Update README.md

README.md

@@ -1,3 +1,108 @@
----
-license: mit
----
+---
+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