---
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: 19868
    num_examples: 1
  download_size: 7494
  dataset_size: 19868
- config_name: parameters
  features:
  - name: mu1
    dtype: float64
  - name: mu2
    dtype: float64
  splits:
  - name: default
    num_bytes: 1600
    num_examples: 100
  download_size: 3041
  dataset_size: 1600
- config_name: snapshots
  features:
  - name: temperature_dynamics
    list:
      list: float64
  splits:
  - name: default
    num_bytes: 35320400
    num_examples: 100
  download_size: 18878512
  dataset_size: 35320400
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-*
---
# Unsteady Heat Transfer Dataset

## Dataset Description

This dataset contains time-dependent thermal simulations with varying material and boundary condition parameters.

### Dataset Summary

The Unsteady Heat dataset provides numerical simulations of transient heat transfer in a 2D domain with parametrized material properties and boundary conditions. The dataset includes temporal dynamics of temperature fields, making it ideal for time-dependent reduced-order modeling, dynamic system identification, and spatiotemporal machine learning applications.

## Dataset Structure

### Data Instances

The dataset consists of three configurations:

- **geometry**: Mesh information (single geometry for all simulations)
- **snapshots**: Time-series of temperature field solutions
- **parameters**: Material and boundary condition parameters 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_dynamics`: Time series of temperature fields (2D array: time steps × nodes) (float64)

#### Parameters Configuration
- `mu1`: First parameter characterizing material properties or boundary conditions (float64)
- `mu2`: Second parameter characterizing material properties or boundary conditions (float64)

### Data Splits

- `default`: Contains all simulations

## Dataset Creation

### Source Data

The dataset was generated using finite element simulations of the unsteady heat equation with time-varying boundary conditions or heat sources. Each simulation captures the temporal evolution of the temperature field.

### Preprocessing

Temperature solutions are stored as 2D arrays where the first dimension represents time steps and the second dimension represents spatial nodes. This allows efficient access to both spatial snapshots at specific times and temporal evolution at specific locations.

## 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/unsteady-heat", name="geometry")

# Load snapshots
ds_data = load_dataset("SISSAmathLab/unsteady-heat", name="snapshots")

# Load parameters
ds_params = load_dataset("SISSAmathLab/unsteady-heat", name="parameters")

# Access temporal dynamics for simulation 20
temp_dynamics = np.array(ds_data['default']['temperature_dynamics'][20])
# temp_dynamics.shape = (num_timesteps, num_nodes)

# Visualize temperature at final time step
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]
final_temperature = temp_dynamics[-1]  # Last time step

mu1 = ds_params['default']['mu1'][20]
mu2 = ds_params['default']['mu2'][20]

triang = mtri.Triangulation(pts_x, pts_y, connectivity)
plt.tripcolor(triang, final_temperature, cmap='hot')
plt.colorbar(label='Temperature')
plt.title(f'Unsteady Heat (μ₁={mu1:.3f}, μ₂={mu2:.3f}) - Final Time')
plt.xlabel('x')
plt.ylabel('y')
plt.axis('equal')
plt.show()
```


## Contact

For questions or issues, please contact SISSA mathLab.