README.md

---
dataset_info:
- config_name: geometry
  features:
  - name: node_coordinates_x
    list: float64
  - name: node_coordinates_y
    list: float64
  - name: connectivity
    list:
      list: int32
  splits:
  - name: default
    num_bytes: 13548
    num_examples: 1
  download_size: 9866
  dataset_size: 13548
- config_name: parameters
  features:
  - name: conductivity
    list: float64
  splits:
  - name: default
    num_bytes: 160
    num_examples: 8
  download_size: 1182
  dataset_size: 160
- config_name: snapshots
  features:
  - name: temperature
    list: float64
  splits:
  - name: default
    num_bytes: 19488
    num_examples: 8
  download_size: 23138
  dataset_size: 19488
configs:
- config_name: geometry
  data_files:
  - split: default
    path: geometry/default-*
- config_name: parameters
  data_files:
  - split: default
    path: parameters/default-*
- config_name: snapshots
  data_files:
  - split: default
    path: snapshots/default-*
---
# Thermal Block Dataset

## Dataset Description

This dataset contains thermal diffusion simulations on a 2D block geometry with varying thermal conductivity parameters.

### Dataset Summary

The Thermal Block dataset provides numerical simulations of heat transfer in a 2D block with parametrized thermal conductivity. The dataset is useful for reduced-order modeling, surrogate modeling, and physics-informed machine learning applications in thermal analysis.

## Dataset Structure

### Data Instances

The dataset consists of three configurations:

- **geometry**: Mesh information (nodes and connectivity)
- **snapshots**: Temperature field solutions
- **parameters**: Thermal conductivity values for each simulation

### Data Fields

#### Geometry Configuration
- `node_coordinates_x`: Sequence of x-coordinates of mesh nodes (float64)
- `node_coordinates_y`: Sequence of y-coordinates of mesh nodes (float64)
- `connectivity`: Sequence of element connectivity (triangular elements, int32)

#### Snapshots Configuration
- `temperature`: Temperature field at each node (float64)

#### Parameters Configuration
- `conductivity`: Thermal conductivity parameter for each simulation (float64)

### Data Splits

- `default`: Contains all simulations

## Dataset Creation

### Source Data

The dataset was generated using finite element simulations of the heat equation with varying thermal conductivity parameters.

### Preprocessing

Solutions are stored as 1D arrays corresponding to the nodal values on the mesh.

## Usage

```python
from datasets import load_dataset
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.tri as mtri

# Load geometry
ds_geom = load_dataset("SISSAmathLab/thermal-block", name="geometry")

# Load snapshots
ds_data = load_dataset("SISSAmathLab/thermal-block", name="snapshots")

# Load parameters
ds_params = load_dataset("SISSAmathLab/thermal-block", name="parameters")

# Visualize temperature distribution for first simulation
pts_x = np.asarray(ds_geom['default']['node_coordinates_x']).flatten()
pts_y = np.asarray(ds_geom['default']['node_coordinates_y']).flatten()
connectivity = ds_geom['default']['connectivity'][0]
temperature = ds_data['default']['temperature'][0]

triang = mtri.Triangulation(pts_x, pts_y, connectivity)
plt.tripcolor(triang, temperature)
plt.colorbar(label='Temperature')
plt.title('Thermal Block - Temperature Distribution')
plt.xlabel('x')
plt.ylabel('y')
plt.show()
```

## Contact

For questions or issues, please contact SISSA mathLab.