node_coordinates_x list | node_coordinates_y list | connectivity list |
|---|---|---|
[
0,
0.05,
0.1,
0.15,
0.2,
0.25,
0.3,
0.35,
0.4,
0.45,
0.5,
0.55,
0.6,
0.65,
0.7,
0.75,
0.8,
0.85,
0.9,
0.95,
1,
0,
0.05,
0.1,
0.15,
0.2,
0.25,
0.3,
0.35,
0.4,
0.45,
0.5,
0.55,
0.6,
0.65,
0.7,
0.75,
0.8,
0.85,
0.9,
0.95,
1,
0,
0.05,... | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.05,
0.05,
0.05,
0.05,
0.05,
0.05,
0.05,
0.05,
0.05,
0.05,
0.05,
0.05,
0.05,
0.05,
0.05,
0.05,
0.05,
0.05,
0.05,
0.05,
0.05,
0.1,
0.1,
0.1,
0.1,
0.1,
0.1,
0... | [
[
1,
21,
0
],
[
22,
21,
1
],
[
44,
43,
23
],
[
23,
43,
22
],
[
23,
1,
2
],
[
22,
1,
23
],
[
101,
100,
80
],
[
80,
100,
79
],
[
34,
12,
13
],
[
33,
12,
34
],
... |
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
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.
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