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---
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
dataset = load_dataset("nicholasleland/heat1d-pde-dataset")
# Access the data
initial_states = dataset['train']['initial_states']
final_states = dataset['train']['final_states']
parameters = dataset['train']['parameters']
```
### Dataset Creator
Nicholas Leland
### Licensing Information
license: mit |