ruth Boersma Nubius Brandner Anna Büttner Robin Delabays Fenja Drauschke Valentin Duruisseaux Chao Gao 0001 Maximilian Gelbrecht Asier Gil-de-Muro Rohan Gorantla Veit Hagenmeyer Langzhou He Holm Hinners Dongpeng Hou Ingrid Isenhardt Xiaohan Jing Niki Kilbertus Raphael Kogler Julia Monika Koulen K. Hauke Kraemer Jürgen Kurths Sebastian Liemann Lucas Lincoln Michael Lindner Jan Liße Norbert Marwan Julia Merino Antonia S. J. S. Mey Nora Molkenthin Klaus-Robert Müller Christian Nauck Jakob Niehues Anton Plietzsch Johannis Porst Sebastian Pütz Jörg Raisch Anne Riegler Martin Sadric Marcel Sarstedt Benjamin Schäfer 0001 Johannes Schiffer Eckehard Schöll Paul Schultz Konstantin Schürholt Thomas Seel Lia Strenge Zhen Su 0002 Christina Vogel Alistair White Hans Würfel Philip S. Yu Haoming Zhang Junyou Zhu Ekaterina Zolotarevskaia