README.md

metadata

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

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.