Update README.md

README.md

@@ -52,3 +52,95 @@ configs:
   - 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.