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: 62508
    num_examples: 1
  download_size: 35333
  dataset_size: 62508
- config_name: parameters
  features:
  - name: youngs_modulus
    list: float64
  splits:
  - name: default
    num_bytes: 46000
    num_examples: 500
  download_size: 54144
  dataset_size: 46000
- config_name: snapshots
  features:
  - name: displacement_x
    list: float64
  - name: displacement_y
    list: float64
  splits:
  - name: default
    num_bytes: 10772000
    num_examples: 500
  download_size: 11268439
  dataset_size: 10772000
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-*
---
# Elastic Block Dataset

## Dataset Description

This dataset contains structural mechanics simulations of an elastic block under varying Young's modulus parameters.

### Dataset Summary

The Elastic Block dataset provides numerical simulations of elastic deformation in a 2D block with parametrized material properties. The dataset includes displacement fields in both x and y directions, making it suitable for reduced-order modeling, surrogate modeling, and machine learning applications in structural mechanics.

## Dataset Structure

### Data Instances

The dataset consists of three configurations:

- **geometry**: Mesh information (nodes and connectivity)
- **snapshots**: Displacement field solutions
- **parameters**: Young's modulus 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
- `displacement_x`: Displacement field in x-direction at each node (float64)
- `displacement_y`: Displacement field in y-direction at each node (float64)

#### Parameters Configuration
- `youngs_modulus`: Young's modulus parameter for each simulation (float64)

### Data Splits

- `default`: Contains all simulations

## Dataset Creation

### Source Data

The dataset was generated using finite element simulations of linear elasticity with varying Young's modulus parameters.

### Preprocessing

Displacement solutions are stored as 1D arrays (one for each direction) 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/elastic-block", name="geometry")

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

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

# Visualize displacement field 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]
displacement_x = np.asarray(ds_data['default']['displacement_x'][0])

triang = mtri.Triangulation(pts_x, pts_y, connectivity)
plt.tripcolor(triang, displacement_x)
plt.colorbar(label='Displacement X')
plt.title('Elastic Block - X Displacement')
plt.xlabel('x')
plt.ylabel('y')
plt.axis('equal')
plt.show()
```

## Contact

For questions or issues, please contact SISSA mathLab.