heat1d-pde-dataset

This dataset contains numerical solutions of the 1D heat equation with cooling terms, designed for machine learning applications in scientific computing and physics-informed neural networks.

Dataset Description

Dataset Summary

The dataset consists of spatiotemporal solutions to the 1D heat equation with boundary conditions and a cooling term. Each sample includes initial states, final states (with and without noise), simulation parameters, and elapsed times.

Supported Tasks

• PDE Solution Prediction
• Parameter Inference
• Physics-Informed Machine Learning
• Scientific Machine Learning Benchmarking

Dataset Structure

{
    'initial_states': [N, 200],      # Initial temperature distribution
    'final_states': [N, 200],        # Final temperature distribution (with noise)
    'clean_initial_states': [N, 200], # Initial states without noise
    'clean_final_states': [N, 200],   # Final states without noise
    'parameters': [N, 3],            # [alpha, k, t_env]
    'elapsed_times': [N],            # Time between initial and final states
}

Data Fields

• initial_states: Temperature distribution at t=0
• final_states: Temperature distribution at t=elapsed_time
• clean_initial_states: Noise-free initial states
• clean_final_states: Noise-free final states
• parameters:
  • alpha: Thermal diffusivity [1e-5, 1e-4]
  • k: Cooling coefficient [0.01, 0.1]
  • t_env: Environmental temperature [15, 35]
• elapsed_times: Time difference between states

Data Splits

All data is provided in the training set. Users should create their own validation/test splits.

Source Code

The dataset was generated using a finite difference solver for the heat equation:

∂T/∂t = α∂²T/∂x² - k(T - T_env)

with boundary conditions:

• T(x=0, t) = temp1
• T(x=L, t) = temp2

Noise Levels

• Input states: 1% of temperature range
• Output states: 0.5% of temperature range
• Parameters: 1% of parameter values

Usage

Install the datasets library:

pip install datasets

Load the dataset:

from datasets import load_dataset

# Download files locally
dataset = load_dataset("nick-leland/heat1d-pde-dataset", download_mode="force_redownload")

# Read the initial structure (h5py files)
df = dataset['train'].data.to_pandas()
file_path = df['image'][0]['path']
data = h5py.File(file_path, 'r')

# Access data
initial_states = data['initial_states'][:]
final_states = data['final_states'][:]
parameters = data['parameters'][:]
elapsed_times = data['elapsed_times'][:]

Dataset Creator

Nicholas Leland

Licensing Information

license: mit