README.md

---
license: mit
task_categories:
- tabular-regression
language:
- en
tags:
- physics,
- scientific,
- pin,
- physics-informed-network,
- pde,
- partial-differential-equations,
- heat-equation,
- heat,
- equation,
pretty_name: 1D Heat Equation PDE Dataset
size_categories:
- 1K<n<10K
---
# 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:
```bash
pip install datasets
```

Load the dataset:
```python
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