PIK-ICoN-landscape/Stability_Landscapes

📚 Overview: Kuramoto-Stability-Landscape (KSL)

The dataset contains synthetic oscillator network topologies generated from the second-order Kuramoto model, widely used to analyze synchronization dynamics in complex systems like 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 SNBS heatmaps, providing detailed spatial stability information per node.

---

🗃️ Data Structure and Content

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).

---

🚀 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.

---

🧪 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.

---

⚙️ 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).

---

📖 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)