---
pretty_name: Stability-Landscape
license: cc-by-4.0
language:
- en
tags:
- graph-neural-networks
- kuramoto-oscillators
- basin-stability
- power-grids
- physics
- long-range-dependencies
size_categories:
- 100M<n<1B
datasets:
- name: KSL
  annotation_type: synthetic
  source_datasets: []
task_categories:
- graph-ml
- other
---

# 📚 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.

---
## 🗃️ Data Structure and Content of Targets

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

```text
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`).

---
## 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.

---

## 🧪 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:

```bash
tar -xvf num_sections_20.tar
```

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

```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)
```