PIK-ICoNe-landscape/Stability_Landscapes

📚 Overview: Kuramoto-Stability-Landscape (KSL)

The dataset consists of synthetic oscillator network topologies created using a random growth algorithm. Dynamical simulations are conducted by applying the second-order Kuramoto model to the nodes. This model is widely recognized for its effectiveness in analyzing synchronization dynamics in complex systems such as power grids and neuronal networks.

Two ensembles are included, each containing 10,000 unique network topologies:

• dataset20: Networks consisting of 20 nodes each.
• dataset100: Networks consisting of 100 nodes each.

Each topology is associated with single-node basin stability (SNBS) heatmaps, providing detailed spatial stability information per node.

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🗃️ Data Structure and Content of Targets

The archive num_sections_20.tar contains two main directories within a single compressed .tar file:

num_sections_20/
├── ds20/
│   ├── heatmap_grid_00001.h5
│   ├── heatmap_grid_00002.h5
│   └── ...
└── ds100/
    ├── heatmap_grid_00001.h5
    ├── heatmap_grid_00002.h5
    └── ...

Sub-dataset	# Graphs	Nodes / graph	Files	Heat-maps / file	Resolution
dataset20	10 000	20	10 000 HDF5	40 (20×basin_heatmap_i + 20×samples_heatmap_i)	20 × 20
dataset100	10 000	100	10 000 HDF5	200 (100×basin_heatmap_i + 100×samples_heatmap_i)	20 × 20

Each .h5 file represents one unique oscillator network and includes:

• basin_heatmap_i (target variable):

  • Continuous stability landscape representing dynamic stability intensity (values in [0, 1]).
  • Shape: (20, 20) per node.

• samples_heatmap_i (auxiliary information):

  • Number of Monte-Carlo perturbation samples per heatmap cell.
  • Shape: (20, 20) per node.

• i corresponds to node indices:

  • Nodes 1 to 20 for dataset20.
  • Nodes 1 to 100 for dataset100.

Examples:

• dataset20:
  Each file contains 40 heatmaps (20 basin_heatmap_X + 20 samples_heatmap_X).

• dataset100:
  Each file contains 200 heatmaps (100 basin_heatmap_X + 100 samples_heatmap_X).

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Data Structure and Content of Inputs

• node_features (input node features):

  • injected power at each node {-1,1}
  • Shape: (num_nodes, 1)

• edge_index (adjacency matrix):

  • encoding of the topology
  • Shape: (2, num_edges)

• edge_attr (edge feautres):

  • homogeneous edge features (value = 9.0)
  • Shape: `(num_Edges, 1)

🚀 Intended Tasks

This dataset introduces a novel machine-learning task:

• Graph-to-Image Regression:
  Predicting detailed SNBS heatmap landscapes directly from graph topology and nodal attributes.

Downstream Application

• Single-node basin stability (SNBS) probability prediction.
• Stability analysis and robustness assessment of dynamical networks.

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🧪 Data Splits

Each ensemble in our submission is pre-split into:

• Training set: 70%
• Validation set: 15%
• Test set: 15%

These splits enable consistent benchmarking and out-of-distribution evaluation.

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⚙️ Generation Methodology

• Underlying Dynamical Model: Second-order Kuramoto oscillators.
• Perturbations: Monte Carlo sampled perturbations (φ, φ̇) applied per node.
• Heatmap Computation: Stability status (continuous stability value) and perturbation density computed per 20x20 spatial bins from raw simulation outcomes.

The dataset was generated using extensive computational resources (>500,000 CPU hours).

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📖 Usage and Loading

To load and access data conveniently, first unpack the provided .tar file:

tar -xvf num_sections_20.tar

Then, for example, load .h5 files in Python:

import h5py
import numpy as np

with h5py.File('num_sections_20/ds20/heatmap_grid_00001.h5', 'r') as f:
    basin_heatmap_node1 = np.array(f['basin_heatmap_1'])
    samples_heatmap_node1 = np.array(f['samples_heatmap_1'])
print(basin_heatmap_node1.shape)  # (20, 20)